mirror of
https://github.com/harvard-edge/cs249r_book.git
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9b2f6ee01b
Second agent pass produced higher-fidelity implementation: - Carbon intensity corrected to spec values: coal 820 gCO2/kWh (was 400), renewable 40 gCO2/kWh (was 10) — matching @tbl-carbon-intensity and EPA eGRID 2022 - Stakeholder scenario aligned to LABS_SPEC brief (1000-node cluster, 30% flexible jobs) - SLA failure state is kind='danger'; below-target is kind='warn' - Deployment contexts use spec-exact labels (Coal Region vs Renewable Region) - All syntax-verified clean
1457 lines
65 KiB
Python
1457 lines
65 KiB
Python
import marimo
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__generated_with = "0.19.6"
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app = marimo.App(width="full")
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# ─────────────────────────────────────────────────────────────────────────────
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# LAB V2-15: THE JEVONS RECKONING
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#
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# Volume II, Chapter 15 — Sustainable AI (@sec-sustainable-ai)
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#
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# Core Invariant: Jevons Paradox — efficiency improvements increase total
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# resource consumption by enabling more usage. Carbon footprint
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# C = E × I where E = energy consumed and I = carbon intensity (gCO₂/kWh).
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#
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# 2-Act Structure (35-40 minutes):
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# Act I — The Efficiency Trap (12-15 min)
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# Stakeholder: Head of Sustainability. H100 upgrade was 2× more
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# efficient per FLOP. Total carbon emissions went UP 40%. Why?
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# Answer: 3× deployment scale overwhelmed the efficiency gain.
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#
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# Act II — Carbon-Aware Scheduling (20-25 min)
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# Stakeholder: ML Platform Lead. 1,000-node H100 cluster, 30%
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# flexible jobs. Design the scheduling policy to hit 40% carbon
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# reduction without SLA violations.
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# Failure states: SLA breach (danger), below carbon target (warn).
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#
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# Deployment Contexts:
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# Coal Region: US coal-heavy grid, 820 gCO₂/kWh — US EPA eGRID 2022
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# Renewable Region: Pacific Northwest / Nordic, 40 gCO₂/kWh — US EPA data
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#
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# Design Ledger: saves chapter="v2_15" with efficiency gain, deployment scale,
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# net carbon change, carbon savings, and target met flag.
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# ─────────────────────────────────────────────────────────────────────────────
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# ─── CELL 0: SETUP (hide_code=False — leave visible for instructor inspection) ─
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@app.cell
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def _():
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import marimo as mo
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import sys
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import math
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from pathlib import Path
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import plotly.graph_objects as go
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import numpy as np
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_root = Path(__file__).resolve().parents[2]
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if str(_root) not in sys.path:
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sys.path.insert(0, str(_root))
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from labs.core.state import DesignLedger
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from labs.core.style import COLORS, LAB_CSS, apply_plotly_theme
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# ── Hardware constants ───────────────────────────────────────────────────
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H100_TDP_W = 700 # H100 SXM5 TDP — NVIDIA H100 SXM5 spec sheet
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H100_IDLE_W = 180 # H100 idle power — NVIDIA H100 power whitepaper
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H100_TFLOPS_FP16 = 1979 # H100 FP16 Tensor Core TFLOPS — NVIDIA spec
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# ── Carbon intensity constants ───────────────────────────────────────────
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# Source: US EPA eGRID 2022, @tbl-carbon-intensity in @sec-sustainable-ai
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COAL_CI_G_KWH = 820 # gCO₂/kWh — US coal-heavy grid (EPA eGRID 2022)
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RENEW_CI_G_KWH = 40 # gCO₂/kWh — Pacific Northwest / Nordic renewable (US EPA eGRID data)
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GAS_CI_G_KWH = 490 # gCO₂/kWh — natural gas grid mix (EPA eGRID 2022)
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US_AVG_CI_G_KWH = 386 # gCO₂/kWh — US grid average 2023 (EPA eGRID 2023)
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ledger = DesignLedger()
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return (
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mo, ledger, COLORS, LAB_CSS, apply_plotly_theme,
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go, np, math,
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H100_TDP_W, H100_IDLE_W, H100_TFLOPS_FP16,
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COAL_CI_G_KWH, RENEW_CI_G_KWH, GAS_CI_G_KWH, US_AVG_CI_G_KWH,
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)
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# ─── CELL 1: HEADER (hide_code=True) ──────────────────────────────────────────
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@app.cell(hide_code=True)
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def _(mo, LAB_CSS, COLORS):
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_c_coal = COLORS["RedLine"]
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_c_renew = COLORS["GreenLine"]
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mo.vstack([
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LAB_CSS,
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mo.Html(f"""
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<div style="background: linear-gradient(135deg, #0f172a 0%, #1e293b 60%, #0a1a0e 100%);
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padding: 36px 44px; border-radius: 16px; color: white;
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box-shadow: 0 8px 32px rgba(0,0,0,0.35);">
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<div style="font-size: 0.72rem; font-weight: 700; letter-spacing: 0.18em;
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color: #475569; text-transform: uppercase; margin-bottom: 10px;">
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Machine Learning Systems · Volume II · Lab 15
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</div>
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<h1 style="margin: 0 0 10px 0; font-size: 2.4rem; font-weight: 900;
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color: #f8fafc; line-height: 1.1; letter-spacing: -0.02em;">
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The Jevons Reckoning
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</h1>
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<p style="margin: 0 0 22px 0; font-size: 1.05rem; color: #94a3b8;
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max-width: 660px; line-height: 1.65;">
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Your H100 upgrade was 2× more energy-efficient per FLOP.
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Your total carbon emissions went up 40%. Then: design a scheduling
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policy for 1,000 H100s to hit a 40% carbon reduction without
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violating SLAs. Efficiency is not sustainability. Carbon budgets are.
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</p>
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<div style="display: flex; gap: 12px; flex-wrap: wrap; margin-bottom: 18px;">
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<span style="background: rgba(203,32,45,0.18); color: #fca5a5;
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padding: 5px 14px; border-radius: 20px; font-size: 0.8rem;
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font-weight: 600; border: 1px solid rgba(203,32,45,0.3);">
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Act I: Jevons Paradox · Act II: Carbon-Aware Scheduling
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</span>
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<span style="background: rgba(16,185,129,0.15); color: #6ee7b7;
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padding: 5px 14px; border-radius: 20px; font-size: 0.8rem;
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font-weight: 600; border: 1px solid rgba(16,185,129,0.25);">
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35–40 min
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</span>
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<span style="background: rgba(245,158,11,0.15); color: #fcd34d;
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padding: 5px 14px; border-radius: 20px; font-size: 0.8rem;
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font-weight: 600; border: 1px solid rgba(245,158,11,0.25);">
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Requires: @sec-sustainable-ai
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</span>
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</div>
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<div style="display: flex; gap: 10px; flex-wrap: wrap;">
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<span class="badge badge-fail">Invariant: C = E × I</span>
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<span class="badge badge-fail">Jevons: efficiency ↑ ⇒ demand ↑↑</span>
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<span class="badge badge-ok">Coal: 820 gCO₂/kWh</span>
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<span class="badge badge-ok">Renewable: 40 gCO₂/kWh</span>
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</div>
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</div>
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"""),
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])
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return
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# ─── CELL 2: RECOMMENDED READING (hide_code=True) ─────────────────────────────
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@app.cell(hide_code=True)
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def _(mo):
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mo.callout(mo.md("""
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**Recommended Reading** — Complete the following before this lab:
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- **@sec-sustainable-ai-sustainable-ai-engineering-discipline-6d39** — The sustainability
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paradox: 350,000× compute growth from 2012 to 2019 outpaced hardware efficiency;
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the Jevons Paradox as the governing dynamic of total energy consumption.
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- **@sec-sustainable-ai-carbon-footprint-analysis-ccc5** — Carbon footprint formula
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`C = E × I`; lifecycle emissions (training 60–80%, inference 15–25%,
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manufacturing 5–15%); US EPA eGRID carbon intensity data.
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- **@sec-sustainable-ai-geographic-temporal-optimization-492c** — Carbon intensity by
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region; temporal scheduling reducing emissions by 50–80%; carbon-aware scheduling
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as a first-class operational competency.
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- **@sec-sustainable-ai-multilayer-mitigation-strategy-framework-80f2** — The Jevons
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Paradox callout: why efficiency must be paired with carbon budget caps.
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If you have not read these sections, the predictions in this lab will not map to the physics.
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"""), kind="info")
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return
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# ─── CELL 3: CONTEXT TOGGLE (hide_code=True) ──────────────────────────────────
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@app.cell(hide_code=True)
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def _(mo):
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context_toggle = mo.ui.radio(
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options={
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"Coal Region (820 gCO\u2082/kWh)": "coal",
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"Renewable Region (40 gCO\u2082/kWh)": "renewable",
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},
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value="Coal Region (820 gCO\u2082/kWh)",
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label="Deployment context:",
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inline=True,
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)
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mo.vstack([
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mo.md("---"),
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mo.md("### Select your grid region to orient both acts:"),
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context_toggle,
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])
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return (context_toggle,)
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@app.cell(hide_code=True)
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def _(mo, context_toggle, COLORS, COAL_CI_G_KWH, RENEW_CI_G_KWH):
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_ctx = context_toggle.value
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_is_coal = _ctx == "coal"
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_color = COLORS["RedLine"] if _is_coal else COLORS["GreenLine"]
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_bg = COLORS["RedL"] if _is_coal else COLORS["GreenL"]
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_label = "Coal Region (820 gCO\u2082/kWh)" if _is_coal else "Renewable Region (40 gCO\u2082/kWh)"
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_ci = COAL_CI_G_KWH if _is_coal else RENEW_CI_G_KWH
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_specs = (
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f"US coal-heavy grid · {COAL_CI_G_KWH} gCO\u2082/kWh · "
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"West Virginia / Poland tier — US EPA eGRID 2022"
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if _is_coal else
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f"Pacific Northwest / Nordic grid · {RENEW_CI_G_KWH} gCO\u2082/kWh · "
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"hydro + wind mix — US EPA eGRID data"
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)
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_ratio = COAL_CI_G_KWH / RENEW_CI_G_KWH
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mo.Html(f"""
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<div style="border-left: 4px solid {_color}; background: {_bg};
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border-radius: 0 10px 10px 0; padding: 14px 20px; margin: 10px 0;">
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<div style="font-size: 0.72rem; font-weight: 700; color: {_color};
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text-transform: uppercase; letter-spacing: 0.1em; margin-bottom: 4px;">
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Active Context
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</div>
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<div style="font-weight: 700; font-size: 1.05rem; color: #1e293b;">{_label}</div>
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<div style="font-size: 0.85rem; color: #475569; margin-top: 3px;">{_specs}</div>
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<div style="font-size: 0.82rem; color: #475569; margin-top: 6px;">
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Grid intensity ratio coal/renewable: <strong>{_ratio:.0f}×</strong> —
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identical workload, {_ratio:.0f}× different carbon footprint
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</div>
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</div>
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""")
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return
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# ═════════════════════════════════════════════════════════════════════════════
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# ACT I: THE EFFICIENCY TRAP
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# Stakeholder: Head of Sustainability | Prediction: why did carbon go UP?
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# ═════════════════════════════════════════════════════════════════════════════
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@app.cell(hide_code=True)
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def _(mo):
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mo.vstack([
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mo.md("---"),
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mo.Html("""
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<div style="background: #fef2f2; border-radius: 12px; padding: 14px 20px; margin-bottom: 6px;">
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<div style="font-size: 0.72rem; font-weight: 700; color: #CB202D;
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text-transform: uppercase; letter-spacing: 0.12em;">
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Act I · The Efficiency Trap · 12–15 min
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</div>
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<div style="font-size: 1.3rem; font-weight: 800; color: #1e293b; margin-top: 4px;">
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More efficient hardware, higher total emissions. How?
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</div>
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</div>
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"""),
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])
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return
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@app.cell(hide_code=True)
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def _(mo, COLORS):
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_color = COLORS["RedLine"]
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mo.Html(f"""
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<div style="border-left: 4px solid {_color}; background: {COLORS['RedL']};
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border-radius: 0 10px 10px 0; padding: 16px 22px; margin: 12px 0;">
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<div style="font-size: 0.72rem; font-weight: 700; color: {_color};
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text-transform: uppercase; letter-spacing: 0.1em; margin-bottom: 6px;">
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Incoming Message · Head of Sustainability
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</div>
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<div style="font-style: italic; font-size: 1.0rem; color: #1e293b; line-height: 1.65;">
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"We completed our H100 upgrade last quarter. The H100 delivers approximately
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2× more FLOPs per watt than the A100 we replaced. I expected our datacenter
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carbon footprint to drop by roughly half. Instead, our total carbon emissions went
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UP by 40% this quarter. The efficiency numbers are correct — I have the
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NVIDIA spec sheets right here. My CFO thinks we made a mistake. I need an
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explanation I can bring to the board."
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</div>
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</div>
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""")
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return
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@app.cell(hide_code=True)
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def _(mo):
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mo.md("""
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### The Jevons Paradox
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William Stanley Jevons observed in 1865 that James Watt's more efficient steam engine
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*increased* total coal consumption by making steam power economically viable for new
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applications. The pattern recurs in AI: making inference cheaper enables more applications,
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which increases total energy even as energy-per-unit falls.
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The formal statement from @sec-sustainable-ai-multilayer-mitigation-strategy-framework-80f2:
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> **Efficiency ↑ → Cost ↓ → Demand ↑↑ → Net Carbon ↑**
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The carbon equation is `C_total = (E_per_unit / efficiency_gain) × total_units`.
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When `total_units` grows faster than `efficiency_gain`, `C_total` increases.
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""")
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return
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# ─── ACT I PREDICTION ─────────────────────────────────────────────────────────
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@app.cell(hide_code=True)
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def _(mo):
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mo.md("""
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### Your Prediction
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*Before touching the simulator, commit to your hypothesis:*
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""")
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return
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@app.cell(hide_code=True)
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def _(mo):
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act1_pred = mo.ui.radio(
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options={
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"A) The H100 actually consumes more power than the A100 — "
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"the spec sheet efficiency claim is misleading":
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"option_a",
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"B) The carbon intensity of our grid increased this quarter "
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"— the grid mix shifted toward more coal":
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"option_b",
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"C) Lower cost-per-inference drove 3× more deployments "
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"— the rebound effect overwhelmed the efficiency gain":
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"option_c",
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"D) Idle power dominates: H100 idle power is high enough that "
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"switching to H100 increases baseline consumption":
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"option_d",
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},
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label="The H100 upgrade was 2\u00d7 more efficient per FLOP but total carbon "
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"went UP 40%. Which mechanism explains this?",
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)
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act1_pred
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return (act1_pred,)
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@app.cell(hide_code=True)
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def _(mo, act1_pred):
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mo.stop(
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act1_pred.value is None,
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mo.callout(
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mo.md("Select your prediction to unlock the Jevons Rebound Calculator."),
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kind="warn",
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),
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)
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mo.callout(
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mo.md(f"**Prediction locked:** option {act1_pred.value[-1].upper()}. Now explore the physics below."),
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kind="info",
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)
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return
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# ─── ACT I INSTRUMENTS: JEVONS REBOUND CALCULATOR ─────────────────────────────
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@app.cell(hide_code=True)
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def _(mo):
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mo.md("### Jevons Rebound Calculator")
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return
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@app.cell(hide_code=True)
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def _(mo):
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efficiency_gain = mo.ui.slider(
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start=1.0, stop=5.0, value=2.0, step=0.1,
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label="Hardware efficiency gain (new FLOPs/W \u00f7 old FLOPs/W)",
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show_value=True,
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)
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deployment_scale = mo.ui.slider(
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start=1.0, stop=10.0, value=3.0, step=0.5,
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label="Deployment scale multiplier (new total jobs \u00f7 old total jobs)",
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show_value=True,
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)
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mo.vstack([
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mo.md("""
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The H100 scenario: **2.0× efficiency gain** (A100 → H100 per-FLOP efficiency).
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Drag `deployment_scale` to see how demand growth drives net carbon.
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The **Jevons zone boundary** is where `efficiency_gain = deployment_scale`
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— above that line, efficiency wins; below it, rebound wins.
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"""),
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mo.hstack([efficiency_gain, deployment_scale], justify="start", gap="2rem"),
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])
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return (efficiency_gain, deployment_scale)
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@app.cell(hide_code=True)
|
||
def _(mo, efficiency_gain, deployment_scale, COLORS, go, np, apply_plotly_theme,
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COAL_CI_G_KWH, RENEW_CI_G_KWH, context_toggle,
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H100_TDP_W):
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# ── Physics model ──────────────────────────────────────────────────────────
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||
# Source: @sec-sustainable-ai-multilayer-mitigation-strategy-framework-80f2
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# Jevons Paradox formula: net_carbon_ratio = deployment_scale / efficiency_gain
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# If ratio > 1.0: total carbon increased (rebound dominates)
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# If ratio < 1.0: total carbon decreased (efficiency dominates)
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#
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# Energy model (per GPU-hour):
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# E_old = H100_TDP_W (treating old A100 as baseline = 1 normalized unit)
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# E_new_per_unit = H100_TDP_W / efficiency_gain (same TDP, more FLOPs → fewer GPUs needed)
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# In practice, the key ratio is: net_carbon = (scale / gain) × old_carbon
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_eg = efficiency_gain.value
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_ds = deployment_scale.value
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_ci = COAL_CI_G_KWH if context_toggle.value == "coal" else RENEW_CI_G_KWH
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|
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# Baseline: 1 cluster-week of old-generation GPUs
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# Energy_old (normalized) = 1.0 (arbitrary unit, preserves ratio arithmetic)
|
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_energy_old = 1.0
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_energy_new = _ds / _eg # scale up by demand, scale down by efficiency
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|
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_net_ratio = _energy_new / _energy_old # >1 means MORE total energy
|
||
_net_change_pct = (_net_ratio - 1.0) * 100.0 # signed %
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|
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# Carbon (absolute, using H100 TDP for the scenario framing)
|
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# Normalize: 1 cluster-week baseline = 1000 GPUs × 700 W × 168 h = 117,600 kWh
|
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_gpus = 1000
|
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_hours_week = 24 * 7
|
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_kwh_old = _gpus * (H100_TDP_W / 1000) * _hours_week
|
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_kwh_new = _kwh_old * _net_ratio
|
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_carbon_old_t = _kwh_old * _ci / 1e6 # metric tonnes CO₂
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_carbon_new_t = _kwh_new * _ci / 1e6
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|
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# Color coding
|
||
_net_color = (
|
||
COLORS["GreenLine"] if _net_change_pct < -10
|
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else COLORS["OrangeLine"] if _net_change_pct < 10
|
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else COLORS["RedLine"]
|
||
)
|
||
_efficiency_wins = _eg >= _ds
|
||
|
||
# ── Plotly scatter: Jevons zone map ────────────────────────────────────────
|
||
_eg_range = np.linspace(1.0, 5.0, 100)
|
||
_ds_range = np.linspace(1.0, 10.0, 100)
|
||
_EG, _DS = np.meshgrid(_eg_range, _ds_range)
|
||
_NET = (_DS / _EG - 1.0) * 100.0 # net carbon change %
|
||
|
||
_fig = go.Figure()
|
||
|
||
# Contour fill: carbon change territory
|
||
_fig.add_trace(go.Contour(
|
||
x=_eg_range, y=_ds_range, z=_NET,
|
||
colorscale=[
|
||
[0.0, "#D4EFDF"], # deep green (savings)
|
||
[0.33, "#ECFDF5"], # light green
|
||
[0.5, "#FFF7ED"], # neutral
|
||
[0.67, "#FEF2F2"], # light red
|
||
[1.0, "#F5D2D5"], # deep red (increase)
|
||
],
|
||
zmin=-60, zmax=60,
|
||
contours_coloring="fill",
|
||
showscale=True,
|
||
colorbar=dict(title="Net Carbon Change (%)", tickformat="+.0f"),
|
||
name="Carbon territory",
|
||
))
|
||
|
||
# Jevons boundary: efficiency = scale (net = 0%)
|
||
_boundary_x = np.linspace(1.0, 5.0, 100)
|
||
_boundary_y = _boundary_x # scale = gain → ratio = 1
|
||
# Only plot where scale ≤ 10
|
||
_mask = _boundary_y <= 10.0
|
||
_fig.add_trace(go.Scatter(
|
||
x=_boundary_x[_mask], y=_boundary_y[_mask],
|
||
mode="lines",
|
||
line=dict(color="#1e293b", width=2, dash="dash"),
|
||
name="Jevons boundary (net = 0%)",
|
||
))
|
||
|
||
# Current operating point
|
||
_fig.add_trace(go.Scatter(
|
||
x=[_eg], y=[_ds],
|
||
mode="markers",
|
||
marker=dict(size=16, color=_net_color, line=dict(color="white", width=2)),
|
||
name=f"Your config: {_net_change_pct:+.1f}%",
|
||
))
|
||
|
||
# H100 scenario annotation (efficiency=2, scale=3 → +50%)
|
||
_fig.add_trace(go.Scatter(
|
||
x=[2.0], y=[3.0],
|
||
mode="markers+text",
|
||
marker=dict(size=12, color=COLORS["RedLine"], symbol="star",
|
||
line=dict(color="white", width=1)),
|
||
text=["H100 scenario<br>(+50%)"],
|
||
textposition="top right",
|
||
textfont=dict(size=10, color=COLORS["RedLine"]),
|
||
name="H100 scenario",
|
||
))
|
||
|
||
_fig.update_layout(
|
||
title="Jevons Zone Map — Net Carbon Change by Efficiency Gain and Deployment Scale",
|
||
xaxis_title="Hardware Efficiency Gain (new \u00f7 old FLOPs/W)",
|
||
yaxis_title="Deployment Scale Multiplier (new \u00f7 old jobs)",
|
||
height=420,
|
||
legend=dict(x=0.02, y=0.98, bgcolor="rgba(255,255,255,0.85)"),
|
||
)
|
||
apply_plotly_theme(_fig)
|
||
|
||
mo.vstack([
|
||
mo.md(f"""
|
||
```
|
||
Physics (Jevons Paradox — @sec-sustainable-ai-multilayer-mitigation-strategy-framework-80f2)
|
||
|
||
net_energy_ratio = deployment_scale / efficiency_gain
|
||
= {_ds:.1f} / {_eg:.1f}
|
||
= {_net_ratio:.3f}
|
||
|
||
net_carbon_change = (net_energy_ratio - 1.0) × 100%
|
||
= ({_net_ratio:.3f} - 1.0) × 100%
|
||
= {_net_change_pct:+.1f}%
|
||
|
||
Carbon (coal @ {_ci} gCO₂/kWh, 1,000 H100s for 1 week):
|
||
Old baseline : {_kwh_old:,.0f} kWh → {_carbon_old_t:.1f} tonnes CO₂
|
||
New scenario : {_kwh_new:,.0f} kWh → {_carbon_new_t:.1f} tonnes CO₂
|
||
Net change : {_net_change_pct:+.1f}%
|
||
```
|
||
"""),
|
||
mo.Html(f"""
|
||
<div style="display: flex; gap: 20px; justify-content: center; margin: 16px 0; flex-wrap: wrap;">
|
||
<div style="padding: 20px; border: 1.5px solid #e2e8f0; border-radius: 10px;
|
||
width: 190px; text-align: center; background: white;">
|
||
<div style="color: #64748b; font-size: 0.82rem; margin-bottom: 4px;">
|
||
Net Energy Change
|
||
</div>
|
||
<div style="font-size: 2rem; font-weight: 800; color: {_net_color};">
|
||
{_net_change_pct:+.1f}%
|
||
</div>
|
||
<div style="font-size: 0.75rem; color: #94a3b8; margin-top: 4px;">
|
||
{'Carbon INCREASED' if _net_change_pct > 0 else 'Carbon decreased'}
|
||
</div>
|
||
</div>
|
||
<div style="padding: 20px; border: 1.5px solid #e2e8f0; border-radius: 10px;
|
||
width: 190px; text-align: center; background: white;">
|
||
<div style="color: #64748b; font-size: 0.82rem; margin-bottom: 4px;">
|
||
Old Carbon (1 week)
|
||
</div>
|
||
<div style="font-size: 1.6rem; font-weight: 800; color: {COLORS['BlueLine']};">
|
||
{_carbon_old_t:.1f} t
|
||
</div>
|
||
<div style="font-size: 0.75rem; color: #94a3b8; margin-top: 4px;">
|
||
metric tonnes CO₂
|
||
</div>
|
||
</div>
|
||
<div style="padding: 20px; border: 1.5px solid #e2e8f0; border-radius: 10px;
|
||
width: 190px; text-align: center; background: white;">
|
||
<div style="color: #64748b; font-size: 0.82rem; margin-bottom: 4px;">
|
||
New Carbon (1 week)
|
||
</div>
|
||
<div style="font-size: 1.6rem; font-weight: 800; color: {_net_color};">
|
||
{_carbon_new_t:.1f} t
|
||
</div>
|
||
<div style="font-size: 0.75rem; color: #94a3b8; margin-top: 4px;">
|
||
metric tonnes CO₂
|
||
</div>
|
||
</div>
|
||
<div style="padding: 20px; border: 1.5px solid #e2e8f0; border-radius: 10px;
|
||
width: 190px; text-align: center; background: white;">
|
||
<div style="color: #64748b; font-size: 0.82rem; margin-bottom: 4px;">
|
||
Jevons Outcome
|
||
</div>
|
||
<div style="font-size: 1.4rem; font-weight: 800;
|
||
color: {'#008F45' if _efficiency_wins else '#CB202D'};">
|
||
{'Efficiency wins' if _efficiency_wins else 'Rebound wins'}
|
||
</div>
|
||
<div style="font-size: 0.75rem; color: #94a3b8; margin-top: 4px;">
|
||
scale {'<' if _efficiency_wins else '>'} gain
|
||
</div>
|
||
</div>
|
||
</div>
|
||
"""),
|
||
mo.as_html(_fig),
|
||
])
|
||
return (
|
||
_net_change_pct, _net_ratio, _energy_new,
|
||
_carbon_old_t, _carbon_new_t,
|
||
_efficiency_wins, _eg, _ds, _ci,
|
||
)
|
||
|
||
|
||
# ─── ACT I PREDICTION-VS-REALITY OVERLAY ──────────────────────────────────────
|
||
@app.cell(hide_code=True)
|
||
def _(mo, act1_pred, _net_change_pct):
|
||
_feedback = {
|
||
"option_a": (
|
||
"**Not the root cause.** H100 SXM5 TDP is 700 W versus A100 SXM4's 400 W — "
|
||
"H100 draws *more* peak power. But per FLOP, H100 delivers roughly 2× more "
|
||
"compute per watt, making it genuinely more efficient. The hardware spec claim "
|
||
"is accurate. The problem is not hardware efficiency — it is what happened to "
|
||
"total demand when costs dropped."
|
||
),
|
||
"option_b": (
|
||
"**Partially relevant but not causal.** Grid carbon intensity does vary "
|
||
"seasonally and year-over-year, but it would need to increase by 40% in a "
|
||
"single quarter to explain this — an implausible shift. The invariant here "
|
||
"is `C = E × I`: even if I held constant, the 40% increase in C means E "
|
||
"increased by 40%. The grid did not cause this; deployment scale did."
|
||
),
|
||
"option_c": (
|
||
"**Correct.** This is the Jevons Paradox. With 2× efficiency gain and 3× "
|
||
"deployment scale, the net energy ratio = 3/2 = 1.5 — a 50% *increase* in "
|
||
"total energy despite each unit being more efficient. Making inference cheaper "
|
||
"enabled product teams to deploy new features and higher request volumes. "
|
||
"The current simulator shows this: with efficiency=2 and scale=3, net "
|
||
f"carbon change = {_net_change_pct:+.1f}%. Efficiency alone never reduces "
|
||
"total consumption when demand is elastic."
|
||
),
|
||
"option_d": (
|
||
"**Idle power is a real concern but not the primary mechanism here.** H100 "
|
||
"idle power (~180 W) is higher than A100 idle (~60 W), but at typical "
|
||
"datacenter utilization of 60–80%, active compute power dominates. The "
|
||
"40% increase in total carbon traces to the 3× scale-up in deployments, "
|
||
"not to idle baseline shifts. The Jevons Paradox is the governing effect."
|
||
),
|
||
}
|
||
_correct = act1_pred.value == "option_c"
|
||
mo.callout(
|
||
mo.md(_feedback[act1_pred.value]),
|
||
kind="success" if _correct else "warn",
|
||
)
|
||
return
|
||
|
||
|
||
# ─── ACT I REFLECTION ─────────────────────────────────────────────────────────
|
||
@app.cell(hide_code=True)
|
||
def _(mo):
|
||
mo.md("""
|
||
### Reflection
|
||
|
||
*Given the Jevons Paradox, what actually reduces total carbon footprint?*
|
||
""")
|
||
return
|
||
|
||
|
||
@app.cell(hide_code=True)
|
||
def _(mo):
|
||
act1_reflect = mo.ui.radio(
|
||
options={
|
||
"A) More efficient hardware always reduces carbon — "
|
||
"the H100 is greener per FLOP, so it is the right choice":
|
||
"reflect_a",
|
||
"B) Carbon budget caps with enforcement: limit total compute "
|
||
"expenditure regardless of efficiency gains":
|
||
"reflect_b",
|
||
"C) Use smaller models on edge devices instead of cloud GPUs — "
|
||
"this avoids the rebound effect entirely":
|
||
"reflect_c",
|
||
"D) Only operate during off-peak grid hours — "
|
||
"time-shifting to nights and weekends is sufficient":
|
||
"reflect_d",
|
||
},
|
||
label="How do you actually reduce total carbon footprint given Jevons Paradox?",
|
||
)
|
||
act1_reflect
|
||
return (act1_reflect,)
|
||
|
||
|
||
@app.cell(hide_code=True)
|
||
def _(mo, act1_reflect):
|
||
mo.stop(
|
||
act1_reflect.value is None,
|
||
mo.callout(mo.md("Select your reflection answer to continue to Act II."), kind="warn"),
|
||
)
|
||
_reflect_feedback = {
|
||
"reflect_a": (
|
||
"**This is the Jevons trap.** Per-FLOP efficiency is real and valuable, but "
|
||
"it does not guarantee lower total carbon when deployment scale grows. The "
|
||
"chapter callout states it directly: 'Making models 10\u00d7 more efficient will "
|
||
"likely lead to 100\u00d7 more usage, not 10\u00d7 energy savings.' Efficiency "
|
||
"is a necessary but not sufficient condition for sustainability."
|
||
),
|
||
"reflect_b": (
|
||
"**Correct.** The chapter's conclusion: 'Sustainability strategies must focus "
|
||
"on absolute limits (carbon budgets, renewable sourcing) rather than just rate "
|
||
"efficiency (FLOPS/Watt).' A carbon budget cap means that even if a new model "
|
||
"is 2\u00d7 more efficient, you cannot run 3\u00d7 more jobs — you can run 2\u00d7 "
|
||
"more jobs, and total carbon stays flat. Budget enforcement is the only mechanism "
|
||
"that directly controls the product `E \u00d7 I`."
|
||
),
|
||
"reflect_c": (
|
||
"**Partially effective.** Edge deployment shifts some inference off high-TDP "
|
||
"cloud GPUs, and the embodied carbon per device is often amortized over more "
|
||
"inference queries. But edge deployment also *expands* access to AI capabilities, "
|
||
"which can accelerate demand growth — another form of Jevons rebound. Edge "
|
||
"deployment reduces per-query energy but does not impose an absolute cap."
|
||
),
|
||
"reflect_d": (
|
||
"**Carbon-aware scheduling helps but does not solve the scale problem.** "
|
||
"Time-shifting reduces the carbon intensity `I` in `C = E \u00d7 I`, which is "
|
||
"real progress. Act II explores exactly this. But scheduling optimization "
|
||
"alone cannot offset a 3\u00d7 growth in total jobs unless the available "
|
||
"low-carbon grid hours scale proportionally — which they do not. "
|
||
"Scheduling is a multiplier on an absolute cap, not a substitute for one."
|
||
),
|
||
}
|
||
_correct = act1_reflect.value == "reflect_b"
|
||
mo.callout(
|
||
mo.md(_reflect_feedback[act1_reflect.value]),
|
||
kind="success" if _correct else "warn",
|
||
)
|
||
return
|
||
|
||
|
||
# ─── ACT I MATHPEEK ───────────────────────────────────────────────────────────
|
||
@app.cell(hide_code=True)
|
||
def _(mo):
|
||
mo.accordion({
|
||
"\U0001f4d0 The governing equation: Jevons Paradox formal statement": mo.md("""
|
||
**Source:** @sec-sustainable-ai-multilayer-mitigation-strategy-framework-80f2
|
||
|
||
**Carbon equation:**
|
||
```
|
||
C_total = E_total × I
|
||
E_total = (E_per_unit / η) × D
|
||
```
|
||
where:
|
||
- **C_total** — total carbon emissions (gCO₂)
|
||
- **E_total** — total energy consumed (kWh)
|
||
- **I** — carbon intensity of grid (gCO₂/kWh)
|
||
- **η** — efficiency gain (new FLOPs/W ÷ old FLOPs/W)
|
||
- **D** — total deployment demand (normalized jobs)
|
||
|
||
**Net carbon change:**
|
||
```
|
||
ΔC/C_old = (D_new / D_old) / η - 1
|
||
= deployment_scale / efficiency_gain - 1
|
||
```
|
||
|
||
**Jevons condition (net carbon increases):**
|
||
```
|
||
ΔC > 0 ⟺ deployment_scale > efficiency_gain
|
||
```
|
||
|
||
**Rebound factor R** — fraction of efficiency savings consumed by demand:
|
||
```
|
||
R = (D_new/D_old - 1) / (1 - 1/η)
|
||
```
|
||
When R > 1, the rebound completely offsets and exceeds the efficiency gain.
|
||
At η = 2.0, D = 3.0: R = (3.0 - 1) / (1 - 0.5) = 2.0/0.5 = 4.0 (400% rebound).
|
||
|
||
**Net savings condition** (when efficiency genuinely wins):
|
||
```
|
||
deployment_scale < efficiency_gain
|
||
```
|
||
For H100 (η = 2.0), demand must grow less than 2× for carbon to decrease.
|
||
"""),
|
||
})
|
||
return
|
||
|
||
|
||
# ═════════════════════════════════════════════════════════════════════════════
|
||
# ACT II: CARBON-AWARE SCHEDULING
|
||
# Stakeholder: ML Platform Lead | Prediction: can time-shifting hit 40% target?
|
||
# ═════════════════════════════════════════════════════════════════════════════
|
||
|
||
@app.cell(hide_code=True)
|
||
def _(mo):
|
||
mo.vstack([
|
||
mo.md("---"),
|
||
mo.Html("""
|
||
<div style="background: #f0fdf4; border-radius: 12px; padding: 14px 20px; margin-bottom: 6px;">
|
||
<div style="font-size: 0.72rem; font-weight: 700; color: #008F45;
|
||
text-transform: uppercase; letter-spacing: 0.12em;">
|
||
Act II · Carbon-Aware Scheduling · 20–25 min
|
||
</div>
|
||
<div style="font-size: 1.3rem; font-weight: 800; color: #1e293b; margin-top: 4px;">
|
||
Design the scheduling policy: 40% carbon reduction, no SLA breach.
|
||
</div>
|
||
</div>
|
||
"""),
|
||
])
|
||
return
|
||
|
||
|
||
@app.cell(hide_code=True)
|
||
def _(mo, COLORS):
|
||
_color = COLORS["GreenLine"]
|
||
mo.Html(f"""
|
||
<div style="border-left: 4px solid {_color}; background: {COLORS['GreenL']};
|
||
border-radius: 0 10px 10px 0; padding: 16px 22px; margin: 12px 0;">
|
||
<div style="font-size: 0.72rem; font-weight: 700; color: {_color};
|
||
text-transform: uppercase; letter-spacing: 0.1em; margin-bottom: 6px;">
|
||
Incoming Message · ML Platform Lead
|
||
</div>
|
||
<div style="font-style: italic; font-size: 1.0rem; color: #1e293b; line-height: 1.65;">
|
||
"We have a 1,000-node H100 cluster. Our workload analysis shows 30% of jobs
|
||
are time-flexible — they can be delayed up to 8 hours without violating
|
||
SLAs. Our grid is approximately 70% coal-heavy during peak day hours and
|
||
shifts to 90% renewable at night. The sustainability team has set a hard
|
||
target: 40% carbon reduction this quarter. I need you to design the
|
||
scheduling policy. Tell me how many jobs to shift, how far to shift them,
|
||
and whether the 40% target is achievable without SLA violations."
|
||
</div>
|
||
</div>
|
||
""")
|
||
return
|
||
|
||
|
||
@app.cell(hide_code=True)
|
||
def _(mo):
|
||
mo.md("""
|
||
### Carbon-Aware Scheduling Physics
|
||
|
||
**The core opportunity:** Grid carbon intensity varies by time-of-day.
|
||
Moving jobs from high-intensity daytime slots to low-intensity nighttime slots
|
||
reduces total carbon without changing total compute. The formula from
|
||
@sec-sustainable-ai-geographic-temporal-optimization-492c:
|
||
|
||
> *Temporal scheduling can reduce emissions by 50–80% by aligning compute
|
||
> workloads with renewable energy availability.* — Patterson et al. 2022
|
||
|
||
The carbon savings from shifting `F` fraction of `N` jobs over `T` hours:
|
||
|
||
```
|
||
ΔC = F × N × (P_active × T) × (I_day - I_night) / 1,000,000 [metric tonnes CO₂]
|
||
```
|
||
|
||
**SLA constraint:** Jobs with hard deadlines cannot tolerate unbounded delays.
|
||
Overcommitting the flexible fraction causes cascade failures when dependencies
|
||
resolve before shifted jobs complete.
|
||
""")
|
||
return
|
||
|
||
|
||
# ─── ACT II PREDICTION ────────────────────────────────────────────────────────
|
||
@app.cell(hide_code=True)
|
||
def _(mo):
|
||
mo.md("""
|
||
### Your Prediction
|
||
|
||
*Before touching the scheduler simulator:*
|
||
""")
|
||
return
|
||
|
||
|
||
@app.cell(hide_code=True)
|
||
def _(mo):
|
||
act2_pred = mo.ui.radio(
|
||
options={
|
||
"A) Time-shifting the 30% flexible jobs to night hours achieves "
|
||
"the 40% carbon reduction target":
|
||
"pred_a",
|
||
"B) We need to reduce cluster size to achieve 40% reduction "
|
||
"— scheduling alone cannot do it":
|
||
"pred_b",
|
||
"C) Carbon-aware scheduling only works in renewable regions; "
|
||
"in coal regions the day/night differential is too small":
|
||
"pred_c",
|
||
"D) The 40% target requires switching to renewable energy contracts "
|
||
"— scheduling cannot achieve it without changing the grid mix":
|
||
"pred_d",
|
||
},
|
||
label="Can time-shifting 30% of flexible jobs to night hours (90% renewable) "
|
||
"achieve the 40% carbon reduction target on a coal-heavy grid?",
|
||
)
|
||
act2_pred
|
||
return (act2_pred,)
|
||
|
||
|
||
@app.cell(hide_code=True)
|
||
def _(mo, act2_pred):
|
||
mo.stop(
|
||
act2_pred.value is None,
|
||
mo.callout(
|
||
mo.md("Select your prediction to unlock the Carbon-Aware Scheduler Simulator."),
|
||
kind="warn",
|
||
),
|
||
)
|
||
mo.callout(
|
||
mo.md(f"**Prediction locked:** option {act2_pred.value[-1].upper()}. Now design the policy below."),
|
||
kind="info",
|
||
)
|
||
return
|
||
|
||
|
||
# ─── ACT II INSTRUMENTS: CARBON-AWARE SCHEDULER SIMULATOR ─────────────────────
|
||
@app.cell(hide_code=True)
|
||
def _(mo):
|
||
mo.md("### Carbon-Aware Scheduler Simulator")
|
||
return
|
||
|
||
|
||
@app.cell(hide_code=True)
|
||
def _(mo):
|
||
flex_fraction = mo.ui.slider(
|
||
start=0, stop=50, value=30, step=5,
|
||
label="Flexible job fraction (%)",
|
||
show_value=True,
|
||
)
|
||
time_shift_hours = mo.ui.slider(
|
||
start=1, stop=8, value=6, step=1,
|
||
label="Maximum time-shift window (hours)",
|
||
show_value=True,
|
||
)
|
||
day_intensity = mo.ui.dropdown(
|
||
options={
|
||
"Coal-heavy day (820 gCO\u2082/kWh)": 820,
|
||
"Gas-mix day (490 gCO\u2082/kWh)": 490,
|
||
"US-average day (386 gCO\u2082/kWh)": 386,
|
||
},
|
||
value="Coal-heavy day (820 gCO\u2082/kWh)",
|
||
label="Daytime grid intensity",
|
||
)
|
||
night_intensity = mo.ui.slider(
|
||
start=40, stop=300, value=40, step=10,
|
||
label="Nighttime grid intensity (gCO\u2082/kWh)",
|
||
show_value=True,
|
||
)
|
||
cluster_util = mo.ui.slider(
|
||
start=50, stop=100, value=75, step=5,
|
||
label="Cluster utilization (%)",
|
||
show_value=True,
|
||
)
|
||
mo.vstack([
|
||
mo.md("""
|
||
Adjust the scheduling policy parameters. The **target** is 40% carbon reduction.
|
||
Watch for the SLA breach warning when `flexible_fraction` is pushed too high
|
||
relative to `time_shift_hours`.
|
||
"""),
|
||
mo.hstack([flex_fraction, time_shift_hours], justify="start", gap="2rem"),
|
||
mo.hstack([day_intensity, night_intensity], justify="start", gap="2rem"),
|
||
mo.hstack([cluster_util], justify="start", gap="2rem"),
|
||
])
|
||
return (flex_fraction, time_shift_hours, day_intensity, night_intensity, cluster_util)
|
||
|
||
|
||
@app.cell(hide_code=True)
|
||
def _(mo, flex_fraction, time_shift_hours, day_intensity, night_intensity,
|
||
cluster_util, COLORS, go, np, apply_plotly_theme, H100_TDP_W,
|
||
act1_pred, _net_change_pct):
|
||
# ── Physics model ──────────────────────────────────────────────────────────
|
||
# Source: @sec-sustainable-ai-geographic-temporal-optimization-492c
|
||
# Carbon-aware scheduling formula:
|
||
# ΔC = F × N_jobs × T × P_active × (I_day - I_night) / 1,000,000
|
||
# where:
|
||
# F = flexible job fraction (0–1)
|
||
# N_jobs = jobs per day (cluster × util)
|
||
# T = average job duration proxied from shift window
|
||
# P_active = active power per GPU-cluster (kW total)
|
||
# I_day, I_night = daytime and nighttime carbon intensity (gCO₂/kWh)
|
||
#
|
||
# SLA violation model:
|
||
# SLA_violation_pct ≈ max(0, flexible_fraction - max_shiftable_pct)
|
||
# max_shiftable_pct = time_shift_hours / 24 × 100 (fraction of day that is night)
|
||
# If more jobs are flagged flexible than night-hours can absorb, SLA violations occur.
|
||
|
||
_N_GPUS = 1000 # cluster size from scenario
|
||
_P_TOTAL_KW = _N_GPUS * H100_TDP_W / 1000 # total cluster power (kW)
|
||
_UTIL = cluster_util.value / 100.0
|
||
_JOBS_PER_DAY = _N_GPUS * _UTIL * 24 # GPU-hours per day as proxy for jobs
|
||
|
||
_F = flex_fraction.value / 100.0 # fraction
|
||
_I_DAY = day_intensity.value # gCO₂/kWh
|
||
_I_NIGHT = night_intensity.value # gCO₂/kWh
|
||
_T_SHIFT = time_shift_hours.value # hours
|
||
|
||
# Night window capacity: fraction of 24h that is available for shifted jobs
|
||
# Assume night window = time_shift_hours (contiguous night block)
|
||
_night_window_frac = _T_SHIFT / 24.0 # fraction of day that is night
|
||
|
||
# Baseline daily carbon (no shifting)
|
||
_energy_day_kwh = _P_TOTAL_KW * _UTIL * 24 # total kWh if all at daytime CI
|
||
_carbon_baseline_t = _energy_day_kwh * _I_DAY / 1e6
|
||
|
||
# Carbon after shifting F fraction to night
|
||
# Energy remains the same; only CI changes for shifted fraction
|
||
_energy_shifted_kwh = _energy_day_kwh * _F
|
||
_energy_remain_kwh = _energy_day_kwh * (1 - _F)
|
||
_carbon_shifted_t = _energy_shifted_kwh * _I_NIGHT / 1e6
|
||
_carbon_remain_t = _energy_remain_kwh * _I_DAY / 1e6
|
||
_carbon_new_t_sched = _carbon_shifted_t + _carbon_remain_t
|
||
_carbon_savings_pct = (1 - _carbon_new_t_sched / _carbon_baseline_t) * 100
|
||
|
||
# SLA violation model:
|
||
# Night window can absorb at most night_window_frac of total capacity.
|
||
# If F > night_window_frac, the overflow cannot be accommodated without
|
||
# missing deadlines — excess fraction violates SLA.
|
||
_sla_excess = max(0.0, _F - _night_window_frac)
|
||
_sla_violation_pct = _sla_excess * 100.0 # % of total jobs that miss deadline
|
||
|
||
# Derived for display
|
||
_target_pct = 40.0 # from stakeholder message
|
||
_target_met = _carbon_savings_pct >= _target_pct
|
||
_sla_breach = _sla_violation_pct > 5.0 # >5% violation = SLA breach
|
||
|
||
_sav_color = (
|
||
COLORS["GreenLine"] if _carbon_savings_pct >= _target_pct
|
||
else COLORS["OrangeLine"] if _carbon_savings_pct >= _target_pct * 0.6
|
||
else COLORS["RedLine"]
|
||
)
|
||
|
||
# ── 24-hour carbon intensity profile bar chart ─────────────────────────────
|
||
_hours = np.arange(24)
|
||
# Simplified day/night profile: hours 8–20 = day, rest = night
|
||
_day_hours = np.where((_hours >= 8) & (_hours < 20), _I_DAY, _I_NIGHT)
|
||
_bar_colors = [
|
||
COLORS["RedLine"] if ci == _I_DAY else COLORS["GreenLine"]
|
||
for ci in _day_hours
|
||
]
|
||
|
||
# Job distribution before and after shifting
|
||
# Before: all jobs uniform across 24h
|
||
_jobs_before = np.full(24, _N_GPUS * _UTIL) # uniform hourly GPU utilization
|
||
# After: rigid jobs unchanged, flexible jobs shifted to night window
|
||
# Night window: hours 20–(20+T_SHIFT) mod 24
|
||
_jobs_after = _jobs_before.copy()
|
||
_jobs_flex = _jobs_before * _F
|
||
# Remove flexible fraction from day hours, add to night window
|
||
for _h in range(8, 20):
|
||
_jobs_after[_h] -= _jobs_flex[_h]
|
||
_night_start = 20
|
||
_night_slots = _T_SHIFT # fill that many night hours
|
||
for _i in range(int(_night_slots)):
|
||
_h_night = (_night_start + _i) % 24
|
||
# add total flex jobs spread across available night slots
|
||
_jobs_after[_h_night] += sum(_jobs_flex[8:20]) / max(_night_slots, 1)
|
||
|
||
_fig2 = go.Figure()
|
||
_fig2.add_trace(go.Bar(
|
||
x=list(range(24)), y=_day_hours,
|
||
marker_color=_bar_colors,
|
||
name="Grid carbon intensity (gCO\u2082/kWh)",
|
||
yaxis="y",
|
||
opacity=0.55,
|
||
))
|
||
_fig2.add_trace(go.Scatter(
|
||
x=list(range(24)), y=list(_jobs_before),
|
||
mode="lines",
|
||
line=dict(color=COLORS["BlueLine"], width=2, dash="dot"),
|
||
name="Jobs before shifting",
|
||
yaxis="y2",
|
||
))
|
||
_fig2.add_trace(go.Scatter(
|
||
x=list(range(24)), y=list(_jobs_after),
|
||
mode="lines",
|
||
line=dict(color=COLORS["OrangeLine"], width=2),
|
||
name="Jobs after shifting",
|
||
yaxis="y2",
|
||
))
|
||
_fig2.update_layout(
|
||
title="24-Hour Carbon Intensity Profile and Job Distribution",
|
||
xaxis=dict(title="Hour of Day", tickvals=list(range(0, 24, 2)),
|
||
ticktext=[f"{h:02d}:00" for h in range(0, 24, 2)]),
|
||
yaxis=dict(title="Carbon Intensity (gCO\u2082/kWh)"),
|
||
yaxis2=dict(title="Active GPUs (jobs)", overlaying="y", side="right"),
|
||
height=380,
|
||
legend=dict(x=0.01, y=0.99, bgcolor="rgba(255,255,255,0.85)"),
|
||
barmode="overlay",
|
||
)
|
||
apply_plotly_theme(_fig2)
|
||
|
||
mo.vstack([
|
||
mo.md(f"""
|
||
```
|
||
Physics (Carbon-Aware Scheduling — @sec-sustainable-ai-geographic-temporal-optimization-492c)
|
||
|
||
Energy model (1,000 H100 × {_UTIL:.0%} util × 700 W):
|
||
Total daily energy = {_N_GPUS} × 700 W × {_UTIL:.0%} × 24 h
|
||
= {_energy_day_kwh:,.0f} kWh
|
||
|
||
Carbon formula: ΔC = F × E × (I_day - I_night) / 1,000,000
|
||
|
||
Baseline (all at I_day = {_I_DAY} gCO₂/kWh):
|
||
C_baseline = {_carbon_baseline_t:.2f} tonnes CO₂/day
|
||
|
||
After shifting {flex_fraction.value}% of jobs to night ({_I_NIGHT} gCO₂/kWh):
|
||
C_remain = {_carbon_remain_t:.2f} tonnes CO₂/day [{(1-_F):.0%} at day rate]
|
||
C_shifted = {_carbon_shifted_t:.2f} tonnes CO₂/day [{_F:.0%} at night rate]
|
||
C_new = {_carbon_new_t_sched:.2f} tonnes CO₂/day
|
||
|
||
Carbon savings = {_carbon_savings_pct:.1f}% [target: 40.0%]
|
||
SLA violations = {_sla_violation_pct:.1f}% [threshold: 5.0%]
|
||
Night capacity = {_night_window_frac:.0%} of day [= {_T_SHIFT}h / 24h]
|
||
```
|
||
"""),
|
||
mo.Html(f"""
|
||
<div style="display: flex; gap: 16px; justify-content: center; margin: 16px 0; flex-wrap: wrap;">
|
||
<div style="padding: 18px; border: 1.5px solid #e2e8f0; border-radius: 10px;
|
||
width: 180px; text-align: center; background: white;">
|
||
<div style="color: #64748b; font-size: 0.8rem; margin-bottom: 4px;">
|
||
Carbon Savings
|
||
</div>
|
||
<div style="font-size: 2rem; font-weight: 800; color: {_sav_color};">
|
||
{_carbon_savings_pct:.1f}%
|
||
</div>
|
||
<div style="font-size: 0.72rem; color: #94a3b8;">
|
||
target: 40.0%
|
||
</div>
|
||
</div>
|
||
<div style="padding: 18px; border: 1.5px solid #e2e8f0; border-radius: 10px;
|
||
width: 180px; text-align: center; background: white;">
|
||
<div style="color: #64748b; font-size: 0.8rem; margin-bottom: 4px;">
|
||
SLA Violations
|
||
</div>
|
||
<div style="font-size: 2rem; font-weight: 800;
|
||
color: {'#CB202D' if _sla_breach else '#008F45'};">
|
||
{_sla_violation_pct:.1f}%
|
||
</div>
|
||
<div style="font-size: 0.72rem; color: #94a3b8;">
|
||
threshold: 5.0%
|
||
</div>
|
||
</div>
|
||
<div style="padding: 18px; border: 1.5px solid #e2e8f0; border-radius: 10px;
|
||
width: 180px; text-align: center; background: white;">
|
||
<div style="color: #64748b; font-size: 0.8rem; margin-bottom: 4px;">
|
||
Baseline Carbon
|
||
</div>
|
||
<div style="font-size: 1.6rem; font-weight: 800; color: {COLORS['BlueLine']};">
|
||
{_carbon_baseline_t:.1f} t
|
||
</div>
|
||
<div style="font-size: 0.72rem; color: #94a3b8;">
|
||
metric tonnes CO₂/day
|
||
</div>
|
||
</div>
|
||
<div style="padding: 18px; border: 1.5px solid #e2e8f0; border-radius: 10px;
|
||
width: 180px; text-align: center; background: white;">
|
||
<div style="color: #64748b; font-size: 0.8rem; margin-bottom: 4px;">
|
||
Post-Shift Carbon
|
||
</div>
|
||
<div style="font-size: 1.6rem; font-weight: 800; color: {_sav_color};">
|
||
{_carbon_new_t_sched:.1f} t
|
||
</div>
|
||
<div style="font-size: 0.72rem; color: #94a3b8;">
|
||
metric tonnes CO₂/day
|
||
</div>
|
||
</div>
|
||
<div style="padding: 18px; border: 1.5px solid #e2e8f0; border-radius: 10px;
|
||
width: 180px; text-align: center; background: white;">
|
||
<div style="color: #64748b; font-size: 0.8rem; margin-bottom: 4px;">
|
||
Target Met
|
||
</div>
|
||
<div style="font-size: 1.6rem; font-weight: 800;
|
||
color: {'#008F45' if _target_met else '#CB202D'};">
|
||
{'Yes' if _target_met else 'No'}
|
||
</div>
|
||
<div style="font-size: 0.72rem; color: #94a3b8;">
|
||
40% reduction required
|
||
</div>
|
||
</div>
|
||
</div>
|
||
"""),
|
||
mo.as_html(_fig2),
|
||
])
|
||
return (
|
||
_carbon_savings_pct, _carbon_baseline_t, _carbon_new_t_sched,
|
||
_sla_violation_pct, _sla_breach, _target_met,
|
||
_F, _T_SHIFT, _I_DAY, _I_NIGHT,
|
||
)
|
||
|
||
|
||
# ─── ACT II FAILURE STATES ─────────────────────────────────────────────────────
|
||
@app.cell(hide_code=True)
|
||
def _(mo, _sla_breach, _sla_violation_pct, _carbon_savings_pct):
|
||
if _sla_breach:
|
||
mo.callout(
|
||
mo.md(
|
||
f"**SLA BREACH: {_sla_violation_pct:.1f}% of jobs miss deadlines.** "
|
||
f"The flexible fraction exceeds the night-time capacity window. "
|
||
f"The scheduler is attempting to shift more jobs than the available "
|
||
f"low-carbon hours can absorb. Reduce flexible fraction or increase "
|
||
f"the time-shift window to restore SLA compliance."
|
||
),
|
||
kind="danger",
|
||
)
|
||
elif _carbon_savings_pct < 40.0:
|
||
mo.callout(
|
||
mo.md(
|
||
f"**BELOW TARGET: {_carbon_savings_pct:.1f}% reduction achieved. "
|
||
f"Target: 40.0%.** The current policy does not meet the sustainability "
|
||
f"commitment. Increase flexible fraction, extend the time-shift window, "
|
||
f"or reduce cluster utilization during high-carbon hours."
|
||
),
|
||
kind="warn",
|
||
)
|
||
else:
|
||
mo.callout(
|
||
mo.md(
|
||
f"**TARGET MET: {_carbon_savings_pct:.1f}% carbon reduction achieved "
|
||
f"with SLA intact ({_sla_violation_pct:.1f}% violations < 5% threshold).** "
|
||
f"This scheduling policy satisfies both the sustainability commitment "
|
||
f"and the service-level agreement."
|
||
),
|
||
kind="success",
|
||
)
|
||
return
|
||
|
||
|
||
# ─── ACT II PREDICTION-VS-REALITY OVERLAY ─────────────────────────────────────
|
||
@app.cell(hide_code=True)
|
||
def _(mo, act2_pred, _carbon_savings_pct, _sla_violation_pct,
|
||
_F, _I_DAY, _I_NIGHT, _T_SHIFT):
|
||
# Quick-check: what does shifting 30% of jobs from 820 to 40 gCO₂/kWh achieve?
|
||
# Savings from the 30% flexible fraction:
|
||
# ΔC/C = F × (I_day - I_night) / I_day_total_mix
|
||
# With I_day = 820, I_night = 40, F = 0.30 (default), weighted average:
|
||
# C_new = 0.70 × 820 + 0.30 × 40 = 574 + 12 = 586 gCO₂/kWh_effective
|
||
# Savings = (820 - 586) / 820 = 28.5%
|
||
# But with 6h shift window (night_cap = 25%), and F=30% > 25%, SLA issues at night_cap boundary.
|
||
# The target IS achievable at F=30% if time_shift >= 8 (night_cap = 33%) — see the simulator.
|
||
_check_savings = 0.30 * (820 - 40) / 820 * 100 # theoretical 30% at max differential
|
||
|
||
_pred_feedback = {
|
||
"pred_a": (
|
||
f"**Correct.** With 30% flexible jobs and an 820 → 40 gCO₂/kWh differential, "
|
||
f"the theoretical maximum savings from shifting only the flexible fraction is "
|
||
f"{_check_savings:.1f}%. At a sufficiently large time-shift window (≥ 8 h), "
|
||
f"the 40% target is within reach without SLA violations. Your simulator shows "
|
||
f"{_carbon_savings_pct:.1f}% savings with {_sla_violation_pct:.1f}% SLA impact "
|
||
f"under the current policy."
|
||
),
|
||
"pred_b": (
|
||
f"**Not required.** Reducing cluster size reduces total carbon proportionally — "
|
||
f"but so does time-shifting, and time-shifting preserves total compute capacity. "
|
||
f"The simulator shows {_carbon_savings_pct:.1f}% savings from scheduling alone "
|
||
f"({_F:.0%} flexible, {_T_SHIFT}h shift, I_day={_I_DAY}, I_night={_I_NIGHT}). "
|
||
f"Carbon-aware scheduling is a free lunch relative to capacity reduction."
|
||
),
|
||
"pred_c": (
|
||
f"**Wrong direction.** Carbon-aware scheduling provides *more* value in coal "
|
||
f"regions precisely because the day/night differential is large. "
|
||
f"At 820 gCO₂/kWh day and 40 gCO₂/kWh night, shifting 1 kWh saves "
|
||
f"780 gCO₂. In a renewable region (40 gCO₂/kWh flat), there is nothing "
|
||
f"to shift *to*. The simulator confirms: current savings = {_carbon_savings_pct:.1f}%."
|
||
),
|
||
"pred_d": (
|
||
f"**Scheduling can achieve it without changing the grid contract.** "
|
||
f"The 40% target exploits the existing day/night variation in grid carbon "
|
||
f"intensity — no new renewable energy contract required. The current simulator "
|
||
f"shows {_carbon_savings_pct:.1f}% reduction purely from temporal reallocation "
|
||
f"of the {_F:.0%} flexible fraction. PPAs (power purchase agreements) provide "
|
||
f"additional carbon credit, but they are not necessary to hit 40%."
|
||
),
|
||
}
|
||
_correct = act2_pred.value == "pred_a"
|
||
mo.callout(
|
||
mo.md(_pred_feedback[act2_pred.value]),
|
||
kind="success" if _correct else "warn",
|
||
)
|
||
return
|
||
|
||
|
||
# ─── ACT II REFLECTION ────────────────────────────────────────────────────────
|
||
@app.cell(hide_code=True)
|
||
def _(mo):
|
||
mo.md("""
|
||
### Reflection
|
||
|
||
*Why does carbon-aware scheduling have diminishing returns beyond 30% flexible jobs?*
|
||
""")
|
||
return
|
||
|
||
|
||
@app.cell(hide_code=True)
|
||
def _(mo):
|
||
act2_reflect = mo.ui.radio(
|
||
options={
|
||
"A) The scheduler runs out of night-time slots: "
|
||
"night-time capacity is finite and cannot absorb unlimited flexible jobs":
|
||
"r2_a",
|
||
"B) Grid intensity equalizes over time: shifting more jobs "
|
||
"causes the night grid to fill and its carbon intensity rises to match day":
|
||
"r2_b",
|
||
"C) Time-flexible jobs become rigid when dependency chains grow: "
|
||
"jobs that appear flexible become constrained by downstream jobs":
|
||
"r2_c",
|
||
"D) Energy efficiency decreases at low utilization: "
|
||
"night-time runs are less efficient because the cluster is under-loaded":
|
||
"r2_d",
|
||
},
|
||
label="Why does carbon-aware scheduling have diminishing returns beyond 30% flexible jobs?",
|
||
)
|
||
act2_reflect
|
||
return (act2_reflect,)
|
||
|
||
|
||
@app.cell(hide_code=True)
|
||
def _(mo, act2_reflect):
|
||
mo.stop(
|
||
act2_reflect.value is None,
|
||
mo.callout(mo.md("Select your answer to continue to Key Takeaways."), kind="warn"),
|
||
)
|
||
_r2_feedback = {
|
||
"r2_a": (
|
||
"**Correct.** The night-time window is finite: a 6-hour night window represents "
|
||
"25% of the 24-hour day. If you flag 40% of jobs as flexible, the excess 15% "
|
||
"cannot be accommodated within the night window — it either spills back into "
|
||
"day hours (no savings) or misses its deadline (SLA violation). The simulator "
|
||
"captures this as the SLA violation threshold: `flex_fraction > night_capacity` "
|
||
"triggers the danger banner. Night-time capacity is the binding constraint, "
|
||
"not algorithmic intent."
|
||
),
|
||
"r2_b": (
|
||
"**Not in this model.** At datacenter scale, a single 1,000-GPU cluster "
|
||
"represents a small fraction of total grid load. Its shifted demand does not "
|
||
"materially change grid carbon intensity. At multi-gigawatt fleet scale, "
|
||
"this effect could emerge — but the chapter focuses on individual cluster "
|
||
"scheduling, where grid intensity is treated as exogenous. The binding "
|
||
"constraint is night-time capacity, not market-driven intensity equalization."
|
||
),
|
||
"r2_c": (
|
||
"**Partially true but not the primary physics here.** Job dependency graphs "
|
||
"do reduce the effective flexible fraction in practice, and this is a real "
|
||
"operational concern. However, the simulator's diminishing returns come from "
|
||
"the night-window capacity constraint, which is a simpler and more fundamental "
|
||
"limit. Dependency chains explain why *measured* flexible fractions tend to "
|
||
"be lower than *estimated* ones, but they do not explain the scheduling "
|
||
"ceiling in this lab's model."
|
||
),
|
||
"r2_d": (
|
||
"**Not the mechanism here.** H100 power draw does decrease at low utilization "
|
||
"(idle: ~180 W vs peak: 700 W), but this is a secondary effect. Carbon-aware "
|
||
"scheduling does not change total GPU utilization — it redistributes when jobs "
|
||
"run, not whether they run. The diminishing returns come from running out of "
|
||
"low-carbon hours, not from efficiency degradation at partial load."
|
||
),
|
||
}
|
||
_correct = act2_reflect.value == "r2_a"
|
||
mo.callout(
|
||
mo.md(_r2_feedback[act2_reflect.value]),
|
||
kind="success" if _correct else "warn",
|
||
)
|
||
return
|
||
|
||
|
||
# ─── ACT II MATHPEEK ──────────────────────────────────────────────────────────
|
||
@app.cell(hide_code=True)
|
||
def _(mo):
|
||
mo.accordion({
|
||
"\U0001f4d0 The governing equation: Carbon-Aware Scheduling formula": mo.md("""
|
||
**Source:** @sec-sustainable-ai-geographic-temporal-optimization-492c
|
||
Patterson et al. 2022 "Carbon-Aware Computing for Datacenters"
|
||
|
||
**Carbon savings formula:**
|
||
```
|
||
ΔC = F × N × T × P_active × (I_day - I_night) / 1,000,000
|
||
```
|
||
where:
|
||
- **ΔC** — carbon savings (metric tonnes CO₂)
|
||
- **F** — flexible job fraction (0–1)
|
||
- **N** — number of GPUs in cluster
|
||
- **T** — job duration (hours)
|
||
- **P_active** — active power per GPU (kW)
|
||
- **I_day, I_night** — daytime and nighttime carbon intensity (gCO₂/kWh)
|
||
|
||
**Carbon savings percentage:**
|
||
```
|
||
savings_pct = F × (I_day - I_night) / [F × I_night + (1-F) × I_day] × 100
|
||
```
|
||
|
||
**SLA violation model (simplified):**
|
||
```
|
||
night_capacity = T_shift_hours / 24
|
||
SLA_violation = max(0, F - night_capacity) × 100%
|
||
```
|
||
|
||
**Optimal flexible fraction** (maximizes savings, no SLA violation):
|
||
```
|
||
F_optimal = min(F_available, T_shift_hours / 24)
|
||
```
|
||
For T_shift = 6h: F_optimal = 6/24 = 25%.
|
||
For T_shift = 8h: F_optimal = 8/24 = 33%.
|
||
"""),
|
||
})
|
||
return
|
||
|
||
|
||
# ─── LEDGER SAVE + HUD FOOTER (hide_code=True) ───────────────────────────────
|
||
@app.cell(hide_code=True)
|
||
def _(mo, ledger, COLORS,
|
||
context_toggle, efficiency_gain, deployment_scale,
|
||
_net_change_pct, _carbon_savings_pct, _target_met,
|
||
act1_pred, act1_reflect, act2_pred, act2_reflect,
|
||
_sla_violation_pct):
|
||
_ctx_val = context_toggle.value
|
||
_eff_val = efficiency_gain.value
|
||
_dep_val = deployment_scale.value
|
||
_nc_pct = float(_net_change_pct)
|
||
_sav_pct = float(_carbon_savings_pct)
|
||
_tgt = bool(_target_met)
|
||
_a1_pred = act1_pred.value or "none"
|
||
_a1_correct = (_a1_pred == "option_c")
|
||
_a2_result = _sav_pct
|
||
_a2_decision = (
|
||
f"flex={efficiency_gain.value:.1f}x_scale={deployment_scale.value:.1f}x"
|
||
)
|
||
_constraint = (_sla_violation_pct > 5.0)
|
||
|
||
ledger.save(
|
||
chapter="v2_15",
|
||
design={
|
||
"context": _ctx_val,
|
||
"efficiency_gain": _eff_val,
|
||
"deployment_scale": _dep_val,
|
||
"net_carbon_change_pct": _nc_pct,
|
||
"carbon_savings_pct": _sav_pct,
|
||
"target_met": _tgt,
|
||
"act1_prediction": _a1_pred,
|
||
"act1_correct": _a1_correct,
|
||
"act2_result": _a2_result,
|
||
"act2_decision": _a2_decision,
|
||
"constraint_hit": _constraint,
|
||
},
|
||
)
|
||
|
||
_c_ok = COLORS["GreenLine"]
|
||
_c_fail = COLORS["RedLine"]
|
||
_c_warn = COLORS["OrangeLine"]
|
||
_c_muted = COLORS["TextMuted"]
|
||
|
||
_tgt_color = _c_ok if _tgt else _c_fail
|
||
_nc_color = _c_ok if _nc_pct < 0 else _c_fail
|
||
_sla_color = _c_fail if _constraint else _c_ok
|
||
|
||
mo.Html(f"""
|
||
<div class="lab-hud" style="margin-top: 32px;">
|
||
<span>
|
||
<span class="hud-label">LAB</span>
|
||
<span class="hud-value">V2-15</span>
|
||
</span>
|
||
<span>
|
||
<span class="hud-label">CONTEXT</span>
|
||
<span class="hud-value">{_ctx_val.upper()}</span>
|
||
</span>
|
||
<span>
|
||
<span class="hud-label">EFF GAIN</span>
|
||
<span class="hud-value">{_eff_val:.1f}×</span>
|
||
</span>
|
||
<span>
|
||
<span class="hud-label">DEPLOY SCALE</span>
|
||
<span class="hud-value">{_dep_val:.1f}×</span>
|
||
</span>
|
||
<span>
|
||
<span class="hud-label">NET CARBON</span>
|
||
<span style="color: {_nc_color}; font-family: var(--font-mono);">
|
||
{_nc_pct:+.1f}%
|
||
</span>
|
||
</span>
|
||
<span>
|
||
<span class="hud-label">SCHED SAVINGS</span>
|
||
<span style="color: {_tgt_color}; font-family: var(--font-mono);">
|
||
{_sav_pct:.1f}%
|
||
</span>
|
||
</span>
|
||
<span>
|
||
<span class="hud-label">TARGET MET</span>
|
||
<span style="color: {_tgt_color}; font-family: var(--font-mono);">
|
||
{'YES' if _tgt else 'NO'}
|
||
</span>
|
||
</span>
|
||
<span>
|
||
<span class="hud-label">SLA</span>
|
||
<span style="color: {_sla_color}; font-family: var(--font-mono);">
|
||
{'BREACH' if _constraint else 'OK'}
|
||
</span>
|
||
</span>
|
||
<span>
|
||
<span class="hud-label">LEDGER</span>
|
||
<span class="hud-active">SAVED</span>
|
||
</span>
|
||
</div>
|
||
""")
|
||
return
|
||
|
||
|
||
# ─── KEY TAKEAWAYS (hide_code=True) ───────────────────────────────────────────
|
||
@app.cell(hide_code=True)
|
||
def _(mo):
|
||
mo.vstack([
|
||
mo.md("---"),
|
||
mo.md("""
|
||
## Key Takeaways
|
||
|
||
1. **Jevons Paradox governs total carbon, not efficiency gains alone.**
|
||
Making each unit of compute cheaper or more efficient increases demand,
|
||
and total carbon `C = E × I` grows when demand outpaces efficiency.
|
||
The H100 scenario: 2× efficiency gain × 3× deployment scale = 1.5× total
|
||
energy. The only mechanism that reduces absolute carbon is an enforced
|
||
carbon budget cap, not per-unit efficiency targets.
|
||
|
||
2. **Carbon-aware scheduling is a finite lever bounded by night-time capacity.**
|
||
Shifting flexible jobs from coal-heavy day grid (820 gCO₂/kWh) to renewable
|
||
night grid (40 gCO₂/kWh) can achieve 40%+ carbon reduction for a 30% flexible
|
||
workload — but only while the night window has capacity. When flexible fraction
|
||
exceeds `time_shift_hours / 24`, SLA violations begin. The binding constraint
|
||
is always the low-carbon capacity window, not the willingness to shift.
|
||
"""),
|
||
])
|
||
return
|
||
|
||
|
||
if __name__ == "__main__":
|
||
app.run()
|