A Configurable Thermal-Dynamic Model for AI Data Center Cooling Load Simulation

Chee-Wooi Ten; Cletus Ngwerume; Lang Tong; Yi Hu

REVIEW 3 major objections 5 minor 10 references

A configurable RC-network model simulates hybrid data center cooling electricity demand, reducing mean absolute error from 95.80 to 20.88 kW on Marconi100 telemetry versus a constant-COP baseline.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review

2026-08-03 16:24 UTC pith:RBX5KQMX

load-bearing objection Plausible RC/deadband model for simulating data-center cooling load, but the validation is in-sample only and one key term is undefined. the 3 major comments →

arxiv 2607.28962 v1 pith:RBX5KQMX submitted 2026-07-31 eess.SY cs.SYeess.SP

A Configurable Thermal-Dynamic Model for AI Data Center Cooling Load Simulation

Cletus Ngwerume , Lang Tong , Chee-Wooi Ten , Yi Hu This is my paper

classification eess.SY cs.SYeess.SP

keywords AI data centercooling load simulationhybrid coolingRC thermal networkdeadband controlcoefficient of performanceMarconi100demand flexibility

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tries to establish that cooling electricity consumption in modern AI data centers, which mix air and liquid cooling, can be simulated as the output of a small thermal-dynamic system rather than as a fixed fraction of computing power. The proposed model tracks four temperatures — rack, room air, thermal mass, and liquid coolant — through a network of thermal resistances and capacitances, and switches air and liquid cooling loads on and off with deadband controllers. Validated on telemetry from the Marconi100 supercomputer, the model reduces mean absolute error from 95.80 kW to 20.88 kW and root-mean-square error from 109.79 kW to 27.27 kW relative to a constant coefficient-of-performance baseline. A sympathetic reader would care because this makes long-horizon power system studies of AI data centers feasible without fabricating cooling dynamics.

Core claim

On the paper's own terms, the central discovery is that the time-varying electricity consumed by a hybrid air/liquid data center cooling plant can be reproduced by a four-state RC thermal network plus a single heat-rejection node, driven by IT heat and ambient temperature, with simple hysteresis (deadband) controllers for the air and liquid loops. When configured for Marconi100, this model tracks measured cooling power far more closely than a constant-COP estimate, captures the observed weak correlation between IT power and cooling power, and reproduces the daily peak and variability statistics over roughly 520 daily profiles. The authors present the model as a configurable tool for generati

What carries the argument

The central object is a four-state RC thermal network (thermal resistances and capacitances) with state vector (T_rack, T_air, T_mass, T_liq) representing rack, room air, building thermal mass, and liquid coolant temperatures, plus a fifth node for the liquid-heat-rejection loop. The state equations are discretized at 1-second resolution; a deadband (hysteresis) controller holds the air and liquid cooling units at their previous on/off state until the relevant temperature crosses a setpoint band. This mechanism lets cooling load stay flat while temperatures drift inside the deadbands, which is what constant-COP models cannot represent.

Load-bearing premise

The load-bearing assumption is that parameters manually calibrated on one dataset (Marconi100) and validated on the same dataset give a fair estimate of predictive skill; if the fit has overfit this facility and time window, the reported error reductions will not transfer to other data centers.

What would settle it

Run the published model on measured telemetry from a different hybrid-cooled AI data center without retuning, with an optimized constant-COP baseline for comparison; if the RC model's MAE does not beat the baseline by a large margin, the claim of broad configurable accuracy collapses.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

Power system planners can generate long-duration (year-scale) cooling load profiles for proposed AI data centers without equipment-level simulation, using only IT power and ambient temperature as inputs.
Cooling load flexibility estimates — the amount of load that can be shifted while respecting temperature deadbands — become computable from the same state-space model.
The model's physical interpretability (capacitances, resistances, setpoints) gives engineers a way to reason about how design choices change cooling demand.
Public availability of the implementation and sample data lets other researchers reproduce the reported errors on Marconi100 and adapt the model to other facilities.
The demonstrated correlation statistics suggest the model can reproduce the decoupling between IT load and cooling load that constant-COP models miss.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The reported calibration was done manually on the same Marconi100 data used for evaluation, so the accuracy numbers likely reflect an upper bound; a proper held-out test or an automatic parameter-estimation procedure would be needed to certify the model's portability to other facilities.
Because the model outputs cooling power at 1-second resolution and can be driven by forecast IT and weather traces, it could be embedded in optimal scheduling or demand-response simulations to quantify how much cooling load can be deferred without violating temperature constraints.
The deadband widths and setpoints could be turned into tunable flexibility parameters, letting grid operators ask 'how much headroom does this facility have for load shifting at 3 p.m.?' without access to proprietary building management data.
The same state-space structure could be extended with a model for server fan power or PUE variations, using the rack temperature state as a proxy for computing thermal state.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

Plausible RC/deadband model for simulating data-center cooling load, but the validation is in-sample only and one key term is undefined.

read the letter

The core idea here is sensible: build a configurable RC thermal network with deadband-controlled cooling equipment, and use it to generate dynamic cooling-electricity profiles for power-system studies. That is a real gap, because time-synchronized cooling measurements are rare and constant-COP models miss the thermal inertia that matters for grid flexibility. The authors add a heat-rejection node to the standard four-state RC framework, which is a legitimate extension, and they release code and sample data, which is good practice.

The evaluation on Marconi100 telemetry shows the model tracking daily peaks and variability much better than a constant-COP baseline. But the validation is in-sample. Section II.B says the RC parameters, setpoints, deadbands, and initial states were "manually calibrated and iteratively adjusted" on the M100 data, and Section III.A says the baseline COP was also selected by minimizing RMSE on the same reference. No held-out period, no cross-validation, no second facility. With four capacitances, five resistances, both deadbands, both setpoints, rated powers, and initial states, the model has plenty of flexibility to fit one facility's history. The reported MAE drop from 95.8 to 20.9 kW is exactly what you'd expect from a flexible model tuned on the test set. It is not yet evidence that the "configurable" model transfers to other facilities or time periods.

There is also a concrete specification gap: Algorithm 1 step 11 says "Compute Qliq(k)" and Eq. (7) depends on it, but Qliq is never defined in the text or equations. That blocks reproduction independently of the code release. The authors mention parameter estimation as future work, which is really the missing piece for making this a generalizable tool.

For all that, the modeling approach is physically reasonable, the paper is clearly written, and the authors are transparent about the manual calibration. It deserves a serious referee, but the referee should insist on a held-out evaluation and a complete definition of Qliq before the validation claims are accepted. If those are added, this becomes a useful contribution to the data-center load-modeling literature.

I'd bring it to a reading group as a useful example of how to think about thermal dynamics in grid studies, but I wouldn't cite it yet for its numbers.

Referee Report

3 major / 5 minor

Summary. The paper proposes a state-space thermal-dynamic model of a hybrid air/liquid-cooled AI data center, combining a four-state RC network for rack, air, mass, and coolant temperatures, a one-state heat-rejection node, and deadband-based on/off control to generate cooling electricity load profiles. The model is intended as a configurable, physically interpretable tool for long-duration power system studies. Validation against Marconi100 telemetry reports a reduction in MAE from 95.80 to 20.88 kW and in RMSE from 109.79 to 27.27 kW compared with a constant-COP baseline, together with improved reproduction of daily peak and variability statistics. Source code and sample data are released publicly.

Significance. If the reported performance were demonstrated out of sample, the paper would contribute a useful, computationally tractable alternative to constant-COP approximations for AI data center cooling load simulation. The public release of source code and sample data is commendable and supports reproducibility. However, the current evidence does not establish generalizability: the model parameters are manually tuned on the same facility/time series used for evaluation, the baseline is also optimized on the same reference, and key parts of the model specification (Qliq, Q_rej) are missing. These issues must be addressed before the central 'validated' claim can be accepted.

major comments (3)

[§II.B, §III.A, Table I] The validation is in-sample. Parameters are 'manually calibrated and iteratively adjusted' on the M100 data, and the constant-COP baseline is selected by minimizing RMSE on the same measured reference; Table I and Fig. 3 then report errors on that same reference. With dozens of free parameters (C1–C5, R1–R6, setpoints, deadband widths, rated capacities, initial states), the reported reductions (MAE 95.80→20.88 kW, RMSE 109.79→27.27 kW) may reflect fitting rather than predictive skill. A held-out period, cross-validation over days, or a second facility is needed to support the claim of validation, or the results must be explicitly reframed as in-sample reproduction.
[Algorithm 1, Eq. (7)] The model is not fully specified. Algorithm 1 step 11 says 'Compute Qliq(k)', but no formula for Qliq is given anywhere in the text or equations. Equation (7) depends on Qliq, so without this definition the simulation cannot be reproduced or adapted to another facility. Similarly, Q_rej appears in Eq. (7) and is said to be introduced later, but Algorithm 1 only computes P_liq from the binary deadband state; the coupling between Q_rej, the deadband control, and P_liq is absent. Please add the missing equations and make the control-to-thermal coupling explicit.
[§II.B, §IV] The paper calls the model 'configurable' for other facilities, but no parameter-estimation or calibration procedure is provided. The only calibration described is manual, iterative adjustment within physically reasonable ranges, and parameter estimation is left to future work in the Conclusion. No identifiability or sensitivity analysis is given. A user cannot adapt the model to a new facility without significant ad hoc tuning. At minimum, the authors should provide a concrete calibration recipe (e.g., a least-squares or grid-search procedure) and assess how sensitive the simulated load profiles are to parameter values.

minor comments (5)

[I] Typo: 'presents the a configurable' should be 'presents a configurable'.
[II.A] The notation in Eqs. (2)–(3) has missing spaces (e.g., 'T rack,T air'), and matrices in Eq. (4) are typeset without visible bracket separators. Please fix the formatting for readability.
[III.B] Figure citations are inconsistent: 'Figure 3 (a)' vs. 'Fig. 3(a)'. Use one style.
[Table I] The baseline correlation Corr(Q_IT, P_cool) = 1.0 follows by construction from P_cool = Q_IT / COP; consider noting this explicitly to avoid implying an empirical correlation.
[III.C] The paper says 'approximately 520 daily profiles' but does not state how many of these days, if any, were used during the manual calibration. Please clarify whether the statistical comparison is on the same period used for tuning.

Circularity Check

2 steps flagged

In-sample validation: RC parameters are manually calibrated on Marconi100 data and then evaluated on that same reference, while the baseline COP is also RMSE-optimized on the same reference; the reported error reductions quantify fit, not out-of-sample prediction.

specific steps

fitted input called prediction [Sec. II.B (Parameter Calibration) and Sec. III.A-B (Simulation Setup / One-on-One Evaluation)]
"The parameters of the proposed model, including the equivalent thermal resistances and capacitances, setpoints and deadbands, and initial thermal states, are unavailable in the M100 dataset [5] and are manually calibrated and iteratively adjusted within physically reasonable ranges. ... The proposed model and the optimized baseline are then evaluated against the same measured reference."

The model parameters are tuned directly to the Marconi100 measured cooling load, and the validation in Table I and Fig. 3 is computed on that same reference. No held-out period, cross-validation, or second-facility test is described. The reported error reduction from 95.80 to 20.88 kW MAE therefore reflects in-sample calibration quality, not an independent predictive test. The RC structure is not mathematically forced to equal the measured output, so this is partial circularity rather than definitional identity.
fitted input called prediction [Sec. III.A (Simulation Setup and Baseline Selection)]
"The value COP = 2.650 is selected by minimizing the RMSE between the estimation and measurement. The proposed model and the optimized baseline are then evaluated against the same measured reference."

The baseline itself is fitted to the same reference used for evaluation. Because the baseline COP is optimized in-sample, the comparison between the proposed model and the baseline is an in-sample model-selection exercise: both the calibrated RC parameters and the baseline COP are chosen to minimize error on the same data that later supplies the validation metrics. Thus the reported comparative improvements are not evidence of generalization to unseen conditions.

full rationale

The model derivation itself is not circular: the four-state RC network, heat-rejection node, and deadband controller are physically structured and not mathematically equivalent to the measured cooling power, and the released code and data permit external benchmarking. The circularity is in the validation procedure. Section II.B states that all RC parameters, setpoints, deadbands, and initial states are 'manually calibrated and iteratively adjusted' on the M100 data, and Section III.A states that the baseline COP=2.650 is 'selected by minimizing the RMSE between the estimation and measurement' and that both models are then 'evaluated against the same measured reference.' Consequently, the MAE/RMSE reductions in Table I are in-sample fit errors rather than out-of-sample predictions. The paper also defers automatic parameter estimation to future work ('Future work will address extreme operating conditions and parameter estimation'), which reinforces that the current validation depends on manual tuning to the test facility. Separately, Algorithm 1 step 11 instructs 'Compute Qliq(k)' but Qliq is never defined, and Eq. (7) depends on it; this is a reproducibility defect rather than a circular reduction, but it strengthens the need for a held-out evaluation and a complete model specification. There are no load-bearing self-citations. Overall, the central claim of superior dynamic reproduction is partially circular: the reported numbers are better interpreted as calibrated model fit on the Marconi100 dataset, not as independent predictive validation.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 0 invented entities

The model rests on a conventional lumped RC representation; the main burden is a set of manually calibrated parameters and the untested assumption that the fitted structure generalizes. No new physical entities are required.

free parameters (6)

RC parameters C1-C5, R1-R6 = not reported in paper (in repository)
Manually calibrated and iteratively adjusted within physically reasonable ranges (Sec. II.B); these determine thermal dynamics and therefore the simulated cooling power.
Air setpoint and deadband (T_set_air, ΔT_db_air) = not reported in paper
Deadband controller on/off thresholds; manually configured (Sec. II.B, Algorithm 1).
Rejection setpoint and deadband (T_set_rej, ΔT_db_rej) = not reported in paper
Same manual calibration; controls liquid-side on/off.
Rated cooling powers P_rated_air, P_rated_liq = not reported in paper
Convert on/off states to electricity consumption (Algorithm 1 lines 19-20); likely set from facility characteristics.
Initial states x(1), T_rej(1), d_air(1), d_rej(1) = not reported
Chosen/initialized; affects transient of simulated profile.
Baseline COP = 2.650
Selected by minimizing RMSE between baseline and measured cooling power on the evaluation dataset (Sec. III.A).

axioms (6)

domain assumption Four-node RC network with constant parameters is sufficient to represent hybrid air/liquid data center thermal dynamics
Central modeling premise; Sec. II.A.
domain assumption Linear superposition of heat flows and constant capacitances/resistances
Underlies the state-space model in Sec. II.A; ignores nonlinear/non-stationary effects.
domain assumption Cooling electricity equals rated power times on/off state; no part-load efficiency or fan/pump speed variation
Algorithm 1 lines 19-20; if real cooling load modulates continuously, simulated profile shape and errors change.
domain assumption Deadband thermostat control approximates actual cooling controller behavior
Algorithm 1 implements hysteresis switching; real supervisory controllers may be more complex.
domain assumption Measured cooling power in M100 dataset is accurate ground truth and corresponds to modeled P_cool = P_air + P_liq
Used for all error calculations in Sec. III; no discussion of measurement error.
standard math Euler integration with 1-s step adequately solves the ODE system
The simulation uses explicit Euler updates (Algorithm 1 lines 4 and 12); stability and accuracy are not discussed.

reviewed 2026-08-03 · how reviews work

0 comments

Cite this review

Pith. "Pith review of A Configurable Thermal-Dynamic Model for AI Data Center Cooling Load Simulation." pith.science (2026). https://pith.science/paper/RBX5KQMX

@misc{pith2026260728962,
  author       = {Pith},
  title        = {Pith review of: A Configurable Thermal-Dynamic Model for AI Data Center Cooling Load Simulation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RBX5KQMX}},
  note         = {Machine review of arXiv:2607.28962}
}

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read the original abstract

Cooling demand constitutes a significant and flexible component of AI data center electricity consumption, but time-synchronized measurements are scarce and constant coefficient-of-performance models cannot represent thermal dynamics. This letter proposes a configurable thermal dynamic simulation model for hybrid air- and liquid-cooled data centers. Unlike existing models centered on temperature prediction or equipment-level cooling analysis, the proposed model is designed to generate dynamic cooling electricity profiles for long-duration power system studies. The model is validated using operational telemetry from the Marconi100 supercomputer. Compared with the baseline, the proposed model reduces the mean absolute error from 95.80 to 20.88~kW and the root-mean-square error from 109.79 to 27.27~kW. Evaluation over approximately 520 daily profiles further shows improved reproduction of daily peak demand and intraday variability. The proposed model provides a computationally tractable means of generating physically interpretable cooling load profiles for power system studies.

Figures

Figures reproduced from arXiv: 2607.28962 by Chee-Wooi Ten, Cletus Ngwerume, Lang Tong, Yi Hu.

**Figure 3.** Figure 3: Model validation: (a) measured, simulated, and baseline weekly profiles; (b) daily mean vs. peak and (c) daily mean vs. std over [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

discussion (0)

Reference graph

Works this paper leans on

10 extracted references · 1 linked inside Pith

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arXiv preprint arXiv:2509.07218 , year=

Electricity demand and grid impacts of AI data centers: Challenges and prospects , author=. arXiv preprint arXiv:2509.07218 , year=

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This paper was first reviewed by deepseek-v4-flash on August 3, 2026.

[1] [1]

arXiv preprint arXiv:2509.07218 , year=

Electricity demand and grid impacts of AI data centers: Challenges and prospects , author=. arXiv preprint arXiv:2509.07218 , year=

Pith/arXiv arXiv

[2] [2]

Applied energy , volume=

A Review on efficient thermal management of air-and liquid-cooled data centers: From chip to the cooling system , author=. Applied energy , volume=. 2017 , publisher=

2017

[3] [3]

Journal of Physics: Conference Series , volume=

Immersion cooling as the next technology for data center cooling: A review , author=. Journal of Physics: Conference Series , volume=. 2019 , organization=

2019

[4] [4]

IEEE Transactions on Smart Grid , volume=

An evaluation of the HVAC load potential for providing load balancing service , author=. IEEE Transactions on Smart Grid , volume=. 2012 , publisher=

2012

[5] [5]

Scientific Data , volume=

M100 exadata: a data collection campaign on the cineca’s marconi100 tier-0 supercomputer , author=. Scientific Data , volume=. 2023 , publisher=

2023

[6] [6]

arXiv 2025 , author=

Waste-to-Energy-Coupled AI Data Centers: Cooling Efficiency and Grid Resilience. arXiv 2025 , author=

2025

[7] [7]

Energy , pages=

Modeling and performance analysis of a novel air-liquid hybrid cooling system for high-power containerized AI data centers , author=. Energy , pages=. 2026 , publisher=

2026

[8] [8]

International Journal of Refrigeration , year=

System design, control strategy development and performance comparison analysis for a novel air-liquid hybrid data center cooling system based on cold plates , author=. International Journal of Refrigeration , year=

[9] [9]

Journal of Building Engineering , volume=

Performance optimization of an air source HVAC system for an internet data center building using the integrated COP method , author=. Journal of Building Engineering , volume=. 2022 , publisher=

2022

[10] [10]

Journal of Building Engineering , volume=

Real-time temperature predictions via state-space model and parameters identification within rack-based cooling data centers , author=. Journal of Building Engineering , volume=. 2022 , publisher=

2022

A Configurable Thermal-Dynamic Model for AI Data Center Cooling Load Simulation

Core claim §

What carries the argument

Load-bearing premise §

What would settle it §

If this is right

Where Pith is reading between the lines

discussion (0)

Core claim

Load-bearing premise

What would settle it