A Physics-Aware Framework for Short-Term GPU Power Forecasting of AI Data Centers

Mohammad AlShaikh Saleh; Sanjay Chawla; Sertac Bayhan; Haitham Abu-Rub; Ali Ghrayeb

cs.LGApr 14, 2026

A Physics-Aware Framework for Short-Term GPU Power Forecasting of AI Data Centers

Authors: Mohammad AlShaikh Saleh, Sanjay Chawla, Sertac Bayhan, Haitham Abu-Rub, Ali Ghrayeb

Organizations: College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar · Qatar Computing Research Institute, Hamad Bin Khalifa University, Doha, Qatar · Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, Doha, Qatar · Department of Electrical & Electronic Engineering, Gazi University, Ankara, Turkey

Abstract

AI data centers experience rapid fluctuations in power demand due to the heterogeneity of computational tasks that they have to support. For example, the power profile of inference and training of large language models (LLMs) is quite distinct and big divergences can result in the instability of the underlying electricity grid. In this paper we propose, to the best of our knowledge, the first physics-informed DLinear time-series model that can accurately forecast power utilization of an AI data center 5-80 minutes (short-term forecasting) into the future. The physics, based on a multi-node lumped thermal resistance-capacitance (RC) network consistent with Newton's law of cooling, is captured using newly derived time-dependent ordinary differential equations (ODE) that separately models and interlinks power consumption with the GPU compute and memory utilization and temperature. The resulting model, that we refer to as PI-DLinear, trained and evaluated on a real AI data center dataset and is not only more accurate than the state-of-the-art (SOTA) models tested, but the forecast profile respects the underlying physics under power throttling and load transient events. Relative to the SOTA transformer-based and non-transformer-based models, improvements in forecasting accuracy (averaged across all look-back and prediction windows) range from 0.782%-39.08% for MSE, 0.993%-51.82% for MAE, and 0.370%-22.28% for RMSE.

Figures & tables

Panel of Figure 1 — Figure 1: Comparison of DLinear and PI-DLinear across power throttling, transient recovery, and post-event stability regimes. PI-DLinear consistently achieves lower prediction error, enabling accurate throttling characterization, faster recovery from sudden AI load changes, and stable forecasting behavior.

Figure 2: PI-DLinear Architecture. The base DLinear model (top) decomposes the input look-back window $\mathbf{X}\in\mathbb{R}^{L\times C}$ into seasonal/remainder ( $\mathbf{X}_{s}$ ) and trend ( $\mathbf{X}_{t}$ ) components, which are independently projected to the forecast horizon via linear layers $\mathbf{H}_{s}$ and $\mathbf{H}_{t}$ , then summed to produce the full multivariate forecast $\widehat{\mathbf{Y}}\in\mathbb{R}^{H\times C}$ , from which the power channel $\widehat{\mathbf{y}}\in\mathbb{R}^{H}$ is extracted. Our physics-informed extension introduces three loss components: (1) $\mathcal{L}_{\text{data}}$ : standard MSE loss with ground truth, (2) $\mathcal{L}_{r}$ : coupled RC thermal network residual enforcing consistency between predicted power and observed temperatures $T^{g}$ , $T^{m}$ , and (3) $\mathcal{L}_{\text{throttle}}$ : utilization-based constraint encoding that high GPU/memory utilization should precede power reduction. The RC parameters for the aggregate GPU rack ( $C_{g}=5.408\times 10^{6}$ $\mathrm{J}$ , $C_{m}=5.481\times 10^{6}$ $\mathrm{J}$ , $R_{ga}=2.037\times 10^{-3}$ $\mathrm{K}$ , $R_{ma}=2.055\times 10^{-3}$ $\mathrm{K}$ , $R_{gm}=6.064\times 10^{-4}$ $\mathrm{K}$ , $T_{a}=27^{\circ}$ $\mathrm{C}$ , $\alpha=0.5085$ ) are pre-estimated via RLS using the training data and then are kept fixed for validation and testing.

Panel of Figure 3 — Figure 3: Relationships observed in the MIT Supercloud dataset: power vs. utilization (left), power vs. temperature (right), and temperature vs. utilization (bottom). Lighter regions indicate higher count, and darker regions indicate lower count.

Attribute	MIT Supercloud GPU Trace
Co-variates	7 (GPU utilization, memory utilization, free memory, used memory, GPU temperature, memory temperature, power draw)
# Timesteps	$\sim$ 330,500
Granularity	1 $\mathrm{min}$
Duration	$\sim$ 238 days

Table 1: Summary of the MIT Superclouddataset used in this study.

Figure 4: Computational job distribution across the AI workloads present in the MIT Supercloud dataset, namely, vision networks, large language models (LLMs), and graph neural networks (GNNs).

	$T=240$ $\mathrm{min}$				$T=360$ $\mathrm{min}$				$T=480$ $\mathrm{min}$				$T=600$ $\mathrm{min}$
Model	MAE	MSE	MAPE	RMSE	MAE	MSE	MAPE	RMSE	MAE	MSE	MAPE	RMSE	MAE	MSE	MAPE	RMSE
iTransformer	$0.1481$	$0.1636$	$1.1323$	$0.4000$	$0.1527$	$0.1665$	$1.1603$	$0.4039$	$0.1533$	$0.1694$	$1.1537$	$0.4071$	$0.1555$	$0.1708$	$1.2052$	$0.4087$
Transformer	$0.1670$	$0.1722$	$1.2211$	$0.4095$	$0.1726$	$0.1674$	$1.4009$	$0.4058$	$0.1754$	$0.1727$	$1.3291$	$0.4115$	$0.1785$	$0.1747$	$1.3318$	$0.4140$
TimeXer	$0.1474$	$0.1580$	$1.1021$	$0.3941$	$0.1631$	$0.1664$	$1.2364$	$0.4053$	$0.1511$	$0.1637$	$1.1139$	$0.4014$	$0.1636$	$0.1674$	$1.2195$	$0.4065$
TiDE	0.1422	$0.1561$	$1.0628$	$0.3912$	$0.1436$	$0.1578$	$1.0743$	$0.3933$	$0.1441$	$0.1585$	$1.0708$	$0.3943$	$0.1451$	$0.1584$	$1.0860$	$0.3941$
TSMixer	$0.1507$	$0.1605$	$1.0999$	$0.3968$	$0.1547$	$0.1654$	$1.1798$	$0.4030$	$0.1549$	$0.1657$	$1.1491$	$0.4036$	$0.1640$	$0.1697$	$1.2085$	$0.4082$

Table 2: Average performance across prediction horizons

L\in\{5,10,20,40,80\}

\mathrm{min}

for multivariate forecasting on MIT Supercloud under different history lengths (

T\in\{240,360,480,600\}

\mathrm{min}

) for the proposed and baseline models. It is apparent that the proposed PI-DLinear model not only outperforms the baseline models in terms of performance, but it (the error values) is relatively stable as the sequence length increases (see Fig. 5 ) as well, a feature that is crucial when deploying such a model in data center control units, where multi-scaling and model flexibility is required at any given history and time step. The models were tested with 5 seeds, yet the standard deviation across runs for all models was negligible.

Panel of Figure 5 — Figure 5: PI-DLinear forecasting results shown as heatmaps for input sequence length $T\in\{240,360,480,600\}\,$ \mathrm{min} $and prediction length $L\in\{5,10,20,40,80\}\,$\mathrm{min}$ . PI-DLinear prediction error is stable for different sequence lengths and a shorter prediction horizon is more accurate than longer prediction horizons.

Figure 6: Bubble chart showing model efficiency comparison under input-240-predict-80 for the top 4 models. PI-Dlinear has the lowest MSE error with a computational time slightly higher than baseline DLinear. GPU model used: NVIDIA GeForce RTX 4080, CUDA version: 12.9. The model size was obtained from the checkpoint MB saved on disk.

Model	#Params	Time ( $\mathrm{s}$ )	Memory ( $\mathrm{MB}$ )
TiDE	$1\,624\,359$	$29.10$	$6.210$
FiLM	$12\,923\,662$	$271.38$	$49.30$
DLinear	$96\,160$	$10.43$	$0.376$
PI-DLinear	$96\,160$	$20.27$	$0.376$

Table 3: Model complexity and inference efficiency for a single forward pass, reported in terms of parameter count, runtime (seconds), and peak memory usage (MB).

	Horizon 5		Horizon 10		Horizon 20		Horizon 40		Horizon 80
Model	MAPE	MSE	MAPE	MSE	MAPE	MSE	MAPE	MSE	MAPE	MSE
Derived ODE Solution	$0.7409$	$0.1002$	$0.8420$	$0.1233$	$0.9574$	$0.1525$	$1.1963$	0.1886	$1.5252$	0.2150
DLinear	$0.7331$	$0.0994$	$0.8422$	$0.1236$	$0.9606$	$0.1531$	$1.1951$	$0.1897$	$1.5250$	$0.2172$
PI-DLinear + Constant $\lambda$	0.7317	0.0993	0.8407	0.1234	0.9561	0.1527	1.1939	$0.1893$	1.5088	0.2165
Self-Adaptive PI-DLinear	0.7309	0.0992	0.8377	0.1232	0.9554	0.1526	1.1780	0.1886	1.4987	0.2155

Table 4: Ablation study across the investigated forecasting horizons for multivariate power forecasting of AI data centers. We report MAPE and MSE (lower is better) for DLinear, PI-DLinear (fixed

\lambda

), and self-adaptive PI-DLinear.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Quantity	Thermal Domain	Electrical Domain
Potential (Across variable)	Temperature $T$ [K]	Voltage $V$ [V]
Flow (Through variable)	Heat flow $\dot{Q}$ [W]	Current $I$ [A]
Resistance	Thermal resistance $R_{th}$ [K/W]	Electrical resistance $R$ [ $\Omega$ ]
Capacitance	Thermal capacitance $C_{th}$ [J/K]	Electrical capacitance $C$ [F]
Source	Heat source $P$ [W]	Current source $I$ [A]

Appendix

Table 5: Thermal-Electrical Analogy

Panel of Figure 7 — Figure 7: Equivalent RC thermal circuit for coupled GPU-Memory system. Current sources represent heat input from electrical power dissipation ( $P$ split by factor $\alpha$ ). Capacitors represent thermal mass (ability to store thermal energy). Resistors represent thermal resistance to heat flow. Applying Kirchhoff’s Current Law at each node yields the governing ODEs.

Symbol	Name	Units	Physical Meaning
$C_{g}$	GPU thermal capacitance	J/K	Heat required to raise GPU temp by 1K
$C_{m}$	Memory thermal capacitance	J/K	Heat required to raise memory temp by 1K
$R_{ga}$	GPU-to-ambient resistance	K/W	Temp rise per watt dissipated to ambient
$R_{ma}$	Memory-to-ambient resistance	K/W	Temp rise per watt dissipated to ambient
$R_{gm}$	GPU-memory coupling resistance	K/W	Thermal coupling strength between components
$T_{a}$	Ambient temperature	K	Reference/environment temperature

Appendix

Table 6: Physical interpretation of RC thermal network parameters

		Detection Rate (%)			Throttle MAE			Throttle RMSE
$L$	$T$	DLinear	PI-DLinear	$\Delta$ (pp)	DLinear	PI-DLinear	$\Delta$ (%)	DLinear	PI-DLinear	$\Delta$ (%)
240	5	61.92	44.35	-17.57	0.1106	0.1221	-10.39	0.1721	0.2734	-58.85
240	10	65.45	71.52	+6.06	0.1455	0.1398	+3.92	0.3177	0.2925	+7.94
240	20	62.92	76.47	+13.55	0.1638	0.1635	+0.17	0.3790	0.3725	+1.70
240	40	63.85	74.41	+10.56	0.2051	0.2058	-0.36	0.4993	0.5187	-3.89
240	80	68.70	87.54	+18.85	0.2290	0.2358	-2.96	0.5279	0.5233	+0.88

Appendix

Table 7: Throttle Detection Performance. Comparison of DLinear (baseline) and PI-DLinear across different sequence lengths (

L

) and prediction horizons (

T

). Detection Rate measures the percentage of true throttle events identified. Throttle MAE and RMSE measure prediction accuracy specifically at throttle event timesteps. Bold indicates better performance.

\Delta

columns show improvement of PI-DLinear over DLinear.

		Det. Rate (%)		Thr. MAE		Thr. RMSE
$L$	$T$	DL	PI	DL	PI	DL	PI
240	5	61.9	44.4	0.111	0.122	0.172	0.273
240	10	65.5	71.5	0.146	0.140	0.318	0.293
240	20	62.9	76.5	0.164	0.164	0.379	0.373
240	40	63.9	74.4	0.205	0.206	0.499	0.519
240	80	68.7	87.5	0.229	0.236	0.528	0.523

Appendix

Table 8: Throttle Detection Performance. Detection Rate (%), Throttle MAE, and Throttle RMSE for DLinear (DL) and PI-DLinear (PI). Bold indicates better performance.

Panel of Figure 8 — Figure 8: Learned linear projection weights of PI-DLinear over the look-back window for each forecast step. The x-axis denotes the look-back index $(0,...,L-1)$ up to $L=240$ $\mathrm{min}$ , the y-axis denotes the forecast step $(0,...,T)$ up to $T=5$ $\mathrm{min}$ , and the colors encode the signed weight magnitude, indicating whether each lag contributes positively or negatively to the forecast.

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AI-driven Thermal-aware Data Center Capacity Planning

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The emerging of large language models (LLMs) has posed significant challenges to the thermal management of data center. Intense GPU computation for LLMs results in localized hotspots. Moreover, spiking thermal loads during training and inference bursts make real-time cooling response more difficult to predict and control. Thermal-aware capacity planning of data center requires massive expensive high-fidelity CFD simulations. AI models can perform real-time prediction for unseen designs. However, existing works either have large prediction error, or have over-simplified assumptions for data center operations. This work presents an AI-driven framework that can perform thermal-aware capacity planning for a real-world data center in seconds. The embedded AI model learns from numerous key parameters (rack power, server power, server placement, HVAC settings etc.), and provides temperature prediction within milliseconds. This AI model is tested against high-fidelity CFD simulations, and results show that for unseen data center designs, model can achieve high accuracy with 10000X speedup. Driven by the AI model, the authors design the thermal-aware capacity planning framework. This framework can help data center designers and operators instantaneously optimize both workload distribution and HVAC cooling efficiency.

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