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
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
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 X∈RL×C into seasonal/remainder ( Xs ) and trend ( Xt ) components, which are independently projected to the forecast horizon via linear layers Hs and Ht , then summed to produce the full multivariate forecast Y∈RH×C , from which the power channel y∈RH is extracted. Our physics-informed extension introduces three loss components: (1) Ldata : standard MSE loss with ground truth, (2) Lr : coupled RC thermal network residual enforcing consistency between predicted power and observed temperatures Tg , Tm , and (3) Lthrottle : utilization-based constraint encoding that high GPU/memory utilization should precede power reduction. The RC parameters for the aggregate GPU rack ( Cg=5.408×106J , Cm=5.481×106J , Rga=2.037×10−3K , Rma=2.055×10−3K , Rgm=6.064×10−4K , Ta=27∘C , α=0.5085 ) are pre-estimated via RLS using the training data and then are kept fixed for validation and testing.
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
∼ 330,500
Granularity
1 min
Duration
∼ 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=240min
T=360min
T=480min
T=600min
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∈{5,10,20,40,80}min for multivariate forecasting on MIT Supercloud under different history lengths ( T∈{240,360,480,600}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.
Figure 5: PI-DLinear forecasting results shown as heatmaps for input sequence length T∈{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 ( s )
Memory ( MB )
TiDE
1624359
29.10
6.210
FiLM
12923662
271.38
49.30
DLinear
96160
10.43
0.376
PI-DLinear
96160
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 λ
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 λ ), 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 Q˙ [W]
Current I [A]
Resistance
Thermal resistance Rth [K/W]
Electrical resistance R [ Ω ]
Capacitance
Thermal capacitance Cth [J/K]
Electrical capacitance C [F]
Source
Heat source P [W]
Current source I [A]
Appendix
Table 5: Thermal-Electrical Analogy
Figure 7: Equivalent RC thermal circuit for coupled GPU-Memory system. Current sources represent heat input from electrical power dissipation ( P split by factor α ). 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
Cg
GPU thermal capacitance
J/K
Heat required to raise GPU temp by 1K
Cm
Memory thermal capacitance
J/K
Heat required to raise memory temp by 1K
Rga
GPU-to-ambient resistance
K/W
Temp rise per watt dissipated to ambient
Rma
Memory-to-ambient resistance
K/W
Temp rise per watt dissipated to ambient
Rgm
GPU-memory coupling resistance
K/W
Thermal coupling strength between components
Ta
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
Δ (pp)
DLinear
PI-DLinear
Δ (%)
DLinear
PI-DLinear
Δ (%)
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. Δ 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.
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=240min , the y-axis denotes the forecast step (0,...,T) up to T=5min , and the colors encode the signed weight magnitude, indicating whether each lag contributes positively or negatively to the forecast.
Time series forecasting predicts future values from ordered observations using statistical, neural, and probabilistic models to support decisions under uncertainty.
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Philip Colangelo, Charles Dawson, Shayan Sengupta +2
Large Language Model (LLM) inference workloads are a rapidly growing contributor to data center energy consumption. Optimizing these deployments requires matching specific LLMs to the most efficient GPUs, but operators currently lack the tools to do so without exhaustively profiling each combination. While some predictive models exist, they still require profiling data and struggle to generalize to hardware unseen during training. To address this, we introduce WattGPU, featuring two predictive models for mean GPU power draw and Inter-Token Latency (ITL). Our approach leverages only publicly available LLM metadata and GPU specifications, eliminating the need for hardware access or profiling while enabling generalization to unseen NVIDIA server-grade GPUs and LLMs. We evaluate our models using rigorous leave-one-GPU-out and leave-one-LLM-out cross-validation on a dataset of 42 open-source LLMs (0.1B--27B parameters) and 8 GPUs under both offline and server scenarios. The mean power draw model achieves a median absolute percentage error of ≤3.4% for offline and ≤13.5% for server scenarios on unseen GPUs, while the latency model achieves ≤8.5% in server mode, both maintaining strong GPU ranking correlations for server scenarios (Kendall τ≥0.76). Compared to standard physically grounded baselines -- Load-Scaled Thermal Design Power (TDP) for power draw and roofline for latency -- our models reduce median absolute percentage error by approximately 4× on unseen LLM-GPU combinations for server scenarios or approximately 2× for completely unseen GPUs. WattGPU's data and code are publicly available at https://github.com/maufadel/wattgpu.
Mauricio Fadel Argerich, Jonathan Fürst, Marta Patiño-Martínez
Universidad Politécnica de Madrid, C. de los Ciruelos, 28660 Boadilla del Monte, Madrid, Spain · Zurich University of Applied Sciences, Gertrudstrasse 15, 8400 Winterthur, Switzerland