A newly published investigation into data center thermal modeling demonstrates that deep neural architectures rely predominantly on immediate residual history when predicting server temperatures under changing operating workloads. Conducted by researcher Safaa Hriez and detailed in Frontiers in Big Data, the study established an explainable artificial intelligence framework to probe the internal decision-making process of a hybrid SARIMAX-GRU forecasting model. Modern facilities dedicated to artificial intelligence calculations, cloud platforms, and large-scale digital services encounter heavy energy overheads, with dedicated cooling infrastructure representing a substantial proportion of aggregate electricity consumption. Although integrating statistical models with recurrent neural networks provides accurate temperature forecasts that can support proactive cooling strategies, such deep learning architectures frequently operate as opaque systems. By deploying four distinct explainability methods across diverse thermal conditions, the research confirms that predictions are governed by short-term thermal dependencies rather than arbitrary mathematical artifacts.
The underlying prediction framework evaluated in this work builds upon a previously designed hybrid SARIMAX-GRU pipeline created to anticipate server temperature variations across diverse operating conditions. In this two-stage forecasting structure, a Seasonal Autoregressive Integrated Moving Average with Exogenous Regressors model, configured with orders of one autoregressive term, one difference step, and three moving average terms, first calculates baseline linear temporal projections while incorporating exogenous data from a secondary thermal sensor. The residual discrepancies remaining between the measured temperature values and the initial SARIMAX forecasts are subsequently extracted and supplied to a Gated Recurrent Unit network. This neural component, constructed with a single recurrent layer containing thirty-two hidden units followed by a dense output layer, is trained with the Adam optimizer at a learning rate of 0.001 using mean squared error loss to capture nonlinear dependencies that linear statistical formulas cannot identify. Combining the baseline statistical output with the residual adjustment produced by the recurrent network yields the final one-step-ahead forecast.
To evaluate the forecasting architecture and its explanatory mechanisms, the investigation utilized transient temperature records derived from computational fluid dynamics simulations conducted on a modeled server room within the Poznan Supercomputing and Networking Center testbed. The computational fluid dynamics installation reproduced an operating environment featuring two equipment racks with heterogeneous server assemblies cooled by a roof-mounted cooling unit. Time-series observations gathered across experimental runs were chronologically divided, allocating the opening eighty percent of the sequential timeline to training the predictive architecture and reserving the remaining twenty percent exclusively for testing.
The analytical core of the study centered on interpreting how the trained recurrent component utilizes sequences of ten consecutive scaled residual lags, spanning from Residual_t1 representing the most recent error term to Residual_t10 representing the oldest historical residual. To avoid the selective biases associated with relying upon an isolated interpretability technique, the author deployed four distinct explainable artificial intelligence methodologies: SHapley Additive exPlanations, Permutation Feature Importance, Local Interpretable Model-agnostic Explanations, and Integrated Gradients. SHapley Additive exPlanations derived global importance metrics by computing the mean absolute Shapley values across evaluated samples, measuring individual feature contributions against cooperative game-theoretic foundations. Integrated Gradients calculated the path integral of output gradients along a linear trajectory between a neutral baseline and the true input sequence across fifty samples. Permutation Feature Importance systematically scrambled individual feature values across twenty repetitions with a fixed random seed of forty-two to measure error increases, while Local Interpretable Model-agnostic Explanations fitted linear surrogate models across fifty local neighborhoods.
Because raw attribution values generated across diverse explainable artificial intelligence techniques occupy distinct numerical scales, all importance scores were transformed through Min-Max scaling into a standardized interval between zero and one. The author subsequently deployed both Pearson correlation coefficients and Spearman rank correlation coefficients to evaluate the consistency of the resulting explanations from complementary angles. While Pearson calculations measured the linear alignment and proportional similarity existing among the attribution values, Spearman rank evaluations quantified the monotonic agreement between the relative orderings of the explanatory features. Visualized through comparative heatmaps, these statistical assessments enabled researchers to distinguish between mere differences in numerical score magnitude and genuine disagreements regarding which temporal residual inputs actually steered the neural network forecast. This comparative structure supported an evidence-based assessment of whether the hybrid model captures short-term residual memory or depends on distant operational history.
The experimental evaluation tested nine operational scenarios encompassing three distinct ambient cooling environments alongside three server workload shifts. Operating baselines included a low data center ambient temperature of 24 degrees Celsius, a moderate ambient level of 27 degrees Celsius, and an elevated high-temperature state of 30 degrees Celsius. Within each ambient tier, the model was subjected to three distinct operational load transitions: a moderate increase from 50 percent to 75 percent server processing utilization, a subsequent shift from 75 percent to 100 percent load, and an abrupt doubling from 50 percent directly to 100 percent processing intensity. Evaluating this matrix of nine operational conditions allowed the investigation to verify whether the predictive mechanisms of the deep learning architecture adapted consistently across changing operational demands or displayed erratic feature dependencies under extreme environmental heat.
Across the 24 degrees Celsius baseline scenarios, the attribution outcomes revealed that the hybrid forecasting model depended heavily on recent residual inputs, particularly Residual_t1 through Residual_t4, while older terms provided little influence. Under Scenario 1.1, which introduced a moderate processing change from 50 percent to 75 percent, all four explainability methods identified Residual_t2 as the most prominent feature for the inlet monitor, closely trailed by Residual_t3 and Residual_t1. When workload shifts became larger in Scenarios 1.2 and 1.3, feature prominence shifted toward the most immediate residual observation, making Residual_t1 the leading predictive factor for both sensors. In this low-temperature setting, SHAP, Integrated Gradients, and Permutation Importance exhibited robust consistency, generating Pearson correlation coefficients between 0.96 and 1.00 and Spearman rank coefficients ranging from 0.8788 to 1.000 for the inlet sensor and reaching 1.000 across outlet tests. Conversely, LIME produced lower Pearson correlations, falling between 0.26 and 0.46 for inlet monitoring and between 0.05 and 0.32 for outlet readings during the 50 percent to 100 percent transition, primarily because its surrogate fitting assigned zero importance to Residual_t1.
When ambient conditions were elevated to the moderate 27 degrees Celsius setting, the forecasting network maintained its focus on recent operational discrepancies while exhibiting slight variations across sensor sites. In Scenario 2.1, Residual_t2 retained its position as the foremost explanatory variable for both inlet and outlet positions, followed directly by Residual_t1 and Residual_t3, whereas Residual_t10 dropped toward zero. In Scenario 2.2, Residual_t2 remained the leading feature while the contribution from Residual_t1 lessened. In Scenario 2.3, the inlet sensor shifted its highest reliance toward Residual_t1, whereas the outlet sensor continued to prioritize Residual_t2, followed by Residual_t3 and Residual_t1. Correlation coefficients among SHAP, Integrated Gradients, and Permutation Importance remained between 0.96 and 1.00 for Pearson metrics and between 0.8788 and 1.000 for Spearman rankings. LIME improved its linear correspondence with the other three methods during Scenario 2.2, attaining Pearson values from 0.91 to 0.95 at the inlet and 0.87 to 0.91 at the outlet, though its inlet agreement dropped to between 0.11 and 0.35 during Scenario 2.3.
Under the high-temperature setting of 30 degrees Celsius, temporal dependency structures became noticeably more intricate, especially for outlet temperature predictions. In Scenario 3.1, inlet predictions reflected close competition between Residual_t1 and Residual_t2, with SHAP and Permutation Importance favoring the former while Integrated Gradients favored the latter, whereas the outlet sensor prioritized Residual_t3 and Residual_t2 followed by Residual_t4. Scenario 3.2 saw inlet forecasts return to the dominance of Residual_t1, while outlet calculations remained centered on Residual_t2. In Scenario 3.3, inlet predictions relied primarily on Residual_t3 and Residual_t2, whereas outlet estimations stayed anchored on Residual_t2. Despite these changing weights, SHAP, Integrated Gradients, and Permutation Importance demonstrated Pearson correlations between 0.93 and 1.00, achieving perfect Spearman rank alignment across Scenarios 3.2 and 3.3 for the inlet sensor and near-perfect or perfect rank agreement across all three outlet cases. LIME demonstrated scenario-dependent variability, recording Spearman correlations ranging from 0.5106 to 0.8511 for the inlet sensor, while achieving strong agreement between 0.8936 and 0.9058 for the outlet sensor in Scenario 3.1.
To synthesize the scenario-specific findings into an overarching view, the study implemented a global boxplot analysis illustrating the distribution and dispersion of feature importance scores across all nine operational environments. For both inlet and outlet monitoring locations, the resulting distributions confirmed that the central tendencies of feature weights were concentrated within the recent residual span of Residual_t1 through Residual_t4. The interquartile spans and outer whiskers illustrated that recent residuals exhibited wider dispersion, reflecting genuine shifts in operational relevance across changing workloads and cooling baselines rather than static predictive rules. In contrast, older residuals covering Residual_t8 through Residual_t10 showed tightly compressed distributions resting near the bottom of the scale, confirming their negligible contribution to forecasting outcomes. The boxplot visualization further showed that while Permutation Feature Importance yielded smaller absolute scores than SHAP and Integrated Gradients, their relative ranking profiles remained congruent, whereas LIME displayed distinct attribution spreads across multiple operational cases.
The study notes that the observed variations in temporal dependencies align with known physical properties of server cooling, where inlet air reflects fresh supply conditions while outlet air absorbs thermal energy from hardware components. This dynamic means outlet conditions can retain thermal memory across preceding intervals, explaining why outlet forecasts drew upon several recent residual time steps during high-temperature runs. However, the author emphasizes that mathematical feature importance identifies predictive associations captured by the neural network rather than providing direct physical measurements of heat accumulation or confirming causal mechanisms. Furthermore, the variable correlation values and shifting p-values observed with LIME demonstrate that local linear approximations can be sensitive to rapid operational shifts. By validating that hybrid SARIMAX-GRU networks consistently base their decisions on short-term residual trends, the explainability framework offers a verified foundation to support automated, energy-efficient cooling decisions across critical data center infrastructures.
Subject of Research: Explainable artificial intelligence evaluation of hybrid temperature forecasting in data centers
Article Title: A multi-method explainable AI for analyzing hybrid SARIMAX-GRU temperature forecasting in high-temperature data centers
Article References: Hriez, S. (2026). A multi-method explainable AI for analyzing hybrid SARIMAX-GRU temperature forecasting in high-temperature data centers. Frontiers in Big Data, 9, Article 1941665. https://doi.org/10.3389/fdata.2026.1941665
Image Credits: AI Generated
DOI: 10.3389/fdata.2026.1941665
Keywords: explainable artificial intelligence, data center thermal management, hybrid forecasting models, SARIMAX-GRU, SHAP, Integrated Gradients, Permutation Feature Importance, LIME, multi-method, explainable, analyzing, hybrid
News Source: Denise Maddox. (November 6, 2026). Explainable AI Decodes Thermal Forecasting in High Temperature Data Centers. Scienmag.
