Physically interpretable surrogate modeling of thermal fields in electronics cooling using combined proper orthogonal decomposition and neural networks

As advances in semiconductor technology drive higher power densities, thermal management is becoming increasingly crucial to maintaining the performance and reliability of devices. In recent decades, computational fluid dynamics (CFD) has been widely used for thermal management system design. However, the computational requirement of CFD makes it impractical for iterative design-optimization, which requires thousands of high-fidelity simulations. Data-driven surrogate models address the speed limitations of CFD but are often treated as black boxes whose predictions lack physical interpretability. Neural networks (NNs) combined with proper orthogonal decomposition (POD) constrain predictions to dominant modes that have the potential to align with physical features of the underlying system. The interpretability of POD-NN learned representations remains largely unexplored. This work demonstrates a POD-NN surrogate model framework for predicting 2D thermal fields for a liquid-cooled dual-chip cold plate with the goal of establishing it as a trusted model for future multi-objective cold plate design optimization. The resultant model achieves a per-sample speedup over CFD that depends on batch size, ranging from approximately 1 0 3 × for single-sample inference to over 1 0 6 × at large batch sizes. This range supports use across both iterative design optimization and real-time digital twin or control applications. An error decomposition analysis quantifies POD truncation and NN regression error contributions across dataset sizes, identifying a POD-truncation error floor that defines the surrogate’s accuracy ceiling. A Pearson correlation analysis is used to link all four POD coefficients to identifiable thermal features demonstrating that the surrogate’s predictions are physically grounded and that prediction errors can be attributed to interpretable physical modes rather than to opaque latent dimensions. Latent space mapping further demonstrates that thermal resistance varies along physically meaningful gradients. These results characterize POD-NN as a fast, interpretable, and trustworthy forward model suitable for use in subsequent optimization and digital twin studies.