Neural network-based reconstruction of steady-state temperature systems with unknown material composition

Effective thermal management is crucial for the performance and longevity of devices such as computer chips and batteries. A fundamental challenge in this field is accurately determining temperature distributions, which are often limited by incomplete observations. We introduce a neural-network-based approach to overcome these challenges. Specifically, a physics-informed fully convolutional auto-encoder coupled with a preceding spatial propagator network module is used to reconstruct complete temperature fields from partial observations, without requiring additional information about the spatial distribution of materials with varying thermal properties. This paper details the development and validation of our model, demonstrating its effectiveness in virtual sensing setups for both simulated and real-world thermal systems. The reconstruction capabilities for different sampling strategies are investigated. The most challenging of which is the "grid-edge" sampling where only discrete temperature sensors on the periphery of the systems are taken as input, amounting to a sampling ratio as low as 3.12%. The presented method is able to reconstruct the full temperature field with a relative average error of 1.1%. The NN-based approach outperforms the standard Kriging method in predicting the maximum temperature in a system, and proves more robust when the available measurements contain little information.