PAPM: A Physics-aware Proxy Model for Process Systems

Abstract

Process systems, which play a fundamental role in various scientific and engineering fields, often rely on computational models to capture their complex temporal-spatial dynamics. However, due to limited insights into the intricate physical principles, these models can be imprecise or inapplicable, coupled with a significant computational demand exacerbating inefficiencies. To address these challenges, we propose a physics-aware proxy model (PAPM) to explicitly incorporate partial prior mechanistic knowledge, including conservation and constitutive relations. Additionally, to enhance the inductive biases about strict physical laws and broaden the applicability scope, we introduce a holistic temporal and spatial stepping method (TSSM) aligned with the distinct equation characteristics of different process systems, resulting in better out-of-sample generalization. We systematically compare state-of-the-art pure data-driven models and physics-aware models, spanning five two-dimensional non-trivial benchmarks in nine generalization tasks. Notably, PAPM achieves an average absolute performance improvement of 6.4%, while requiring fewer FLOPs, and only 1% of the parameters compared to the prior leading method, PPNN. Through such analysis, the structural design and specialized spatio-temporal modeling schemes (i.e., TSSM) of PAPM exhibit not only the most balanced trade-off between accuracy and computational efficiency among all methods evaluated, but also an impressive out-of-sample generalization.