Data and physics requirements for reliable physics‐informed neural networks in process modeling
TL;DR
This work develops a theoretical framework for analyzing the generalization error of PINNs under model misspecification, establishing both an architecture‐independent error bound and an explicit bound for a specific PINN architecture.
Abstract
Physics‐informed neural networks (PINNs) have gained increasing attention in chemical process modeling since they can embed first‐principles knowledge into neural network training. However, in practice, the embedded physics is often inaccurate, and experimental data are costly to obtain, raising fundamental questions about the required physics‐model accuracy and data volume required to achieve a target prediction accuracy. This work develops a theoretical framework for analyzing the generalization error of PINNs under model misspecification. We establish both an architecture‐independent error bound and an explicit bound for a specific PINN architecture. The bound is further related to the solution error with respect to the true system, yielding quantitative conditions on admissible model discrepancy, data requirements, and loss‐weight selection. Based on these conditions, two adaptive algorithms are proposed to guide physics‐model refinement and data collection. The theoretical findings are demonstrated using a chemical process network.