Picard-KKT-hPINN: Enforcing Nonlinear Enthalpy Balances for Physically Consistent Neural Networks

Surrogate modeling plays a crucial role in simplifying and approximating complex physical models, making them suitable for large-scale simulations and optimization studies of industrial relevance. Machine learning models, such as neural networks (NNs), are particularly well-suited for this purpose due to their simplicity and strong regression capabilities [1]. However, despite exceptional advancements in machine learning, issues and skepticism regarding the black-box nature and physical inconsistency of these models hinder the adoption of machine learning-based tools (and, more broadly, artificial intelligence) in industrial applications [2, 3]. To mitigate this limitation, significant research has been carried out to enforce known mechanistic relationships between inputs and predictions in NNs. Soft-constrained neural networks represent an approach in which physical equations are included as penalty terms in the loss function [4, 5].