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

Neural networks are widely used as surrogate models but they do not guarantee physically consistent predictions thereby preventing adoption in various applications. We propose a method that can enforce NNs to satisfy physical laws that are nonlinear in nature such as enthalpy balances. Our approach, inspired by Picard successive approximations method, aims to enforce multiplicatively separable constraints by sequentially freezing and projecting a set of the participating variables. We demonstrate our PicardKKThPINN for surrogate modeling of a catalytic packed bed reactor for methanol synthesis. Our results show that the method efficiently enforces nonlinear enthalpy and linear atomic balances at machine-level precision. Additionally, we show that enforcing conservation laws can improve accuracy in data-scarce conditions compared to vanilla multilayer perceptron.