Picard-KKT-hPINN: Enforcing Nonlinear Enthalpy Balances for Physically Consistent Neural Networks
This work addresses the issue of physically inconsistent predictions in neural network surrogate models, which is crucial for applications like catalytic reactor modeling, though it appears incremental as it builds on existing constraint enforcement techniques.
The authors tackled the problem of neural networks lacking physical consistency by proposing a method to enforce nonlinear physical laws like enthalpy balances, resulting in machine-level precision enforcement and improved accuracy in data-scarce conditions compared to standard models.
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.