Adaptive Weighting and Collocation in Physics-Informed Neural Networks for Chemical Process Modeling

Physics-informed neural networks (PINNs) embed physical constraints into neural network training and are effective for modeling chemical processes. However, standard PINNs with uniformly sampled collocation points and manually tuned or fixed loss weights often suffer from poor training efficiency and accuracy, as adjusting loss weights is challenging and problem-dependent. To address these issues, this work proposes a Pareto-guided regional sampling (PaRS) framework for adaptive collocation point sampling and loss balancing. PaRS integrates residual decomposition, adaptive loss weighting, and dynamic resampling. The spatial domain is partitioned into subregions, and residuals from different regions are treated as competing objectives, forming a Pareto front that captures trade-offs among losses. A Pareto-guided weighting strategy then assigns adaptive weights based on training progress, which further guides region-wise resampling to focus on error-prone or underexplored areas. Case studies in chemical engineering demonstrate that PaRS-PINNs outperform standard PINNs and existing adaptive collocation methods.