Abstract Physics-informed neural networks (PINNs) represent a promising paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully reflect the physical structure embedded in the governing equations remains an open challenge. This stems from a fundamental limitation: standard neural networks lack an inherent notion of physical admissibility , leaving them vulnerable to producing mathematical artifacts that satisfy the training loss but lack physical meaning. In this work, we address this issue by introducing a simple, generalized, yet robust irreversibility-regularized strategy that enforces hidden physical laws as soft constraints during training, thereby recovering the missing physics associated with irreversible processes in the conventional PINN. This approach ensures that the learned solutions consistently respect the intrinsic one-way nature of irreversible physical processes. Across a wide range of benchmarks spanning traveling wave propagation, steady combustion, ice melting, corrosion evolution, and crack growth, we observe substantial performance improvements over state-of-the-art PINN baseline equipped with advanced training techniques, demonstrating that our regularization scheme reduces predictive errors by up to more than one order of magnitude, while requiring only minimal modification to existing PINN frameworks.
Chen et al. (Sat,) studied this question.