Enforcing hidden physics in physics-informed neural networks

Abstract: Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, despite their foundational role, the hidden irreversibility implied by the Second Law of Thermodynamics is often neglected during training, leading to unphysical solutions or even training failures in conventional PINNs. In this paper, we identify this critical gap and introduce a simple, generalized, yet robust irreversibility-regularized strategy that enforces hidden physical laws as soft constraints during training. 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 propagation, we demonstrate that our regularization scheme reduces predictive errors by more than an order of magnitude, while requiring only minimal modification to existing PINN frameworks. We believe that the proposed framework is broadly applicable to a wide class of PDE-governed physical systems and will have significant impact within the scientific machine learning community.