Enforcing hidden physics in physics-informed neural networks

2025-11-18

AI Summary

Traditional physics-informed neural networks (PINNs) for solving partial differential equations often neglect the irreversibility mandated by the second law of thermodynamics, leading to unphysical solutions or training failure. To address this, we propose a general and robust irreversibility regularization strategy: soft constraints—based either on entropy production rate or temporal monotonicity—are incorporated into the PINN loss function without altering the network architecture, requiring only minimal adaptation. This work is the first to explicitly embed thermodynamic irreversibility into the PINN training process, thereby enforcing the unidirectional evolution characteristic of physical processes. Evaluated across diverse irreversible phenomena—including traveling wave propagation, combustion, ice melting, corrosion, and crack propagation—the method reduces prediction errors by over one order of magnitude. It significantly enhances both physical consistency and training stability of learned solutions.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• Enforcing hidden irreversibility from thermodynamics in PINN training
• Addressing unphysical solutions in conventional physics-informed neural networks
• Regularizing irreversible physical processes as soft constraints during learning

Innovation

• Enforcing hidden physics as soft constraints
• Introducing irreversibility-regularized strategy in PINNs
• Minimally modifying existing PINN frameworks