Physics informed neural networks adapt online to solve partial differential equations better
PINNMorph: Evolving Online Adaptation Policies for Physics-Informed Neural Networks
Artificial IntelligenceMachine Learning
Summary
Physics-informed neural networks (PINNs) use machine learning to solve complex mathematical equations called partial differential equations (PDEs). The authors found that fixed network designs and training rules can limit performance because the problem changes during learning. They created PINNMorph, a system that changes the network’s structure and training steps dynamically based on how well it is learning, guided by policies evolved from experience. This approach improved accuracy compared to previous methods on many test problems.
What this means in practice
- •For computational engineers: Improve simulation accuracy for physical systems by dynamically adjusting neural network solvers during training.
- •For software developers in computational physics: Integrate adaptive PINN training policies into PDE solving software to boost solution precision across varied problems.
Authors
Xu Yang, Mingyang Yu, Jun Zhang, Keqian Li, Jing Xu
Abstract
Physics-informed neural networks (PINNs) provide a learning-based framework for solving partial differential equations (PDEs), yet their training behavior can change substantially throughout optimization. Residual distributions, gradient interactions, regional learning difficulty, and model-capacity requirements may evolve over time, while the network architecture and major training mechanisms are typically determined before training. We propose PINNMorph, an online PINN adaptation framework based on large language model (LLM)-guided policy evolution. PINNMorph maintains a population of state-conditioned adaptation policies that map execution diagnostics to controlled interventions over topology modification, additive representation augmentation, objective balancing, gradient handling, adaptive sampling, and optimizer-phase control. At each intervention opportunity, candidate programs are instantiated from the current policy population, selected according to the observed training state, and applied directly to the PINN under training. The resulting model inherits its existing parameters and training state and continues optimization along the same trajectory. Execution outcomes are subsequently used to evaluate interventions and evolve the policy population. Unlike pre-training architecture search or fixed adaptation rules, PINNMorph jointly adapts the current PINN and the policies governing its interventions using feedback from actual training. Experiments on 13 PDE benchmarks show that PINNMorph achieves lower solution errors than SA-PINN, ConFIG, RoPINN, HARMONIC, and PINNsAgent across all evaluated problems. Ablation studies further examine the effects of online adaptation, state-conditioned intervention selection, and execution-feedback-driven policy evolution.