PINNMorph: Evolving Online Adaptation Policies for Physics-Informed Neural Networks

2026-09-26

AI Summary

This study addresses the mismatch between the dynamically evolving training process and the fixed architecture of Physics-Informed Neural Networks (PINNs) by proposing an online adaptive framework guided by large language model (LLM)-driven strategy evolution. The framework jointly optimizes network topology, sampling distributions, and optimizer configurations, leveraging training feedback to drive the neuroevolution of a strategy population and thereby achieving co-adaptation between model architectures and intervention strategies. Evaluated across 13 partial differential equation benchmarks, the proposed method significantly outperforms mainstream baselines such as SA-PINN in accuracy. By enabling synergistic adaptation throughout training, this work establishes an efficient and generalizable new paradigm for the dynamic, adaptive training of PINNs.

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.

Problem

• Physics-Informed Neural Networks
• Partial Differential Equations
• Online Adaptation
• Training Dynamics
• Policy Evolution

Innovation

• Physics-Informed Neural Networks
• Online Adaptation
• Large Language Models
• Policy Evolution
• Partial Differential Equations