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This research introduces PINNMorph, an online adaptation framework that uses large language models to dynamically evolve training policies for physics-informed neural networks. By continuously adjusting topology, sampling strategies, and gradient handling based on real-time diagnostics, the system outperforms static architectures across diverse partial differential equation benchmarks. The approach represents a significant step toward self-correcting AI systems capable of managing complex optimization landscapes without manual intervention.
PINNMorph: Evolving Online Adaptation Policies for Physics-Informed Neural Networks
arXiv:2609.32685v1 Announce Type: cross 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.
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.
Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2609.32685 [cs.AI]
(or arXiv:2609.32685v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.32685 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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