Physics‑informed neural networks (PINNs) require coordinated choices of network architecture, sampling strategy, loss formulation, and optimizer when solving partial differential equations. Optimal settings vary widely across PDEs, and existing automated design methods typically generate candidates without leveraging information gathered during training, leading to repeated trial‑and‑error and inefficient use of the training budget.
PINNsForge introduces an LLM‑driven evolutionary framework that grounds design decisions in execution feedback. The LLM first draws on a PDE‑related knowledge base to produce diverse candidate configurations. Each candidate is trained end‑to‑end, and its performance metrics are recorded. High‑performing designs together with accumulated execution evidence are fed back to the LLM, which, guided by observed optimization behavior, refines, recombines, and explores coupled components such as network topology, sampling, loss terms, and optimizer settings. This creates a continual loop of generation, execution, feedback, and evolution.
Unlike one‑shot search or evaluation‑only feedback, PINNsForge progressively converts training experience into improved design decisions for the target PDE. Across 25 benchmark PDEs, it achieves the lowest mean squared error (MSE) on 24 tasks compared with RoPINN, PINNsFormer, and PINNsAgent.
Ablation studies confirm the importance of the PDE knowledge base, execution feedback, and evolutionary search: removing the knowledge base raises mean MSE by $3.74\times$, removing feedback by $12.10\times$, and removing evolutionary search by $10.10\times$.
Review: PINNsForge tightly couples LLM generation with real training feedback, enabling adaptive iteration of PINNs design and highlighting the promise of large models for automated scientific computing.