EvoPINN uses LLM agents to autonomously discover better PINN algorithms

Physics-Informed Neural Networks (PINNs) are powerful for solving PDEs, but their performance depends on tedious manual engineering of architectures, loss functions, and optimizers. While LLMs could automate design, unconstrained code generation often produces invalid or unstable solutions. To bridge this gap, researchers introduced EvoPINN, an agentic framework that turns PINN development into a rigorous, execution-grounded algorithm discovery problem. EvoPINN uses a modular search space separating neural representations from training programs, with an LLM agent that iteratively proposes memory-conditioned modifications. All candidates undergo structural verification and budget-matched PDE evaluation to ensure scientific validity.

Extensive experiments across diverse PDE regimes—oscillatory, elliptic, dissipative, and nonlinear transport—show that EvoPINN discovers specialized learning algorithms that significantly reduce relative L2 error compared to baselines. Crucially, the framework autonomously invented SLRC-PINN, a novel architecture whose performance gains persist under strict parameter-matched comparisons. This demonstrates that execution-grounded agents can genuinely discover new scientific computing mechanisms, potentially reducing the trial-and-error burden in PINN development and accelerating PDE solving across physics and engineering.