EvoPINN: Agentic AI Discovers Novel Physics-Informed Neural Networks.

Physics-informed neural networks (PINNs) are powerful for solving partial differential equations (PDEs), but their effectiveness heavily depends on labor-intensive, manual engineering of neural architectures, loss functions, and optimization strategies. Traditional large language model (LLM) approaches to automate this often produce mathematically unsound or numerically unstable code. EvoPINN addresses this by introducing an agentic framework that reframes PINN development as an execution-grounded algorithm discovery challenge. It systematically explores a modular search space, decoupling neural representations from training programs. An LLM agent iteratively proposes memory-conditioned programmatic modifications, which are then subjected to strict structural verification and budget-matched PDE evaluation to ensure scientific validity. Extensive experiments across diverse PDE regimes (oscillatory, elliptic, dissipative, nonlinear transport) demonstrate that EvoPINN successfully discovers PDE-specialized learning algorithms that significantly outperform baselines by reducing relative L2 error. Notably, EvoPINN autonomously invented SLRC-PINN, a novel architecture whose performance gains were confirmed under rigorous comparisons, validating the potential of execution-grounded agents for genuine scientific computing innovation.