EvoPINN: Agentic Discovery of Executable Algorithms for Physics-Informed Neural Networks

Researchers introduced EvoPINN, an agentic framework that uses a large language model (LLM) to automatically discover executable algorithms for physics-informed neural networks (PINNs), reducing relative L2 error across diverse partial differential equation (PDE) regimes. The framework autonomously invented a novel architecture, SLRC-PINN, whose performance gains persist under parameter-matched comparisons, demonstrating the viability of execution-grounded agents for scientific computing.

arXiv:2607.26490v1 Announce Type: new Abstract: Physics-informed neural networks PINNs have emerged as a powerful paradigm for solving partial differential equations PDEs , yet their performance heavily relies on the manual, trial-and-error engineering of neural representations, loss formulations, and optimization dynamics. While Large Language Models LLMs offer a promising avenue for automated design, unconstrained code generation often yields mathematically invalid or numerically unstable solutions under strict scientific computing constraints. To bridge this gap, we propose \textbf{EvoPINN}, an agentic framework that reformulates PINN development from labor-intensive manual design into a rigorous, execution-grounded algorithm discovery problem. EvoPINN navigates a modular search space by decoupling neural representations from training programs, utilizing an LLM agent to iteratively propose memory-conditioned programmatic modifications. To ensure scientific validity, all candidates undergo strict structural verification and budget-matched PDE evaluation. Extensive experiments across diverse PDE regimes oscillatory, elliptic, dissipative, and nonlinear transport demonstrate that EvoPINN discovers PDE-specialized learning algorithms that significantly reduce relative $L {2}$ error compared to baselines. Crucially, EvoPINN autonomously invented SLRC-PINN, a novel architecture whose performance gains persist under rigorous parameter-matched comparisons, establishing the viability of execution-grounded agents for discovering genuinely new scientific computing mechanisms.