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

2026-07-29

AI Summary

This work addresses the heavy reliance of physics-informed neural networks (PINNs) on manual design and the absence of automated discovery mechanisms. To overcome this limitation, we propose EvoPINN, a novel framework that introduces large language model agents into scientific computing for the first time. By leveraging a modular search space and an execution-validation mechanism, EvoPINN autonomously evolves and validates complete PINN training programs. The method discovers a new architecture, SLRC-PINN, which achieves substantially lower relative L₂ errors across multiple partial differential equations. Notably, SLRC-PINN maintains a clear performance advantage even under parameter-matched conditions, demonstrating both effectiveness and strong generalization capability. This result marks a significant departure from conventional hand-crafted design paradigms in scientific machine learning.

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.

Problem

• Physics-Informed Neural Networks
• Partial Differential Equations
• Automated Algorithm Discovery
• Scientific Computing
• Neural Architecture Design

Innovation

• EvoPINN
• Physics-Informed Neural Networks
• Algorithm Discovery
• Large Language Model Agent
• Execution-Grounded Search