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This paper introduces EvoPINN, an innovative framework that transforms the development of physics-informed neural networks (PINNs) from a manual design process into an automated algorithm discovery task. By leveraging a large language model (LLM) to propose modifications in a modular search space, EvoPINN ensures the scientific validity of generated solutions through rigorous verification and evaluation against partial differential equations (PDEs). Experimental results reveal that EvoPINN not only discovers specialized learning algorithms with significantly lower relative \(L_2\) error but also autonomously invents a novel architecture, SLRC-PINN, demonstrating the potential of agentic frameworks in advancing scientific computing.
EvoPINN autonomously discovers new algorithms for physics-informed neural networks, achieving significant performance improvements while ensuring scientific validity.
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.
