EvoPINN: Agentic Discovery of Executable Algorithms for Physics-Informed Neural Networks
06:00 · July 30, 2026 · arXiv cs.AI RSS
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.
Summary
EvoPINN reframes the design of physics-informed neural networks as an automated search for complete learning algorithms rather than a manual tuning exercise. Standard PINNs embed PDE residuals directly into the training loss, yet their accuracy on different equation types still depends on bespoke choices of network features, loss weighting, and optimization schedules. The framework addresses this by representing each candidate as a pair of decoupled modules—one for the neural representation and one for the training program—then letting an LLM agent propose incremental, memory-guided edits to a single module at a time.
Every generated candidate passes through a verification pipeline that checks structural validity, executes the code under a fixed computational budget, and compares solution error against the current best performer. Only modifications that both compile correctly and measurably lower relative L2 error are retained. This execution-grounded loop prevents the mathematically invalid or numerically unstable outputs that unconstrained LLM code generation often produces.
Across oscillatory, elliptic, dissipative, and nonlinear-transport PDEs, the discovered algorithms consistently outperform both the baseline PINN and several expert-designed variants. In one case the system autonomously produced SLRC-PINN, a global–local architecture in which an adaptive bank of localized bases gates a zero-initialized corrective branch; the performance advantage holds under parameter-matched comparisons. The same mechanisms also transfer to unseen equation parameters without retraining, indicating that the search process can surface reusable, PDE-specialized components rather than problem-specific hacks.
Why it matters
High technical depth and novelty make it directly useful for Dutch AI researchers working on scientific machine learning, physics simulation, and automated algorithm design; execution-grounded agent methods align with Netherlands strengths in ethical, reproducible AI.
