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

• URL: http://arxiv.org/abs/2607.26490v1
• Date: Wed, 29 Jul 2026 05:36:28 GMT
• Title: EvoPINN: Agentic Discovery of Executable Algorithms for Physics-Informed Neural Networks
• Abstract summary: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs)<n>We propose textbfEvoPINN, an agentic framework that reformulates PINN development into a rigorous, execution-grounded algorithm discovery problem.
• Score: 21.182571644696075
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System [47.73467147921344]
  Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.<n>Recent Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative but frequently suffer from slow convergence and optimization instability.<n>This article proposes the Physics-Informed Broad Learning System (PIBLS), a novel backpropagation-free framework that reformulates PDE solving as a direct least-squares optimization.
  arXiv  Detail & Related papers  (2026-06-18T03:34:06Z)
• Scale-PINN: Learning Efficient Physics-Informed Neural Networks Through Sequential Correction [33.84065974605524]
  Physics-informed neural networks (PINNs) have emerged as a promising mesh-free paradigm for solving partial differential equations.<n>We introduce the Sequential Correction Algorithm for Learning Efficient PINN (Scale-PINN), a learning strategy that bridges modern physics-informed learning with numerical algorithms.
  arXiv  Detail & Related papers  (2026-02-23T03:38:06Z)
• High precision PINNs in unbounded domains: application to singularity formulation in PDEs [83.50980325611066]
  We study the choices of neural network ansatz, sampling strategy, and optimization algorithm.<n>For 1D Burgers equation, our framework can lead to a solution with very high precision.<n>For the 2D Boussinesq equation, we obtain a solution whose loss is $4$ digits smaller than that obtained in citewang2023asymptotic with fewer training steps.
  arXiv  Detail & Related papers  (2025-06-24T02:01:44Z)
• AL-PINN: Active Learning-Driven Physics-Informed Neural Networks for Efficient Sample Selection in Solving Partial Differential Equations [0.0]
  Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving Partial Differential Equations (PDEs)<n>We propose Active Learning-Driven PINNs (AL-PINN), which integrates Uncertainty Quantification (UQ) and Active Learning strategies to optimize sample selection dynamically.<n>Our results demonstrate that AL-PINN achieves comparable or superior accuracy compared to traditional PINNs while reducing the number of required training samples.
  arXiv  Detail & Related papers  (2025-02-06T10:54:28Z)
• Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks [24.14254861023394]
  In this study, we suggest a path that potentially opens up a possibility for physics-informed neural networks (PINNs) to be considered as one such solver. PINNs have pioneered a proper integration of deep-learning and scientific computing, but they require repetitive time-consuming training of neural networks. We propose a lightweight low-rank PINNs containing only hundreds of model parameters and an associated hypernetwork-based meta-learning algorithm.
  arXiv  Detail & Related papers  (2023-10-14T08:13:43Z)
• Efficient and Flexible Neural Network Training through Layer-wise Feedback Propagation [49.44309457870649]
  Layer-wise Feedback feedback (LFP) is a novel training principle for neural network-like predictors.<n>LFP decomposes a reward to individual neurons based on their respective contributions.<n>Our method then implements a greedy reinforcing approach helpful parts of the network and weakening harmful ones.
  arXiv  Detail & Related papers  (2023-08-23T10:48:28Z)
• NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition [67.46012350241969]
  This paper proposes a general acceleration methodology called NeuralStagger. It decomposing the original learning tasks into several coarser-resolution subtasks. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations.
  arXiv  Detail & Related papers  (2023-02-20T19:36:52Z)
• Auto-PINN: Understanding and Optimizing Physics-Informed Neural Architecture [77.59766598165551]
  Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. Here, we propose Auto-PINN, which employs Neural Architecture Search (NAS) techniques to PINN design. A comprehensive set of pre-experiments using standard PDE benchmarks allows us to probe the structure-performance relationship in PINNs.
  arXiv  Detail & Related papers  (2022-05-27T03:24:31Z)
• Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs [70.51212431290611]
  Partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. We propose the Neural Operator with Regularity Structure (NORS) which incorporates the feature vectors for modeling dynamics driven by SPDEs. We conduct experiments on various of SPDEs including the dynamic Phi41 model and the 2d Navier-Stokes equation.
  arXiv  Detail & Related papers  (2022-04-13T08:53:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.