Evolutionary Algorithm-Guided LLMs for Physics-Informed Neural Network Design

• URL: http://arxiv.org/abs/2607.15560v1
• Date: Fri, 17 Jul 2026 02:03:11 GMT
• Title: Evolutionary Algorithm-Guided LLMs for Physics-Informed Neural Network Design
• Abstract summary: Physics-informed neural networks (PINNs) are sensitive to interacting choices of architecture, activation, loss weighting, collocation, optimization, and constraint enforcement.<n>Large language models (LLMs) can propose these choices, but independent recommendations do not accumulate experience from previously trained PINNs.<n>We propose a closed-loop evolutionary algorithm that guides an LLM to generate complete, executable PINN configurations across generations.
• Score: 10.706452586705375
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Physics-informed neural networks (PINNs) are unusually sensitive to interacting choices of architecture, activation, loss weighting, collocation, optimization, and constraint enforcement. Large language models (LLMs) can propose these choices, but independent recommendations do not accumulate experience from previously trained PINNs. We propose a closed-loop evolutionary algorithm that guides an LLM to generate complete, executable PINN configurations across generations, using measured training outcomes to determine subsequent search decisions. The algorithm maintains an evaluated population and lineage, applies parent-conditioned mutation and crossover, preserves elite and diverse solutions, rejects effective duplicates, and converts parent-relative successes and failures into the next-generation context supplied to the LLM. Every proposed configuration is executed directly under an exact optimizer-step budget. On a one-dimensional multiscale wave equation, two independent ten-generation runs trained 60 PINNs for 600,000 optimizer steps. In both runs, the best configuration appeared in the final generation, with best mean-squared error reduced by 2.97\% and 95.38\% relative to the initial population. The stronger run validated residual connections and increased depth on separate branches, combined them in a later generation, and then refined width and collocation density. It also revealed that low solution error can coexist with a high PDE residual. These results demonstrate the feasibility of evolutionary-algorithm-guided LLMs for PINN design on a controlled PDE while motivating broader, physics-aware evaluation.

Related papers

• EvoPINN: Agentic Discovery of Executable Algorithms for Physics-Informed Neural Networks [21.182571644696075]
  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.
  arXiv  Detail & Related papers  (2026-07-29T05:36:28Z)
• AdamFLIP: Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN Training [9.082213877961541]
  Physics-informed neural networks (PINNs) provide a flexible framework for solving forward and inverse problems governed by partial differential equations (PDEs)<n>Standard PINN training typically relies on soft penalty formulations that combine PDE residuals, data mismatch, and initial/boundary conditions using manually chosen weights.<n>In this work, we reformulate PINN training as an equality-constrained optimization problem and propose a novel Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN (AdamFLIP)
  arXiv  Detail & Related papers  (2026-05-08T19:13:15Z)
• Do physics-informed neural networks (PINNs) need to be deep? Shallow PINNs using the Levenberg-Marquardt algorithm [0.0]
  This work investigates the use of shallow physics-informed neural networks (PINNs) for solving forward and inverse problems of nonlinear partial differential equations (PDEs)<n>The proposed approach is tested on several benchmark problems, including the Burgers, Schrdinger, Allen-Cahn, and three-dimensional Bratu equations.
  arXiv  Detail & Related papers  (2026-02-09T11:05:57Z)
• REvolution: An Evolutionary Framework for RTL Generation driven by Large Language Models [2.127921199213507]
  Large Language Models (LLMs) are used for Register-Transfer Level (RTL) code generation.<n>This paper introduces REvolution, a framework that combines Evolutionary Computation (EC) with LLMs for automatic RTL generation and optimization.
  arXiv  Detail & Related papers  (2025-10-24T12:50:35Z)
• HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions [16.904297509040777]
  We present HyPINO, a multi-physics neural operator designed for zeroshot generalization across a broad class of parametric PDEs.<n>The model maps PDE parametrizations to target Physics-Informed Neural Networks (PINNs) and can handle linear elliptic, hyperbolic, and parabolic equations in two dimensions.<n>HyPINO achieves strong zero-shot accuracy on seven benchmark problems from PINN, outperforming U-Nets, literature, and Physics-Informed Neural Operators (PINO)
  arXiv  Detail & Related papers  (2025-09-05T13:59:25Z)
• Reparameterized LLM Training via Orthogonal Equivalence Transformation [54.80172809738605]
  We present POET, a novel training algorithm that uses Orthogonal Equivalence Transformation to optimize neurons.<n>POET can stably optimize the objective function with improved generalization.<n>We develop efficient approximations that make POET flexible and scalable for training large-scale neural networks.
  arXiv  Detail & Related papers  (2025-06-09T17:59:34Z)
• Efficiently Training Deep-Learning Parametric Policies using Lagrangian Duality [55.06411438416805]
  Constrained Markov Decision Processes (CMDPs) are critical in many high-stakes applications.<n>This paper introduces a novel approach, Two-Stage Deep Decision Rules (TS- DDR) to efficiently train parametric actor policies.<n>It is shown to enhance solution quality and to reduce computation times by several orders of magnitude when compared to current state-of-the-art methods.
  arXiv  Detail & Related papers  (2024-05-23T18:19:47Z)
• RoPINN: Region Optimized Physics-Informed Neural Networks [66.38369833561039]
  Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) This paper proposes and theoretically studies a new training paradigm as region optimization. A practical training algorithm, Region Optimized PINN (RoPINN), is seamlessly derived from this new paradigm.
  arXiv  Detail & Related papers  (2024-05-23T09:45:57Z)
• A Multi-Head Ensemble Multi-Task Learning Approach for Dynamical Computation Offloading [62.34538208323411]
  We propose a multi-head ensemble multi-task learning (MEMTL) approach with a shared backbone and multiple prediction heads (PHs) MEMTL outperforms benchmark methods in both the inference accuracy and mean square error without requiring additional training data.
  arXiv  Detail & Related papers  (2023-09-02T11:01:16Z)
• Joint Deep Reinforcement Learning and Unfolding: Beam Selection and Precoding for mmWave Multiuser MIMO with Lens Arrays [54.43962058166702]
  millimeter wave (mmWave) multiuser multiple-input multiple-output (MU-MIMO) systems with discrete lens arrays have received great attention. In this work, we investigate the joint design of a beam precoding matrix for mmWave MU-MIMO systems with DLA.
  arXiv  Detail & Related papers  (2021-01-05T03:55:04Z)
• Resource Allocation via Model-Free Deep Learning in Free Space Optical Communications [119.81868223344173]
  The paper investigates the general problem of resource allocation for mitigating channel fading effects in Free Space Optical (FSO) communications. Under this framework, we propose two algorithms that solve FSO resource allocation problems.
  arXiv  Detail & Related papers  (2020-07-27T17:38:51Z)
• Self-Directed Online Machine Learning for Topology Optimization [58.920693413667216]
  Self-directed Online Learning Optimization integrates Deep Neural Network (DNN) with Finite Element Method (FEM) calculations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 5 orders of magnitude compared with directly using methods, and outperformed all state-of-the-art algorithms tested in our experiments.
  arXiv  Detail & Related papers  (2020-02-04T20:00:28Z)

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.