LLM Integration into Physics Informed Neural Networks

Abstract

This work introduces LLM-PINN, a novel framework that integrates Large Language Models (LLMs) with Physics-Informed Neural Networks (PINNs) to automate and enhance the modeling of complex physical systems. While conventional PINNs require manual derivation of PDEs and expert-level hyperparameter tuning, our framework leverages a Retrieval-Augmented Generation (RAG) engine to autonomously extract physical laws and constitutive relations from domain-specific knowledge bases. By establishing a closed-loop system, the LLM-PINN agent dynamically translates textual problem descriptions into executable symbolic formulations and loss functions. A key innovation is the autonomous feedback mechanism, where the PINN solver provides residual error data back to the LLM for iterative refinement of boundary conditions and optimization strategies. Benchmark evaluations on fluid dynamics and heat transfer problems demonstrate that LLM-PINN significantly reduces manual configuration time, accelerates training convergence, and achieves superior accuracy in solving stiff differential equations compared to baseline PINN models. This integration represents a pivotal step toward autonomous scientific discovery and self-optimizing physics-based machine learning architectures. © 2026 IEEE.