# Lang-PINN: From Language to Physics-Informed Neural Networks via a Multi-Agent Framework

arXiv: https://arxiv.org/abs/2510.05158 · HTML: https://mlsanity.com/paper/2510.05158/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Web, search, and research agents, one of 16 directions in LLM agents and tool use.
- Builds on 31 of its 42 references that are in the map.
- First posted on arXiv 3 Oct 2025.

## Placed in

- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 30 of 31)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [SWE-agent: Agent-Computer Interfaces Enable Automated Software Engineering](https://mlsanity.com/paper/2405.15793/) (2024)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [StarCoder 2 and The Stack v2: The Next Generation](https://mlsanity.com/paper/2402.19173/) (2024)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [AutoML: A Survey of the State-of-the-Art](https://mlsanity.com/paper/1908.00709/) (2019)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Structured Chain-of-Thought Prompting for Code Generation](https://mlsanity.com/paper/2305.06599/) (2023)
- [Parallel Physics-Informed Neural Networks via Domain Decomposition](https://mlsanity.com/paper/2104.10013/) (2021)
- [PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs](https://mlsanity.com/paper/2306.08827/) (2023)
- [Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs](https://mlsanity.com/paper/2403.12553/) (2024)
- [CodePDE: An Inference Framework for LLM-driven PDE Solver Generation](https://mlsanity.com/paper/2505.08783/) (2025)

## Built on by (most cited first, 11 of 11)

- [AgenticSciML: Collaborative Multi-Agent Systems for Emergent Discovery in Scientific Machine Learning](https://mlsanity.com/paper/2511.07262/) (2025)
- [GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms](https://mlsanity.com/paper/2605.11117/) (2026)
- [OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inference](https://mlsanity.com/paper/2602.01493/) (2026)
- [Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards](https://mlsanity.com/paper/2607.10474/) (2026)
- [EvoPINN: Agentic Discovery of Executable Algorithms for Physics-Informed Neural Networks](https://mlsanity.com/paper/2607.26490/) (2026)
- [Physics-Audited Agentic Discovery in Scientific Machine Learning](https://mlsanity.com/paper/2607.07379/) (2026)
- [Large language models for partial differential equation workflows](https://mlsanity.com/paper/2608.03600/) (2026)
- [PINNForge: Execution-Grounded Evolutionary Design of Physics-Informed Neural Networks](https://mlsanity.com/paper/2609.23023/) (2026)
- [Rules to Tools: Executable Checks for LLM Agents in Scientific Computing](https://mlsanity.com/paper/2610.00313/) (2026)
- [Transferability of Learned States in Neural PDE Solvers](https://mlsanity.com/paper/2610.10972/) (2026)
- [Prior or Feedback? What an LLM Uses When Adapting Neural Operators](https://mlsanity.com/paper/2610.12325/) (2026)

## Abstract (arXiv)

Physics-informed neural networks (PINNs) provide a powerful approach for solving partial differential equations (PDEs), but constructing a usable PINN remains labor-intensive and error-prone. Scientists must interpret problems as PDE formulations, design architectures and loss functions, and implement stable training pipelines. Existing large language model (LLM) based approaches address isolated steps such as code generation or architecture suggestion, but typically assume a formal PDE is already specified and therefore lack an end-to-end perspective. We present Lang-PINN, an LLM-driven multi-agent system that builds trainable PINNs directly from natural language task descriptions. Lang-PINN coordinates four complementary agents: a PDE Agent that parses task descriptions into symbolic PDEs, a PINN Agent that selects architectures, a Code Agent that generates modular implementations, and a Feedback Agent that executes and diagnoses errors for iterative refinement. This design transforms informal task statements into executable and verifiable PINN code. Experiments show that Lang-PINN achieves substantially lower errors and greater robustness than competitive baselines: mean squared error (MSE) is reduced by up to 3--5 orders of magnitude, end-to-end execution success improves by more than 50%, and reduces time overhead by up to 74%.