# FEABench: Evaluating Language Models on Multiphysics Reasoning Ability

arXiv: https://arxiv.org/abs/2504.06260 · HTML: https://mlsanity.com/paper/2504.06260/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 55 references that are in the map.
- First posted on arXiv 8 Apr 2025.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 25 of 25)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [SWE-agent: Agent-Computer Interfaces Enable Automated Software Engineering](https://mlsanity.com/paper/2405.15793/) (2024)
- [ChemCrow: Augmenting large-language models with chemistry tools](https://mlsanity.com/paper/2304.05376/) (2023)
- [Executable Code Actions Elicit Better LLM Agents](https://mlsanity.com/paper/2402.01030/) (2024)
- [Capabilities of Gemini Models in Medicine](https://mlsanity.com/paper/2404.18416/) (2024)
- [SciCode: A Research Coding Benchmark Curated by Scientists](https://mlsanity.com/paper/2407.13168/) (2024)
- [CodeGemma: Open Code Models Based on Gemma](https://mlsanity.com/paper/2406.11409/) (2024)
- [CORE-Bench: Fostering the Credibility of Published Research Through a Computational Reproducibility Agent Benchmark](https://mlsanity.com/paper/2409.11363/) (2024)
- [Advancing Multimodal Medical Capabilities of Gemini](https://mlsanity.com/paper/2405.03162/) (2024)
- [SPIQA: A Dataset for Multimodal Question Answering on Scientific Papers](https://mlsanity.com/paper/2407.09413/) (2024)
- [NESTFUL: A Benchmark for Evaluating LLMs on Nested Sequences of API Calls](https://mlsanity.com/paper/2409.03797/) (2024)
- [LeanAgent: Lifelong Learning for Formal Theorem Proving](https://mlsanity.com/paper/2410.06209/) (2024)
- [Theoretical Physics Benchmark (TPBench) -- a Dataset and Study of AI Reasoning Capabilities in Theoretical Physics](https://mlsanity.com/paper/2502.15815/) (2025)
- [Quantum Many-Body Physics Calculations with Large Language Models](https://mlsanity.com/paper/2403.03154/) (2024)
- [PAPERCLIP: Associating Astronomical Observations and Natural Language with Multi-Modal Models](https://mlsanity.com/paper/2403.08851/) (2024)
- [MyCrunchGPT: A chatGPT assisted framework for scientific machine learning](https://mlsanity.com/paper/2306.15551/) (2023)
- [Collaboration Dynamics and Reliability Challenges of Multi-Agent LLM Systems in Finite Element Analysis](https://mlsanity.com/paper/2408.13406/) (2024)

## Built on by (most cited first, 22 of 22)

- [Foam-Agent 2.0: An End-to-End Composable Multi-Agent Framework for Automating CFD Simulation in OpenFOAM](https://mlsanity.com/paper/2509.18178/) (2025)
- [EngiBench: A Benchmark for Evaluating Large Language Models on Engineering Problem Solving](https://mlsanity.com/paper/2509.17677/) (2025)
- [PhysicsEval: Inference-Time Techniques to Improve the Reasoning Proficiency of Large Language Models on Physics Problems](https://mlsanity.com/paper/2508.00079/) (2025)
- [SciAgent: A Unified Multi-Agent System for Generalistic Scientific Reasoning](https://mlsanity.com/paper/2511.08151/) (2025)
- [EngTrace: A Symbolic Benchmark for Verifiable Process Supervision of Engineering Reasoning](https://mlsanity.com/paper/2511.01650/) (2025)
- [PhySense: Principle-Based Physics Reasoning Benchmarking for Large Language Models](https://mlsanity.com/paper/2505.24823/) (2025)
- [AI Benchmark Democratization and Carpentry](https://mlsanity.com/paper/2512.11588/) (2025)
- [InPhyRe Discovers: Large Multimodal Models Struggle in Inductive Physical Reasoning](https://mlsanity.com/paper/2509.12263/) (2025)
- [Empowering Real-World: A Survey on the Technology, Practice, and Evaluation of LLM-driven Industry Agents](https://mlsanity.com/paper/2510.17491/) (2025)
- [An MLCommons Scientific Benchmarks Ontology](https://mlsanity.com/paper/2511.05614/) (2025)
- [SCICONVBENCH: Benchmarking LLMs on Multi-Turn Clarification for Task Formulation in Computational Science](https://mlsanity.com/paper/2605.18630/) (2026)
- [Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards](https://mlsanity.com/paper/2607.10474/) (2026)
- [SciResearcher: Scaling Deep Research Agents for Frontier Scientific Reasoning](https://mlsanity.com/paper/2605.01489/) (2026)
- [CAX-Agent: A Lightweight Agent Harness for Reliable APDL Automation](https://mlsanity.com/paper/2605.15218/) (2026)
- [VFEAgent: A Multimodal Agent Framework for End-to-End Automated Finite Element Analysis](https://mlsanity.com/paper/2605.28978/) (2026)
- [A Constrained Natural-Language Interface for Variational Multi-Physics Finite Element Simulations in FEniCS](https://mlsanity.com/paper/2606.10928/) (2026)
- [Large language models for partial differential equation workflows](https://mlsanity.com/paper/2608.03600/) (2026)
- [Beyond Executable Models: The Pufibara Agent Harness and the Modelica Agent Workflow Benchmark for Physical System Modeling](https://mlsanity.com/paper/2608.23653/) (2026)
- [What Do CAE Simulation Agents Really Need Beyond a Generic Harness?](https://mlsanity.com/paper/2609.03718/) (2026)
- [EngiWorld: What Can Frontier Agents Deliver in Professional Engineering Environments?](https://mlsanity.com/paper/2609.37686/) (2026)
- [Language models can notice an impossible engineering problem yet still report it as solved](https://mlsanity.com/paper/2610.06668/) (2026)
- [EvoSim: Learning to Model, Modeling to Learn](https://mlsanity.com/paper/2610.11344/) (2026)

## Abstract (arXiv)

Building precise simulations of the real world and invoking numerical solvers to answer quantitative problems is an essential requirement in engineering and science. We present FEABench, a benchmark to evaluate the ability of large language models (LLMs) and LLM agents to simulate and solve physics, mathematics and engineering problems using finite element analysis (FEA). We introduce a comprehensive evaluation scheme to investigate the ability of LLMs to solve these problems end-to-end by reasoning over natural language problem descriptions and operating COMSOL Multiphysics^circledR, an FEA software, to compute the answers. We additionally design a language model agent equipped with the ability to interact with the software through its Application Programming Interface (API), examine its outputs and use tools to improve its solutions over multiple iterations. Our best performing strategy generates executable API calls 88% of the time. LLMs that can successfully interact with and operate FEA software to solve problems such as those in our benchmark would push the frontiers of automation in engineering. Acquiring this capability would augment LLMs' reasoning skills with the precision of numerical solvers and advance the development of autonomous systems that can tackle complex problems in the real world. The code is available at https://github.com/google/feabench