# Large Language Models and their Awareness of Mechanics and Spatial Geometry

arXiv: https://arxiv.org/abs/2608.14615 · HTML: https://mlsanity.com/paper/2608.14615/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 47 references that are in the map.
- First posted on arXiv 10 Jul 2026.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [DreamGaussian: Generative Gaussian Splatting for Efficient 3D Content Creation](https://mlsanity.com/paper/2309.16653/) (2023)
- [Point-E: A System for Generating 3D Point Clouds from Complex Prompts](https://mlsanity.com/paper/2212.08751/) (2022)
- [BigCodeBench: Benchmarking Code Generation with Diverse Function Calls and Complex Instructions](https://mlsanity.com/paper/2406.15877/) (2024)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [Vox-E: Text-guided Voxel Editing of 3D Objects](https://mlsanity.com/paper/2303.12048/) (2023)
- [LLaMA-Mesh: Unifying 3D Mesh Generation with Language Models](https://mlsanity.com/paper/2411.09595/) (2024)
- [Evaluating Spatial Understanding of Large Language Models](https://mlsanity.com/paper/2310.14540/) (2023)
- [MechAgents: Large language model multi-agent collaborations can solve mechanics problems, generate new data, and integrate knowledge](https://mlsanity.com/paper/2311.08166/) (2023)
- [CAD-Coder: Text-to-CAD Generation with Chain-of-Thought and Geometric Reward](https://mlsanity.com/paper/2505.19713/) (2025)
- [LEGO-Puzzles: How Good Are MLLMs at Multi-Step Spatial Reasoning?](https://mlsanity.com/paper/2503.19990/) (2025)
- [Large Language Model Agent as a Mechanical Designer](https://mlsanity.com/paper/2404.17525/) (2024)
- [Toward Engineering AGI: Benchmarking the Engineering Design Capabilities of LLMs](https://mlsanity.com/paper/2509.16204/) (2025)
- [Assessing Large Language Models in Mechanical Engineering Education: A Study on Mechanics-Focused Conceptual Understanding](https://mlsanity.com/paper/2401.12983/) (2024)
- [Foundational Models for 3D Point Clouds: A Survey and Outlook](https://mlsanity.com/paper/2501.18594/) (2025)
- [EngiBench: A Benchmark for Evaluating Large Language Models on Engineering Problem Solving](https://mlsanity.com/paper/2509.17677/) (2025)
- [Exploring and Improving the Spatial Reasoning Abilities of Large Language Models](https://mlsanity.com/paper/2312.01054/) (2023)
- [Large language model-empowered next-generation computer-aided engineering](https://mlsanity.com/paper/2509.11447/) (2025)
- [FEM-Bench: A Structured Scientific Reasoning Benchmark for Evaluating Code-Generating LLMs](https://mlsanity.com/paper/2512.20732/) (2025)
- [GRASP: A Grid-Based Benchmark for Evaluating Commonsense Spatial Reasoning](https://mlsanity.com/paper/2407.01892/) (2024)
- [A Domain Adaptation of Large Language Models for Classifying Mechanical Assembly Components](https://mlsanity.com/paper/2505.01627/) (2025)
- [EngiAI: Capability-Based Evaluation of Tool-Connected LLM Agents for Engineering Design](https://mlsanity.com/paper/2605.19743/) (2026)

## Built on by (most cited first, 1 of 1)

- [Language models can notice an impossible engineering problem yet still report it as solved](https://mlsanity.com/paper/2610.06668/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) perform well on established code-generation and mathematical-reasoning benchmarks, but their capabilities in mechanics and spatial geometry, here denoted as mechanical engineering awareness, has not been quantified systematically. We present MecEng, a fully automated benchmark that evaluates LLMs on the creation of multibody simulation models from parameterized textual descriptions. The benchmark comprises 84 generic tasks on three difficulty levels, ranging from rigid-body systems with joints and contact to flexible multibody systems that require exact 3D geometry generation, tetrahedral finite-element meshing, and Hurty-Craig-Bampton model order reduction of machine parts. A dedicated pipeline with LLMs generates simulation-ready geometry from text using Netgen, and builds multibody system models for the code Exudyn, which are then verified against expert ground truth on several levels: system-graph isomorphism including graph node annotations, numerical solutions, and part-specific measures such as mass, geometry, and eigenfrequencies. In total, 32 open-weight and two proprietary LLMs are evaluated. On rigid-body tasks, the best open-weight model obtains an overall success rate of 86.0%, compared to 91.4% for the strongest proprietary model, while flexible multibody tasks remain considerably harder. Additional studies quantify the influence of sampling temperature, reasoning, prompt design, model size, and LLM-release date. The results indicate rapidly improving, but still error-prone, mechanical engineering awareness of current LLMs.