SPhyR: Spatial-Physical Reasoning Benchmark on Material Distribution
On the map: LLM reasoning → Spatial and embodied reasoning
Abstract (arXiv)
We introduce a novel dataset designed to benchmark the physical and spatial reasoning capabilities of Large Language Models (LLM) based on topology optimization, a method for computing optimal material distributions within a design space under prescribed loads and supports. In this dataset, LLMs are provided with conditions such as 2D boundary, applied forces and supports, and must reason about the resulting optimal material distribution. The dataset includes a variety of tasks, ranging from filling in masked regions within partial structures to predicting complete material distributions. Solving these tasks requires understanding the flow of forces and the required material distribution under given constraints, without access to simulation tools or explicit physical models, challenging models to reason about structural stability and spatial organization. Our dataset targets the evaluation of spatial and physical reasoning abilities in 2D settings, offering a complementary perspective to traditional language and logic benchmarks.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning. Builds on 17 of its 24 references that are in the map. First posted on arXiv 21 May 2025.
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- 2020Language Models are Few-Shot Learnerscited by 32,419
- 2023GPT-4 Technical Reportcited by 18,396
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- 2024GPT-4o System Cardcited by 4,588
- 2024Gemini 1.5: Unlocking multimodal understanding across millions of tokens of contextcited by 3,224
- 2019PIQA: Reasoning about Physical Commonsense in Natural Languagecited by 2,883
- 2016CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoningcited by 1,457
- 2019CLEVRER: CoLlision Events for Video REpresentation and Reasoningcited by 484
- 2025ARC-AGI-2: A New Challenge for Frontier AI Reasoning Systemscited by 190
- 2021Physion: Evaluating Physical Prediction from Vision in Humans and Machinescited by 153
- 2019PHYRE: A New Benchmark for Physical Reasoningcited by 137
- 2018IntPhys: A Framework and Benchmark for Visual Intuitive Physics Reasoningcited by 73
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- 2018ShapeStacks: Learning Vision-Based Physical Intuition for Generalised Object Stackingcited by 55
- 20183D Topology Optimization using Convolutional Neural Networkscited by 29
- 2019A Novel Topology Optimization Approach using Conditional Deep Learningcited by 18
- 2019A deep Convolutional Neural Network for topology optimization with strong generalization abilitycited by 17
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- 2025FEM-Bench: A Structured Scientific Reasoning Benchmark for Evaluating Code-Generating LLMs
- 2026SCALAR: Quantifying Structural Hallucination, Consistency, and Reasoning Gaps in Materials Foundation Models
- 2025Optimize Any Topology: A Foundation Model for Shape- and Resolution-Free Structural Topology Optimization
- 2026Physics as the label for measuring and correcting materials reasoning in multimodal models
- 2026PolyBridgeBench: Benchmarking Multimodal LLMs for Physics-Grounded Bridge Design
- 2025Symbolic Intermediaries as a Linguistic-Numerical Interface for LLM-Driven Geometric Reasoning
- 2024GRASP: A Grid-Based Benchmark for Evaluating Commonsense Spatial Reasoning