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.

翻译：我们引入了一个新颖的数据集，旨在基于拓扑优化方法（一种在设计空间内计算规定载荷与支撑条件下最优材料分布的方法）来评估大型语言模型（LLM）的物理与空间推理能力。在该数据集中，LLM 被提供诸如二维边界、施加的力与支撑等条件，并必须推理出由此产生的最优材料分布。该数据集包含多种任务，范围从在部分结构中填充掩蔽区域到预测完整的材料分布。解决这些任务需要理解力的传递以及在给定约束下所需的材料分布，且无法借助仿真工具或显式物理模型，从而挑战模型对结构稳定性与空间组织的推理能力。我们的数据集旨在评估二维环境下的空间与物理推理能力，为传统的语言与逻辑基准提供了补充视角。