Dataset for "Mapping Microstructure: Manifold Construction for Accelerated Materials Exploration"

Accelerating materials development requires quantitative linkages between processing, microstructure, and properties. In this work, we introduce a framework for mapping microstructure onto a low-dimensional material manifold that is parametrized by processing conditions. A key innovation is treating microstructure as a stochastic process, defined as a distribution of microstructural instances rather than a single image, enabling the extraction of material state descriptors that capture the essential process-dependent features. We leverage the manifold hypothesis to assert that microstructural outcomes lie on a low-dimensional latent space controlled by only a few parameters. Using phase-field simulations of spinodal decomposition as a model material system, we compare multiple microstructure descriptors (two-point statistics, chord-length distributions, and persistent homology) in terms of two criteria: (1) intrinsic dimensionality of the latent space, and (2) invertibility of the processing-to-structure mapping. The results demonstrate that distribution-based descriptors can recover a two-dimensional latent structure aligned with the true processing parameters, yielding an invertible and physically interpretable mapping between processing and microstructure. In contrast, descriptors that do not account for microstructure variability either overestimate dimensionality or lose predictive fidelity. The constructed material manifold is shown to be locally continuous, wherein small changes in process variables correspond to smooth changes in microstructure descriptors. This data-driven manifold mapping approach provides a quantitative foundation for microstructure-informed process design and paves the way toward closed-loop optimization of processing--structure--property relationships in an integrated materials engineering context.加速材料开发需要建立加工过程、微观组织与材料性能之间的定量关联。本研究提出了一种将微观组织映射至由加工条件参数化的低维材料流形的框架。本研究的一项关键创新是将微观组织视为随机过程，即定义为微观组织实例的分布而非单幅图像，由此可提取能够捕捉与工艺相关的核心特征的材料状态描述符。我们利用流形假设，认为微观组织的演化结果位于仅由少数参数控制的低维潜空间中。以调幅分解（spinodal decomposition）的相场（phase-field）模拟作为模型材料体系，我们对比了多种微观组织描述符——包括两点统计（two-point statistics）、弦长分布（chord-length distributions）与持久同调（persistent homology）——并基于两项标准进行评估：(1) 潜空间的本征维度，(2) 加工-结构映射的可逆性。研究结果表明，基于分布的描述符能够恢复出与真实加工参数相一致的二维潜结构，可得到加工过程与微观组织之间可逆且具备物理解释性的映射关系。与之相反，未考虑微观组织变异性的描述符要么会高估维度，要么会丧失预测保真度。所构建的材料流形被证明具有局部连续性，即工艺变量的微小变化对应着微观组织描述符的平滑变化。这种数据驱动的流形映射方法为基于微观组织的工艺设计提供了定量基础，并为集成化材料工程场景下加工-结构-性能关系的闭环优化开辟了道路。