| Abstract Scope |
This talk describes a framework for generating, exploring, and exploiting material manifolds—low-dimensional representations of microstructural state spaces—based on stochastic characterizations of microstructure. Microstructure is formalized as a probabilistic process, with individual instances sampled to define distributions that encode material states. By constructing descriptor-based embeddings using persistence homology, correlation functions, and chord length statistics, we define and navigate manifolds that link processing parameters to structural outcomes. We evaluate manifold quality through intrinsic dimensionality, invertibility of processing-structure mappings, and local/global stability. Deep generative models, including variational and diffusion-based autoencoders, are trained to traverse and sample the manifold, enabling controlled interpolation of microstructural features. Statistical tools assess descriptor fidelity, distinguish synthetic from physical states, and quantify manifold resolvability. This integrated framework supports automated microstructure exploration, inverse design, and informed sampling strategies, providing a robust foundation for data-driven discovery across complex, high-dimensional domains. |