PSP-GEN: Stochastic inversion of the Process–Structure–Property chain in materials design through deep, generative probabilistic modeling

Inverse material design is a cornerstone challenge in materials science, with significant applications across many industries. Traditional approaches that invert the structure–property (SP) linkage to identify microstructures with targeted properties often overlook the feasibility of production processes, leading to microstructures that may not be manufacturable. Achieving both desired properties and a realizable manufacturing procedure necessitates inverting the entire Process-Structure-Property (PSP) chain. However, this task is fraught with challenges, including stochasticity along the whole modeling chain, the high dimensionality of microstructures and process parameters, and the inherent ill-posedness of the inverse problem. This paper proposes a novel framework, named PSP-GEN, for the goal-oriented material design that effectively addresses these challenges by modeling the entire PSP chain with a deep generative model. It employs two sets of continuous, microstructure- and property-aware, latent variables, the first of which provides a lower-dimensional representation that captures the stochastic aspects of microstructure generation, while the second is a direct link to processing parameters. This structured, low-dimensional embedding not only simplifies the handling of high-dimensional microstructure data but also facilitates the application of gradient-based optimization techniques. The effectiveness and efficiency of this method are demonstrated in the inverse design of two-phase materials, where the objective is to design microstructures with target effective permeability. We compare state-of-the-art alternatives in challenging settings involving limited training data, target property regions for which no training data is available, and design tasks where the process parameters and microstructures have high-dimensional representations. • A novel framework named PSP-GEN is introduced that integrates the entire Process-Structure-Property (PSP) chain into a single, deep, generative model, addressing stochasticity and high-dimensionality challenges. • A continuous latent space with two components is utilized: one for stochastic microstructure/property generation and one for linking with the processing parameters. • The goal-oriented design problem with discrete-valued variables is reformulated as a stochastic optimization one with continuous variables enabling efficient solutions with gradient-based techniques, even in high-dimensional processing parameter spaces. • PSP-GEN is illustrated in designing two-phase media where it exhibits superior performance as compared to state-of-the-art and its ability to handle small-data as well as to generalize to unseen, target, property regions.