A multitask latent space learning framework for modeling and inversion of structure–property relationships

The process–structure–property (PSP) linkage forms the foundation of modern materials science. It describes how manufacturing processes shape microstructural features, which in turn govern a material’s properties. Characteristics such as strength, ductility, hardness, and anisotropy define the functional suitability of a component, and tailoring these properties to the intended application is essential. This leads to the concept of inverse design, which seeks to map target material properties onto microstructural evolutions and ultimately onto optimal process parameters. Achieving this goal is highly challenging, as material properties depend on complex and often nonlinear relationships with the underlying microstructure. Effective process optimization therefore requires controlling microstructural evolution through process parameter trajectories, which typically operates in a high-dimensional microstructure space. For instance, if microstructures are represented by orientation distribution functions (ODFs), the resulting complexity can be computationally intensive. Despite decades of experimental and modelling studies, fully exploiting structure–property relationships for predictive and inverse design remains a significant challenge. Machine learning offers powerful and continually advancing capabilities to address this issue by learning high-dimensional, nonlinear structure–property linkages directly from data and extracting near-optimal process paths through systematic exploration and optimization. A prerequisite for such optimization is the specification of goal microstructures that fulfil the desired properties. This identification of microstructures corresponding to desired properties is commonly referred to as the inverse design of structure–property relationships. This work advances data-driven methodologies for modelling and optimization of structure–property relationships in materials science, with the dual objectives of enabling inverse design and reducing the dimensionality of the microstructure space to support efficient optimization. The set of microstructures resulting from inverse design should not only exhibit the desired properties but also satisfy two additional requirements: they must be physically producible through the process, and they should encompass sufficient diversity to provide a broad range of design options. Integrating these requirements into the inverse design framework constitutes a key contribution of this work, ensuring that all microstructures in the solution set are feasible and that process optimization can identify near-optimal paths. The main contribution of this work is the development of a multitask latent space learning approach that provides a low-dimensional representation for microstructures. In this framework, a shared encoder maps microstructures onto the latent space. The required inverse mapping from desired properties to a diverse set of feasible microstructures is performed by an optimizer with a specifically designed objective function, also developed in this work. The diversity requirement for the microstructure set is quantified through the mutual distances among its members. Since microstructures are represented by ODFs, a dedicated distance measure between ODFs is introduced. The resulting efficiency gain in process optimization represents the main advancement over the state of the art, demonstrated in this work through applications of the developed framework to dedicated processes. By interpreting microstructures more generally as process state variables, the multitask framework—with its low-dimensional latent space, reconstruction capability, and property mappings—can be transferred to other processes. This generalizability is illustrated using the example of resistance spot welding.