A physics informed bayesian optimization approach for material design: application to NiTi shape memory alloys 

Danial Khatamsaz, Raymond Neuberger, Arunabha M. Roy, Sina Hossein Zadeh, Richard Otis & Raymundo Arróyave 

npj Computational Materials9: 221 (2023).

A physics informed bayesian optimization approach

In material design applications, complex computational models and/or experiments are employed to gain a better understanding of the material system or to improve its performance. High-fidelity models, however, often exhibit high non-linearity, effectively behaving as black-boxes that hinder intuitive understanding beyond input-output correlations. At the same time, experiments are inherently black-box in nature as intermediate linkages between inputs (e.g. chemistry, processing protocols) and outputs (i.e. properties or performance metrics) tend to be accounted for only in an implicit manner. There is thus a growing need for novel data-efficient approaches that can effectively address these challenges while ensuring that the discovery and/or design process remains comprehensible and effective. Bayesian Optimization (BO) has gained popularity in materials design due to its ability to work with minimal data. However, many BO-based frameworks predominantly rely on statistical information, in the form of input-output data. In practice, designers often possess knowledge of the underlying physical laws governing a material system. Leveraging this partial information could potentially bolster the optimization process’s efficiency and speed. In this work, Danial Khatamsaz et al. from the Materials Science and Engineering Department, Texas A&M University, proposed a physics-informed BO framework. This framework introduces physics into the Gaussian Process (GP) kernel to explore potential efficiency enhancements in material system design and the discovery of optimal processing parameters. The proposed approach combines the advantages of traditional BO techniques with the benefits of employing known governing equations for physical modeling. By infusing statistical information with theoretical insights, they strengthened the GP’s probabilistic modeling capability, resulting in reduced data dependency and faster convergence to the optimal design. The incorporation of physical knowledge not only improves the performance of BO frameworks, but also allows for a deeper understanding of the underlying physics governing the system, which can lead to more informed and efficient design decisions. The applicability of this approach is showcased through the design of NiTi shape memory alloys, where the optimal processing parameters are identified to maximize the transformation temperature. This work lays a foundation for the application of physics-infused kernel design within the BO framework, opening up new possibilities across various materials science applications.