CDS&E: Learning Explainable Microstructure Representations for Material Property Prediction and Design

About This Grant

NON-TECHNICAL SUMMARY Designing new materials often requires extensive computer simulations to explore how a material’s internal structure influences its physical properties. This can be very costly, especially when materials have random or disordered features. While machine learning (ML) can speed up some parts of the design process, it does not always provide clear physical insights, such as why the connectivity of one material phase strongly affects overall conductivity or how certain patterns might enhance stiffness. This project addresses the challenge of making material design both efficient and explainable by focusing on the concept of N-point correlation functions (NPCFs). An NPCF is a statistical measure describing how different regions of a material relate to one another. By systematically learning which NPCFs matter most for a given property, the research will provide both accurate predictions and clear insights about the structure-property relationship. In addition to improving the design of smart composites for soft robotics, the methods developed will lay the foundation for broader applications in biological systems, climate modeling, and other areas where disordered structures play a critical role. The educational activities developed through this project will help K-12 students understand material structure-property relationships through hands-on experiments and contribute to training the next generation of researchers at the intersection of physics, mathematics, and computational science. TECHNICAL SUMMARY This project investigates how to identify concise and complete microstructure representations for two-phase, disordered heterogeneous materials. Since these microstructures can be treated as random fields, the research focuses on N-point correlation functions (NPCFs) as the core representation. Although machine learning models can approximate structure-property mappings, they often do not reveal the underlying physical causes. To address this, the project leverages a strong contrast expansion formalism, which links material properties to microstructure morphology through physics-based governing equations, such as partial differential equations (PDEs). By interpreting linear and nonlinear effective properties as expansions in terms of Green’s functions and NPCFs, the research team will develop new computational algorithms to learn both the necessary Green’s functions and the relevant NPCFs directly from data. These algorithms will provide a physics-driven mechanism for down-selecting which NPCFs are most critical, leading to an explainable and more efficient representation for microstructure reconstruction and property prediction. To demonstrate practical value, the project will apply these methods to the design of a bi-phase composite with specific mechanical and thermal transport properties relevant to soft robotics. By uncovering how different morphological features affect performance, the research aims to streamline the design process for materials that must satisfy coupled mechanical and thermal requirements. Beyond this specific application, the methods and principles developed will be broadly applicable to other random fields where PDE-driven properties dominate, such as multi-phase materials, biological systems, climate science, and cosmology. In addition to advancing knowledge in materials science, the project has a broader impact on data science by prompting new ideas for efficiently representing and modeling random fields. Just as insights into sequence modeling led to transformational language models, and insights into graph structures enabled advanced drug discovery methods, this research explores whether NPCFs can serve as essential building blocks for future architectures that handle large-scale or high-dimensional random fields. The developed educational activities will also contribute to training the next generation of researchers at the intersection of physics, mathematics, and computational science. STATEMENT OF MERIT REVIEW This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.