Novel Model Development for Material Systems: Data-driven Algorithms and Interacting Particle Methods

University Of Arizona, Tucson AZ

Investigators

Abstract

Models for complex materials have traditionally relied on a mixture of physical understanding along with phenomenological guesswork. This project seeks new avenues for model building, incorporating advances in machine learning and novel mathematical paradigms. Experimental and simulation data is combined with physical laws to determine the structure of model equations, leading to more realistic descriptions of physical systems, enhanced prediction ability, and reconstruction of noisy and missing data. A second aim is the development of models involving interacting agents that mimic physical processes. These will be utilized for large scale computations that are currently infeasible. Graduate student training is an integral part of the project. This project investigates new approaches to construct and simulate models in material systems. Regression algorithms are developed for simultaneous parameter and state inference and discovery for partial differential equations, utilizing either experimental data or detailed numerical simulations. These will be used for applications in complex polymer systems, phase field models, model reduction, and reconstruction of materials data. Energy driven models of interacting particles and their mean-field limits are investigated using numerical simulation along with formal and rigorous analysis. Connections with phase-separation, nematic and self-assembling pattern-formation phenomenon are established, and allow for Lagrangian numerical methods that utilize coarse-grained interaction potentials. Project results can be adapted to a vast array of physical and biological models, and can serve as tools for data analysis and assimilation. 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.