From Multi-scale to Data-driven Models for Materials (and Molecules)

Accurate molecular simulation requires computationally expensive quantum chemistry models that makes simulating complex material phenomena or large molecules intractable. This talk will be an overview of classical as well as "modern" data-driven multi-scale and coarse-grained models intended to overcome this barrier. I will focus in particular on analysis and numerical analysis aspects of modelling material defects:

(1) formulation and analysis of model problems;
(2) approximation by multi-scale/hybrid QM/MM models;
(3) approximation by data-driven interatomic potentials based on machine learning methodology.
Mathematical aspects of these topics include for example the analysis of the potential energy surface (regularity, sparsity, ...), high-dimensional approximation under symmetry constraints, and new inverse problems.