Miguel Bessa, Brown University

The talk addresses the challenge of computing complex phenomena at the scale of applications.  In addition to the universal laws (balance of mass, momenta etc.), these phenomena require a constitutive (closure) relation that describes the behavior of the medium at the scale of applications.    Such behavior can be nonlinear, nonlocal, anisotropic, history dependent etc., and thus impossible to characterize to the desired level by the classical approach of postulating a parametrized relation and fitting the parameters to selected experiments.  The talk describes two broad approaches to using data-driven methods to overcome this challenge.  The first approach is multiscale modeling where one recognizes that the effective behavior at the scale of applications is determined by physics at multiple length and time scales: electronic, atomistic, domains, defects etc.  The data-driven constitutive relation is obtained as a neural approximation is trained using data generated by repeated solution of the small scale problem.  The second approach seeks to infer it from automated experiments that are not amenable to easy inversion.  The talk will describe these approaches, challenges they raise and strategies to overcome them.  The ideas will be illustrated with applications from materials science and geology.