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Johann Guilleminot
Assistant Professor of Civil and Environmental Engineering, Duke University
Friday, Dec. 2 | 10:40 A.M. | AERO 120

Abstract: In this talk, we discuss the construction of admissible, physics-consistent and identifiable stochastic models for uncertainty quantification.

We first consider a continuum mechanics setting where variables and fields take values in constrained spaces (the positive-definite cone or the interior of a simplex in Rn, for instance) and are indexed by complex geometries described by nonconvex sets. These constraints arise in many problems ranging from simulations on parts produced by additive manufacturing to multiscale analyses with stochastic connected phases. We present theoretical and computational procedures to ensure well-posedness and generate representations defined by arbitrary transport maps. We provide results pertaining to modeling, sampling, and statistical inverse identification for various applications including additive manufacturing, phase-field fracture modeling, multiscale analyses on nonlinear microstructures, and patient-specific computations on soft biological tissues.

We next address the case of model uncertainties in atomistic simulations. The modeling of such uncertainties raises many challenges associated with the proper randomization of operators in highly nonlinear dynamical systems. We present a new modeling framework where model inaccuracy is captured through the construction of a stochastic reduced-order basis. Leveraging standard and recent results from optimization on manifolds, we show that linear constraints are indeed preserved through Riemannian pushforward and pullback operators to and from the tangent space to the manifold. This property allows us to derive a probabilistic representation that is easy to interpret, to sample, and to identify. In particular, the ability to constraint the Fr´echet mean on the manifold is demonstrated. Numerical examples on graphene-based systems are finally presented to illustrate the relevance of the proposed approach.

Bio: Dr. Johann C. Guilleminot is an assistant professor of Civil and Environmental Engineering at Duke University (with a secondary appointment in Mechanical Engineering and Materials Science). Prior to that, he held a Maˆıtre de Conf´erences position in the Multiscale Modeling and Simulation Laboratory, UMR 8208 CNRS, at Universite´ Gustave Eiffel (France).

He earned an MS (2005) in Mechanical Engineering and Materials Science from Institut Mines T´el´ecom Nord Europe, and an MS (2005) and PhD (2008) in Theoretical Mechanics from the University of Science and Technology in Lille (France). He received his Habilitation (2014) in Mechanics from Universit´e Paris-Est, with certifications in Applied Mathematics and Mechanics.

Guilleminot’s research focuses on computational mechanics, multiscale and multimodel (atomistic/continuum) methods and uncertainty quantification, as well as on topics at the interface between these fields—with a broad range of applications ranging from the modelingrials and structures for aerospace and naval industries to patient-specific simulations on biological tissues.