In past decades, considerable effort has been devoted to first-principles modeling of materials and materials design. However, uncertainty quantification over multiple scales, especially when some of them are inherently stochastic, is not sufficiently understood despite having critical impact on guiding experimental efforts and design. The uncertainty in materials modeling and design can arise either from the stochastic nature of microscopic description, sampling and numerical errors or from improper modeling assumptions, inadequate or inaccurate parametrization of the system and/or the objective functionals that guide the design optimization. Principal mathematical, computational and modeling challenges stem from the multiscale and multi-physics nature of the materials models. Quantifying errors and uncertainties due to combining different models at different scales will be critical for obtaining computational methods with sufficient predictive power to guide synthesis of new materials. For example, molecular simulations use force fields which are approximations of complex quantum mechanical free energy surfaces inducing uncertainty in mesoscopic processes. Similarly, rate constants in kinetic Monte Carlo simulations are subject to uncertainty due to errors in functionals of DFT, limits on the size of unit cells etc. The methods for quantifying the impact of such errors and uncertainties have been recently studied in different communities, including computational quantum chemistry, materials engineering, and mathematics.
Uncertainty quantification and sensitivity analysis for quantities governed by rare events is an area of particular importance in studies of molecular systems. The mathematical and computational methods for estimating sensitivities in these problems also connect directly to the topics of Workshop III. Uncertainty quantification has grown as a vital subject within the applied mathematics community, as witnessed by the emergence of a dedicated SIAM journal and regular SIAM conference. This workshop aims at fostering more interaction between different communities with a particular focus on mathematical tools for uncertainty quantification, sensitivity analysis and modeling error in high-dimensional stochastic systems, the role of rare and extreme events, computational tools and uncertainties due to model reduction and coarse-graining. It will offer an opportunity to discuss future developments in computational and mathematical techniques and transfer of methodologies developed by different communities. Interaction between participating domain scientists and mathematicians will also help stimulate new mathematical research.
This workshop will include a poster session; a request for posters will be sent to registered participants in advance of the workshop.
Virginie Ehrlacher, Co-chair
(École Nationale des Ponts-et-Chaussées, CERMICS)
Markos Katsoulakis (University of Massachusetts Amherst, Mathematics & Statistics)
Tony Lelièvre (Ecole des Ponts ParisTech)
Petr Plechac, Co-chair (University of Delaware)
Andrew Stuart (University of Warwick, Computing and Mathematical Sciences)
Dallas Trinkle (University of Illinois at Urbana-Champaign)