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Center for Nonlinear Studies |
With exascale computing expected to become available within the next decade, computational science is focusing on ever more complex systems involving multiple physical, chemical and biological processes that take place on a wide range of spatial and/or temporal scales. Modeling such ``multiphysics'' problems in an accurate yet efficient way is a challenging endeavor, and a range of computational algorithms have been developed to deal with the various system configurations one may encounter. In the first part of my talk, I will focus on ``algorithm refinement`` hybrids that combine a fine-scale atomistic algorithm with a coarse-scale continuum description. In particular, I will demonstrate the importance of adding stochastic noise to the continuum solver when dealing with highly nonlinear systems driven by microscale fluctuations. I will also discuss a moments approach using a Gaussian closure, which allows a more direct computation of the mean and variance of the quantity of interest. In the second part, I will describe a statistical learning approach to mesoscopic model selection. Using cross-validation and regularization, this approach yields a stochastic coarse-grained description that is learned from microscale ``training'' data and is optimally predictive on unseen microscale ``test'' data. The resulting coarse-scale model may also capture the strength of fine-scale fluctuations more accurately than standard phenomenological approaches.
Host: Luis Chacon