内容简介：

Computational model of multiscale dynamic systems is centered around projecting the high-dimensional full system dynamics onto a set of resolved field variables.  In this talk, we introduce a framework based on both rigorous projection and data-learning algorithms to systematically construct such models so that the non-local correlation and fluctuations arising smaller scale interactions are properly accounted for. To quantify the uncertainty propagation arising from near-equilibrium fluctuations, we develop a numerical method based on compressive sensing and sparsity enhancement algorithm, which enables us to accurately construct a surrogate model within high-dimensional arbitrary random space using limited sampling data. Furthermore, to quantify the non-equilibrium dynamic process, the projected dynamics is casted into the generalized Langevin Equation with un-parameterized free energy term and memory kernel. We further develop a numerical method based on machine-learning algorithm for multi-dimensional density estimation and data-driven memory kernel parameterization that retain consistent fluctuation-dissipation and invariant measure. Our method is demonstrated in challenging systems such as realistic biomolecules and non-equilibrium dynamics such as reaction rate with broad applications in physics, engineering and biological systems.

报告人简介：

Dr. Lei received his Ph.D. on Applied Mathematics from Brown University in 2012. He joined the Pacific Northwest National Laboratory (PNNL) in 2013. Currently, he is a research staff scientist in the Division of Advanced Computing, Mathematics & Data at PNNL. His research work is mainly on statistical learning, stochastic modeling and computational methods with applications to multiscale multi-physics problems. He will move to department of computational mathematics science and engineering in fall 2019.

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