CENTER FOR COMPUTATION & TECHNOLOGY

We propose a data-driven method to quantify quasi-equilibrium and non-equilibrium properties for complex physical systems with high dimensional stochastic space based on generalize polynomial chaos (gPC) expansion and Mori-Zwanzig projection method. For quasi-equilibrium properties, we demonstrate that sparse grid method suffers instability problem due to the high-dimensionality. Alternatively, we
propose a numerical method to enhance the sparsity by defining a set of collective variables within active subspace, yielding more accurate surrogate model recovered by compressive sensing method. Moreover, non-equilibrium properties further depends on the non-local memory term representing the high-dimensional unresolved states. We propose a data-driven method based on appropriate parameterization
to compute the memory kernel of the generalized Langevin Equation (GLE) by merely using trajectory data. The approximated kernel formulation satisfies the second fluctuation-dissipation conditions naturally with invariant measure. The proposed method enables us to characterize transition properties such as reaction rate where Markovian approximation shows limitation.

Huan Lei received his Ph.D. on Applied Mathematics from Brown University in 2012. He joined the Pacific Northwest National Laboratory (PNNL) as a postdoctoral associate. Currently, he is a research staff scientist in the Division of Advanced Computing, Mathematics \& Data at PNNL. His research work is mainly on developing mesoscale models and numerical methods  applicable to multi-physical systems beyond equilibrium; in particular, non-equilibrium  dynamic processes and intrinsic transition between the metastable states.