Dissertation Defense of CMSE Pei Ge

Friday April 4th, 12-2pm

EB 1420

Passcode: CMSE

 

By Pei Ge

 

Abstract:

Multi-scale modeling presents a long-standing challenge in computational mathematics and is pertinent to a wide range of applications in materials science, fluid physics, and chemical engineering. Predicting collective behaviors typically necessitates the integration of modeling dynamics across micro-scale (atomistic), meso-scale (kinetic), and macro-scale (continuum) levels, with the vast range of spatiotemporal scales posing a fundamental obstacle. Existing methods often rely on certain empirical constitutive closures or micro-macro coupling approaches. Despite their broad applications, modeling accuracy and efficiency are often challenged in real applications.  

 

This dissertation aims to develop data-driven approaches for constructing accurate and reliable reduced models of multi-scale systems based on first-principle descriptions. The first part focuses on constructing a meso-scale reduced model of polymer kinetics directly from the full molecular dynamics. We present a data-driven method to learn stochastic reduced models of complex systems that retain a state-dependent memory beyond the standard generalized Langevin equation (GLE) with a homogeneous kernel. The constructed model naturally encodes the heterogeneous energy dissipation by jointly learning a set of state features and the non-Markovian coupling among the features. Numerical results demonstrate the limitation of the standard GLE and the essential role of the broadly overlooked state-dependency nature in predicting molecule kinetics related to conformation relaxation and transition.

 

The second part focuses on learning accurate non-Newtonian hydrodynamic models from meso-scale polymer kinetics. To retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the micro-scale polymer configurations and their macro-scale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the micro-scale model and the relevant terms can be parametrized using machine learning. The final model, named  DeePN$^2$, has shown some success in systematically passing the micro-scale heterogeneous polymer structural mechanics to the macro-scale hydrodynamics without human intervention. 

 

Huan Lei (chair)

Daniel Appelö

Michael Murillo

Yimin Xiao