Final Oral Public Examination

Ab initio multi­scale modeling of crystals: methods and applications in ferroelectrics

Advisors: Weinan E. and Roberto Car 

The ab initio density functional theory (DFT), all­atom molecular dynamics (MD), and coarsegrained dynamics are effective physical models bridging the microscale with the mesoscale. The Born­Oppenheimer approximation and the Mori­Zwanzig formalism indicate the conceptual consistency among these models. However, in multi­scale physical modeling, the numerical consistency among these models is still a long­term pursuit. Machine learning addresses this issue by parameterizing a coarse­grain model with data provided by a fine­grain model. We apply the data­driven approach to the multi­scale modeling of crystalline material and use ferroelectrics for demonstration. We use machine­learned potential energy surface and polarization surface to bridge DFT and all­atom MD. Then, we propose a machine­learned generalized Langevin equation to bridge all­atom MD and coarse­grained lattice dynamics. Consistency on static and dynamical material properties is demonstrated for the prototypical ferroelectric material lead titanate by modeling its paraelectric­ferroelectric phase transition and domain motion. The methodologies described can be readily applied to a lot of other crystals.