Upcoming Event: PhD Dissertation Defense

Efficient computation of multiscale Hamiltonian systems aided by machine learning

Rui Fang, CSEM Ph.D. Candidate

Abstract

Molecular dynamics, classical mechanics, and theoretical physics often involve Hamiltonian systems with multiple time scales, where stable and accurate long-time integration demands small time steps, leading to high computational costs.
   

This dissertation focuses on improving the computational efficiency of multiscale simulations through data-driven methods and parallel-in-time algorithms. We introduce a novel framework for learning the flow map of Hamiltonian systems using neural networks, emphasizing effective data generation and loss regularization via numerical schemes. To further accelerate computations, we integrate the learned flow map with the parareal algorithm, a parallel-in-time method introduced by Lions, Maday, and Turinici. The original parareal algorithm struggles with instability in highly oscillatory problems. To address this, we propose a stabilized variant called the Procrustes parareal, which improves the phase alignment between the coarse and fine solvers by leveraging solutions from previous iterations.
   
We validate our approach on several benchmark problems, including the Fermi-Pasta-Ulam problem, the three-body problem under gravitational interactions, and the α-particle problem in magnetic confinement fusion devices. Our results demonstrate improvements in stability, accuracy, and computational efficiency, offering a promising direction for large-scale multiscale simulations.

Biography

Rui Fang is a CSEM PhD candidate supervised by Prof. Richard Tsai. Her research interests include machine learning, deep learning and scientific computing. Before joining CSEM, she received her BS degree in physics and astronomy from Haverford College and her ME degree in Computational Science and Engineering from Harvard University.