Machine Learning for Effective Computation in Multiscale Hyperbolic Systems

点击翻译按钮获取中文摘要

In physical science and engineering applications, it is often necessary to solve systems of differential equations that involve many temporal and length scales. Direct numerical simulations for these equations are often computationally infeasible. This research program aims to reduce the overall wall-clock computation time for simulations of multiscale dynamical systems found in applications by developing algorithms that leverage recent advancements in machine learning and parallel-in-time algorithms. The goal is to provide a systematic approach that can be generalized to other multiscale time-dependent problems and improve the efficacy of a class of existing methodologies. The algorithms will enable realistic computer simulations in a class of important applications, including molecular dynamics and seismic imaging, on massively parallel exascale computer architectures. The machine learning aspects of this project will attract students to scientific computing and stimulate further interdisciplinary work. Such training will be essential for preparing the future generation of researchers in scientific computing in the era of data science and artificial intelligence. This project concerns multiscale oscillatory dynamical systems, in which phase errors typically dominate the numerical solutions and do not dissipate in time, making accurate long-time simulations very difficult. This research program aims to construct effective solution operators for multiscale dynamical systems by using modern machine learning approaches combined with good training examples that properly sample the physics and causality in the system. Accordingly, a central focus of this research program is to develop a framework for the generation of effective training data that correctly sample the strong causality in the hyperbolic systems. The flow-based ensemble sampling strategy under study exploits the physical properties of the targeted systems. The program also includes a “self-improving” iterative procedure, which not only enables massive parallel-in-time computation but also improves the accuracy of machine learning-based computations. The project will directly involve two graduate students and the mentoring of undergraduate students.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.