Learning to Evolve: Machine Learning for Complex Dynamic Systems

Abstract

Understanding and modeling complex physical dynamics stand as a cornerstone in the realm of modern science and engineering. The conventional manner to approach this is to construct various physics-principled models, which, while interpretable and sample-efficient, heavily rely on domain expertise and computational resources and struggle to address the escalating complexity of scientific problems. Recent progress in Deep Learning (DL) provides promising alternatives for modeling such dynamics, leveraging data-driven optimization and parallel processing to capture intricate patterns from large-scale datasets. The integration of machine learning has thus ushered in a new era of possibilities for modeling these complex dynamics, bridging gaps left by traditional techniques.

In this thesis, we are dedicated to advencing machine learning techniques for modeling complex dynamical systems across diverse senarios. First, we introduce a sequential variational inference framework to facilitate domain generalization in non-stationary environments with evolving distributions. Second, we propose graph neural controlled differential equations to model heterogeneous, continuous-time dynamics through neural parameterized vector fields. Third, we develop a frequency domain adaptation method to enhance the generalization of neural surrogate models across physical systems. Fourth, we devise an efficient framework that characterizes large-scale biological processes by capturing high-dimensional interatomic interactions and non-smooth dynamics for deciphering protein functional mechanisms. These works bridge physics-based modeling with modern machine learning, offering scalable, generalizable, and computational efficient solotions for modeling complex dynamics.

Date of Award	24 Jul 2025
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Haoliang LI (Supervisor)