UCLA

Many scientific problems require a deep understanding of internal structures and complex dynamics,spanning physical interactions within molecules, brain networks, and beyond. These problems can be formulated as modeling interacting dynamical systems using graphs, which represent entities as nodes and their relationship as edges. Traditionally, the dynamics of interacting systems are described by ordinary differential equations (ODEs), offering continuous and interpretable solutions but requiring significant domain expertise. Recent data-driven approaches such as Graph Neural Networks (GNNs) learn system dynamics from observational data, which however, struggle with long-term predictions and irregular observations due to their discrete dynamics. My research aims to develop novel frameworks that bridge these two worlds, i.e. combining the learning power of neural networks (NNs) with the symbolic knowledge encoded in ODEs. In contrast with discrete models, such methods provide a principled approach to model continuous dynamical systems, from synthetic simulations to real-world scenarios like brain network analysis and COVID-19 prediction. Building upon this, I have further strengthened its power in three key areas: 1.) integrating data-driven inductive biases like energy conservation law; 2.) enhancing generalization ability; 3.) enabling causal decision-making. By merging deep graph learning with differential equations, I believe my research will pave the way for breakthroughs in symbolic deep learning for scientific discovery.