Learning System Dynamics without Forgetting

Predicting the trajectories of systems with unknown dynamics (i. e. the governing rules) is crucial in various research fields, including physics and biology. This challenge has gathered significant attention from diverse communities. Most existing works focus on learning fixed system dynamics within one single system. However, real-world applications often involve multiple systems with different types of dynamics or evolving systems with non-stationary dynamics (dynamics shifts). When data from those systems are continuously collected and sequentially fed to machine learning models for training, these models tend to be biased toward the most recently learned dynamics, leading to catastrophic forgetting of previously observed/learned system dynamics. To this end, we aim to learn system dynamics via continual learning. Specifically, we present a novel framework of Mode-switching Graph ODE (MS-GODE), which can continually learn varying dynamics and encode the system-specific dynamics into binary masks over the model parameters. During the inference stage, the model can select the most confident mask based on the observational data to identify the system and predict future trajectories accordingly. Empirically, we systematically investigate the task configurations and compare the proposed MS-GODE with state-of-the-art techniques. More importantly, we construct a novel benchmark of biological dynamic systems, featuring diverse systems with disparate dynamics and significantly enriching the research field of machine learning for dynamic systems.