Adaptive sampling methods for learning dynamical systems

Learning dynamical systems from observed trajectories is a fundamental problem in data-driven science and engineering. While many existing works focus on improving model architectures or training methods, less attention has been directed at how to effectively sample training data to give rise to accurate models. In particular, one of the most basic problems is to select the length of sampled trajectories that balances computational overhead due to sampling and the quality of learned models. This paper deals with the task of improving sampling efficiency for learning dynamics. We first formulate proper target risks to evaluate the model performance of learning in the dynamical setting. This allows us to connect generalization to matching empirical measures with specific target measures. In line with this observation, we propose a class of adaptive algorithms to find effective sampling strategies that control the length of sampled trajectories. Through numerical experiments, we show the adaptive algorithms can achieve more accurate results given a sampling budget compared to baseline sampling methods.