Learning Multiple Nonlinear Dynamical Systems with Side Information

We address the problem of learning multiple dynamical systems, which is a kind of multi-task learning (MTL). The existing methods of MTL do not apply to learning dynamical systems in general. In this work, we develop a regularization method to perform MTL for dynamical systems appropriately. The proposed method is based on an operator-theoretic metric on dynamics that is agnostic of model parametrization and applicable even for nonlinear dynamics models. We calculate the proposed MTL-like regularization by estimating the metric from trajectories generated during training. Learning time varying systems can be regarded as a special case of the usage of the proposed method. The proposed regularizer is versatile as we can straightforwardly incorporate it into off the-shelf gradient-based optimization methods. We show the results of experiments on synthetic and real-world datasets, which exhibits the validity of the proposed regularizer.