Modeling Unknown Stochastic Dynamical System Subject to External Excitation
This addresses the challenge of modeling stochastic systems with time-dependent excitations when governing equations are unavailable, but it appears incremental as it builds on existing data-driven and generative modeling approaches.
The paper tackles the problem of learning unknown nonautonomous stochastic dynamical systems from short bursts of input/output data, and the result is a method that accurately predicts stochastic responses to arbitrary excitation signals not in the training data, as demonstrated through numerical examples for long-term predictions.
We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the stochastic system are unavailable. However, short bursts of input/output (I/O) data consisting of certain known excitation signals and their corresponding system responses are available. When a sufficient amount of such I/O data are available, our method is capable of learning the unknown dynamics and producing an accurate predictive model for the stochastic responses of the system subject to arbitrary excitation signals not in the training data. Our method has two key components: (1) a local approximation of the training I/O data to transfer the learning into a parameterized form; and (2) a generative model to approximate the underlying unknown stochastic flow map in distribution. After presenting the method in detail, we present a comprehensive set of numerical examples to demonstrate the performance of the proposed method, especially for long-term system predictions.