A data-driven model-free physical-informed deep operator network for solving nonlinear dynamic system

The existing physical-informed Deep Operator Networks are mostly based on either the well-known mathematical formula of the system or huge amounts of data for different scenarios. However, in some cases, it is difficult to get the exact mathematical formula and vast amounts of data in some dynamic systems, we can only get a few experimental data or limited mathematical information. To address the cases, we propose a data-driven model-free physical-informed Deep Operator Network (DeepOnet) framework to learn the nonlinear dynamic systems from few available data. We first explore the short-term dependence of the available data and use a surrogate machine learning model to extract the short-term dependence. Then, the surrogate machine learning model is incorporated into the DeepOnet as the physical information part. Then, the constructed DeepOnet is trained to simulate the system's dynamic response for given control inputs and initial conditions. Numerical experiments on different systems confirm that our DeepOnet framework learns to approximate the dynamic response of some nonlinear dynamic systems effectively.