OPCNet: Oscillatory Pattern Capturing Network for Highly Oscillatory Data

Abstract We introduce a novel neural network-based model, called the oscillatory pattern capturing network (OPCNet), to fit highly oscillatory data by identifying the data with the solution of the linear ODE in [14] with perturbations. Given oscillatory data, the model first learns the oscillatory patterns of the data, which can be inferred from the dynamics of the linear ODE, and then fits the data with the solution of the ODE. Incorporating with a suitable loss function, the proposed model succeeds to find the ODE system to represent the oscillatory behavior of the given data. Several numerical results validate that the proposed model predicts the oscillatory pattern of the data well and demonstrate its outperformance compared to the result from the existing method.