Parameter Estimation of Acoustic Wave Equations Using Hidden Physics Models

Abstract

In this article, we present one numerical approach to infer the model parameters and state variables of acoustic wave equations. The method we consider is based on the recently proposed method-the so-called hidden physics model. With placing Gaussian process (GP) prior on the state variables, the structure and model parameters of acoustic wave equations are encoded into the kernel function of a multioutput GP. The purpose of this article includes: 1) testing the applicability of hidden physics model to infer the velocity, density, and state variables of the acoustic wave equation, which is important for many applications in geophysics; 2) adapting the method to handle for both homogeneous and heterogeneous media that are of practical interest; and 3) exploring efficient sequential sampling methods to improve the sampling efficiency. We suggest that the expected-improvement-based sequential sampling method would be effective for most practical problems related to acoustic wave propagation. Besides, we demonstrate the performance of the proposed scheme via several benchmark problems.