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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. [ABSTRACT FROM AUTHOR]

Multiscale elliptic equations with scale separation are often approximated by the corresponding homogenized equations with slowly varying homogenized coefficients (the G-limit). The traditional homogenization techniques typically rely on the periodicity of the multiscale coefficients, thus finding the G-limits often requires sophisticated techniques in more general settings even when multiscale coefficient is known, if possible. Alternatively, we propose a simple approach to estimate the G-limits from (noise-free or noisy) multiscale solution data, either from the existing forward multiscale solvers or sensor measurements. By casting this problem into an inverse problem, our approach adopts physics-informed neural networks (PINNs) algorithm to estimate the G-limits from the multiscale solution data by leveraging a priori knowledge of the underlying homogenized equations. Unlike the existing approaches, our approach does not rely on the periodicity assumption or the known multiscale coefficient during the learning stage, allowing us to estimate homogenized coefficients in more general settings beyond the periodic setting. We demonstrate that the proposed approach can deliver reasonable and accurate approximations to the G-limits as well as homogenized solutions through several benchmark problems. [ABSTRACT FROM AUTHOR]

A numerical approach based on the hidden physics model to estimate the model parameters of elastic wave equations with the sparse and noisy data is presented in this paper. Through discretizing the time derivatives of elastic wave equations and placing the priors of the state variables as Gaussian process, the model parameters and structure of elastic wave equations are encoded in the kernel function of a multi-output Gaussian process. In the learning stage, a parameter bound constraint condition is incorporated to enforce the physical bound of the model parameters. The numerical results from several benchmark problems, including homogeneous media, layer media, anisotropic media, and homogeneous model with an inclusion, demonstrate the feasibility and performance of the hidden physics model. • A hidden physics model is developed for parameter estimation of elastic wave equations. • A Physics-informed kernel is derived to encode the structure and model parameters of elastic wave equations. • An active learning strategy is suggested to improve the efficiency. • The performance of the hidden physics model is demonstrated by several benchmark problems. [ABSTRACT FROM AUTHOR]