Deep Learning–Assisted Computational Modeling of Nonlinear Acoustic Phenomena in Heterogeneous Media

Abstract

Proper simulation of nonlinear acoustic wave propagation in heterogeneous materials is an important computational problem as the finite-amplitude effects are steep, the material properties vary spatially, and the cost and time limitations of standard numerical solutions can be difficult to overcome when one is faced with a multi-scale wave problem being solved. Methods based on classical physics, such as finite-differentiation and finite-element methods, of solving nonlinear acoustic equations, frequently have a serious computational overhead, numerical dispersion, and scalability issues, especially in complicated heterogeneous settings. A computational framework is presented in the given work based on deep learning, providing a substantial design of nonlinear field evolution in acoustics and maintaining key physical features. The framework combines a lower-order nonlinear acoustic solver with a deep neural network which serves as a surrogate neural network that recovers fine scale nonlinear features of high-resolution simulations. The neural surrogate is trained using high-fidelity numerical solutions that permit the prediction of waveform perturbation, harmonic generation as well as shock formation resulting from nonlinear propagation and heterogeneity of the medium with high accuracy. The suggested hybrid method is a cheap method that saves the computational cost whilst preserving the high agreement with full-resolution reference simulations even when used in a variety of heterogeneous configurations. It has been shown numerically that the technique can obtain significant speedup without affecting physical fidelity, and was therefore effective in applications that need rapid or near real-time acoustic analysis. The framework that has been developed offers a physically consistent and scalable the alternative to strictly data-driven or purely numerical modelling and a practical approach to nonlinear acoustic simulations using biomedical ultrasound, nondestructive assessment and geophysical exploration.