Physics-informed Neural Networks (PINNs) for Wave Propagation and Full Waveform Inversions

Abstract

We propose a new approach to the solution of the wave propagation and full waveform inversions (FWIs) based on a recent advance in deep learning called Physics-Informed Neural Networks (PINNs). In this study, we present an algorithm for PINNs applied to the acoustic wave equation and test the model with both forward wave propagation and FWIs case studies. These synthetic case studies are designed to explore the ability of PINNs to handle varying degrees of structural complexity using both teleseismic plane waves and seismic point sources. PINNs' meshless formalism allows for a flexible implementation of the wave equation and different types of boundary conditions. For instance, our models demonstrate that PINN automatically satisfies absorbing boundary conditions, a serious computational challenge for common wave propagation solvers. Furthermore, a priori knowledge of the subsurface structure can be seamlessly encoded in PINNs' formulation. We find that the current state-of-the-art PINNs provide good results for the forward model, even though spectral element or finite difference methods are more efficient and accurate. More importantly, our results demonstrate that PINNs yield excellent results for inversions on all cases considered and with limited computational complexity. Using PINNs as a geophysical inversion solver offers exciting perspectives, not only for the full waveform seismic inversions, but also when dealing with other geophysical datasets (e.g., magnetotellurics, gravity) as well as joint inversions because of its robust framework and simple implementation.

Machine Learning Developments and Applications in Solid‐Earth Geosciences: Fad or Future?

“…(2021), X. Huang and Alkhalifah (2021), and Rasht‐Behesht et al. (2022) improve the efficiency of seismic inversion by accelerating the wave‐equation simulation process. Chen and Saygin (2021) propose to utilize latent‐space representation of the seismic data compressed by the convolutional autoencoder.…”

Physics-informed Neural Networks approach to solve the Blasius function

“…ViscoelasticNet is another PINN framework for stress discovery and model selection [17]. PINNs can also be used to solve Reynoldsaveraged Navier-Stokes equations [18], full waveform seismic inversions in 2D acoustic media, and wave propagation as it seamlessly handles boundary conditions and physical constraints [19]. In addition to addressing ill-posed problems beyond the scope of conventional computing techniques, PINNs can also close the discrepancy between computational and experimental heat transfer [20].…”

Seismic Wave Propagation and Inversion with Neural Operators

“…These approaches to solving PDEs offer not only speedup in computational capabilities, but also low-memory overhead, differentiability, and on-demand solutions. Such advantages facilitate deep learning being used for seismic inversion [26][27][28] . However, one major limitation of these approaches is that the solutions generated by these models are dependent on the specific spatial and temporal discretization in the numerical simulation training set.…”