Physics-informed Neural Networks (PINNs) for Wave Propagation and Full Waveform Inversions (2108.12035v1)

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 2D 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.

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

The paper presents a paper on the application of Physics-Informed Neural Networks (PINNs) for solving wave propagation and full waveform inversion (FWI) problems in seismology. This research is motivated by the technical and computational challenges inherent in these problems, especially when data acquisition is limited to surface observations. The authors propose using PINNs to address these challenges, as these networks can incorporate both boundary conditions and a priori knowledge of subsurface structures in their formulations.

The paper evaluates the performance of PINNs in both forward modeling and inversion scenarios using synthetic data. For forward modeling, the authors focus on the 2D acoustic wave equation and demonstrate how PINNs handle boundary conditions, specifically absorbing boundaries, traditionally challenging for conventional solvers. While PINNs offer flexibility in implementation, the results suggest that traditional methods such as spectral element and finite difference methods are generally more efficient for forward modeling tasks.

More significantly, the paper highlights the advantages of PINNs in inversion modeling. The experimental results indicate that PINNs can perform FWIs with limited computational complexity and with minimal observed data, primarily restricted to seismograms at the surface. The authors detail several synthetic case studies, including homogeneous and heterogeneous models with varying complexities and seismic source types. In each case, PINNs successfully recover the subsurface wavespeed distribution, demonstrating their robustness and simplification in implementation compared to traditional methods.

Key numerical results from this research show PINNs' efficiency in capturing reflections from free surfaces and accurately modeling absorbing boundary conditions without explicitly enforcing them. The paper proposes integrating multiple seismic events within one unified PINN framework to optimize inverse problem solving while maintaining computational efficiency. Additionally, the authors discuss implications for broader geophysical applications, such as magnetotelluric and gravitational datasets, given the adaptable nature of PINNs.

The research showcases the potential of PINNs in addressing inverse problems in geophysics, emphasizing their ability to function with limited labeled data and their meshless formalism. Looking forward, PINNs could be instrumental in expanding the capabilities for joint and Bayesian inversions, paving the way for richer interpretations of subsurface structures.

As with any emerging methodology, there are challenges to address, such as optimizing the hyperparameters involved and the criteria for choosing the neural network architecture. Future work could explore the implementation of PINNs in elastic approximations using domain decomposition strategies on multi-GPU platforms to enhance computational efficiency further. Overall, the paper posits PINNs as a promising approach for improving the accuracy and efficiency of seismic inversions in complex media.