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

2021/08/26 by Majid Rasht‐Behesht, Majid Rasht-Behesht, Christian Huber +2 · 28 citations
Computer Science · Earth and Planetary Sciences · Physics and Astronomy · #Seismic Imaging and Inversion Techniques #Seismic Waves and Analysis #Seismology and Earthquake Studies #physics.comp-ph #physics.geo-ph

paper · pdf · doi:10.1029/2021jb023120

arxiv created 2021/08/26 · openalex publication_date 2022/04/12 · openalex created_date 2022/05/05 · arxiv updated 2022/06/08 · openalex updated_date 2026/07/28

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.

Citations

• SimPEG: An open source framework for simulation and gradient based parameter estimation in geophysical applications
• On the limited memory BFGS method for large scale optimization
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• TensorFlow: A system for large-scale machine learning
• Understanding and mitigating gradient pathologies in physics-informed neural networks
• NSFnets (Navier-Stokes Flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations
• B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
• Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
• Solving the wave equation with physics-informed deep learning
• Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
• A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
• PINNtomo: Seismic tomography using physics-informed neural networks
• Physics-Informed Neural Networks for Heat Transfer Problems
• Physics-informed machine learning
• When and why PINNs fail to train: A neural tangent kernel perspective
• Physics-informed neural networks (PINNs) for fluid mechanics: a review

Cited by

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• Room impulse response reconstruction with physics-informed deep learning
• Accelerating wave simulations with neural dispersion correctors
• RamPINN: Recovering Raman Spectra From Coherent Anti-Stokes Spectra Using Embedded Physics
• Differentiable physics for sound field reconstruction
• Neural network approximation in discrete dual norms with adaptive test spaces
• Physics-informed neural networks for offshore tsunami data assimilation
• Physics-informed neural network solves minimal surfaces in curved spacetime
• Physics-informed waveform inversion using pretrained wavefield neural operators
• Neuro-Spectral Architectures for Causal Physics-Informed Networks
• Neural Networks as Surrogate Solvers for Time-dependent Accretion Disk Dynamics
• An effective physics-informed neural operator framework for predicting wavefields
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• OkadaTorch: A Differentiable Programming of Okada Model to Calculate Displacements and Strains from Fault Parameters
• A physics-informed neural network for modeling fracture without gradient damage: formulation, application, and assessment
• Towards Robust Surrogate Models: Benchmarking Machine Learning Approaches to Expediting Phase Field Simulations of Brittle Fracture
• NeuroPDE: A Neuromorphic PDE Solver Based on Spintronic and Ferroelectric Devices
• Three-dimensional crustal deformation analysis using physics-informed deep learning
• A Neural Operator based on Dynamic Mode Decomposition
• Quantum Physics-Informed Neural Networks for Maxwell's Equations: Circuit Design, "Black Hole" Barren Plateaus Mitigation, and GPU Acceleration
• Neural Tangent Kernel Analysis to Probe Convergence in Physics-informed Neural Solvers: PIKANs vs. PINNs
• Leveraging Influence Functions for Resampling Data in Physics-Informed Neural Networks
• A detailed and comprehensive account of fractional Physics-Informed Neural Networks: From implementation to efficiency
• DiffPINN: Generative diffusion-initialized physics-informed neural networks for accelerating seismic wavefield representation
• iPINNER: An Iterative Physics-Informed Neural Network with Ensemble Kalman Filter
• Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundles
• Deep Reparameterization for Full Waveform Inversion: Architecture Benchmarking, Robust Inversion, and Multiphysics Extension
• Leveraging Deep Operator Networks (DeepONet) for Acoustic Full Waveform Inversion (FWI)

Related

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