Simulating seismic multifrequency wavefields with the Fourier feature physics-informed neural network

Song, Chao; Wang, Yanghua

doi:10.1093/gji/ggac399

Cited by 34 publications

(7 citation statements)

References 51 publications

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“…PINNs have been recently explored for solving geophysical forward modeling ( 31 , 32 , 34 , 59 , 122 – 125 ) and inversion ( 28 , 47 , 126 – 128 ), which involve intensive work on PDEs. Taking seismic modeling and inversion as an example, we can construct a basic framework for PINN-based geophysical forward modeling ( Lower panels in Fig.…”

Section: Integrating Constraints Into Loss Functionsmentioning

confidence: 99%

Sensing prior constraints in deep neural networks for solving exploration geophysical problems

et al. 2023

Proc. Natl. Acad. Sci. U.S.A.

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One of the key objectives in geophysics is to characterize the subsurface through the process of analyzing and interpreting geophysical field data that are typically acquired at the surface. Data-driven deep learning methods have enormous potential for accelerating and simplifying the process but also face many challenges, including poor generalizability, weak interpretability, and physical inconsistency. We present three strategies for imposing domain knowledge constraints on deep neural networks (DNNs) to help address these challenges. The first strategy is to integrate constraints into data by generating synthetic training datasets through geological and geophysical forward modeling and properly encoding prior knowledge as part of the input fed into the DNNs. The second strategy is to design nontrainable custom layers of physical operators and preconditioners in the DNN architecture to modify or shape feature maps calculated within the network to make them consistent with the prior knowledge. The final strategy is to implement prior geological information and geophysical laws as regularization terms in loss functions for training the DNNs. We discuss the implementation of these strategies in detail and demonstrate their effectiveness by applying them to geophysical data processing, imaging, interpretation, and subsurface model building.

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Section: Integrating Constraints Into Loss Functionsmentioning

confidence: 99%

Sensing prior constraints in deep neural networks for solving exploration geophysical problems

et al. 2023

Proc. Natl. Acad. Sci. U.S.A.

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“…These are called surrogate models because they can interpolate PDE solutions between different model parameters. PINN surrogate models perform well for finite-dimensional parameters such as strength and position 27,28 , but cannot be directly applied to infinite-dimensional quantities such as functions and shapes. Although these can be represented in parametric form 24,27 , they incur a trade-off between the expressive power and the training tractability.…”

Section: Physics-informed Deep Surrogate Modelmentioning

confidence: 99%

Fault Geometry Invariance for Physics-Informed Crustal Deformation Learning

Okazaki,

Hirahara,

Ueda

2023

Preprint

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Earthquake-induced crustal deformation provides valuable insights into the mechanisms of tectonic processes. Dislocation models offer a fundamental framework for comprehending such deformation, and two-dimensional antiplane dislocations are used to describe strike-slip faults. Previous earthquake deformation analyses observed that antiplane dislocations due to uniform fault slips are influenced predominantly by fault tips. In this study, we state a general principle of fault geometry invariance in antiplane dislocations and exploit its theoretical consequence to define dislocation potentials that enable a streamlined crustal deformation analysis. To demonstrate the benefits of this theory, we construct a rapid numerical solver for crustal deformation caused by variable fault slip scenarios using physics-informed neural networks, whose mesh-free property is suitable for modeling dislocation potentials. We anticipate that fault geometry invariance and the dislocation potential will further the analysis of antiplane crustal deformation, particularly for uncertainty quantification and inversion analysis regarding unknown fault geometries in realistic crustal structures.

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“…In recent years, with the rapid development of ocean sound field calculation, atmospheric pollution diffusion simulation, seismic wave inversion and prediction, etc [48][49][50], higher requirements are put forward for the accuracy and efficiency of numerical methods, and it is urgent to develop new methods and tools for solving PDE. The researchers have used physics-informed neural networks to solve the frequency-domain wave equation, simulated seismic multifrequency wavefields, and conducted in-depth research on wave propagation and full waveform inversions, and achieved a series of research results [51][52][53][54][55]. It is expected that PINNs can provide a new opportunity to solve a large number of scientific and engineering problems at the present time, and bring breakthroughs in the relevant research.…”

Section: Introductionmentioning

confidence: 99%

Solving nonlinear soliton equations using improved physics-informed neural networks with adaptive mechanisms

Guo

Cao

Peng³

2023

Commun. Theor. Phys.

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Partial differential equation (PDE) is an important tool for scientific research and are widely used in various fields. However, it is usually very difficult to obtain accurate analytical solutions of partial differential equations, and numerical methods to solve PDEs are often computationally intensive and very time-consuming. In recent years, Physics Informed Neural Networks (PINNs) have been successfully applied to find numerical solutions of partial differential equations (PDEs) and have shown great potential. All the while, solitary waves have been of great interest to researchers in the field of nonlinear science. In this paper, we perform numerical simulations of solitary wave solutions of several partial differential equations using improved PINNs. The improved PINNs not only incorporate constraints on the control equations to ensure the interpretability of the prediction results, which is important for physical field simulations. In addition, an adaptive activation function is introduced. By introducing hyperparameters in the activation function to change the slope of the activation function to avoid the disappearance of the gradient, thereby saving computing time and speeding up training. In this paper, the mKdV equation, the improved Boussinesq equation, the CDGSK equation and the p-gBKP equation are selected for study, and the errors of the simulation results are analyzed to assess the accuracy of the predicted solitary wave solution. The experimental results show that the improved PINNs are significantly better than the traditional PINNs with shorter training time but more accurate prediction results. The improved PINNs improve the training speed by more than 1.5 times compared with the traditional PINNs, while maintaining the prediction error less than $10^{-2}$ in this order of magnitude.

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Simulating seismic multifrequency wavefields with the Fourier feature physics-informed neural network

Cited by 34 publications

References 51 publications

Sensing prior constraints in deep neural networks for solving exploration geophysical problems

Sensing prior constraints in deep neural networks for solving exploration geophysical problems

Fault Geometry Invariance for Physics-Informed Crustal Deformation Learning

Solving nonlinear soliton equations using improved physics-informed neural networks with adaptive mechanisms

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