Seismic Wave Propagation and Inversion with Neural Operators

Yang, Yan; Gao, Angela F.; Ramírez‐Castellanos, Julio; Ross, Zachary E.; Azizzadenesheli, Kamyar; Clayton, Robert W.

doi:10.1785/0320210026

Cited by 33 publications

(13 citation statements)

References 51 publications

(75 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although there is a recent example in acoustic wave applications 33 , we are not aware of previous work which attempts to use the FNO to learn the elastic wave equation Green's function and its inverse, for a complex model. In order to explore the feasibility of this approach in complex media, we focused on 2D examples which reduce the computational demand and allows us to constrain the approximate cost and challenges associated with producing reasonable results.…”

Section: D Modelsmentioning

confidence: 99%

Imaging and seismic modelling inside volcanoes using machine learning

O’Brien

Bean

Meiland

et al. 2023

Sci Rep

View full text Add to dashboard Cite

Despite advances in seismology and computing, the ability to image subsurface volcanic environments is poor, limiting our understanding of the overall workings of volcanic systems. This is related to substantive structural heterogeneities which strongly scatters seismic waves obscuring the ballistic arrivals normally used in seismology for wave velocity determination. Here we address this constraint by, using a deep learning approach, a Fourier neural operator (FNO), to model and invert seismic signals in volcanic settings. The FNO is trained using 40,000+ simulations of elastic wave propagation through complex volcano models, and includes the full scattered wavefield. Once trained, the forward network is used to predict elastic wave propagation and is shown to accurately reproduce the seismic wavefield. The FNO is also trained to predict heterogeneous velocity models given a limited set of input seismograms. It is shown to capture details of the complex velocity structure that lie far outside the ability of current methods available in volcano imagery.

show abstract

Section: D Modelsmentioning

confidence: 99%

Imaging and seismic modelling inside volcanoes using machine learning

O’Brien

Bean

Meiland

et al. 2023

Sci Rep

View full text Add to dashboard Cite

show abstract

“…However, solving these equations can be computationally expensive. Yang et al (2021) discuss neural operators as a way to overcome the computation constraints by training the networks on an ensemble of wave equation data represented as low-resolution matrices. The neural operator is trained to learn the 2D acoustic wave equation, defined as the mapping from velocity, defined on an irregular mesh, to the wavefield solution.…”

Section: Seismic Wave Propagationmentioning

confidence: 99%

Fast Resolution Agnostic Neural Techniques to Solve Partial Differential Equations

Viswanath¹,

Rahman²,

Vyas³

et al. 2023

Preprint

View full text Add to dashboard Cite

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering and mathematical problems involving functions of several variables, such as the propagation of heat or sound, fluid flow, elasticity, electrostatics, electrodynamics, and more. While this has led to solving many complex phenomena, there are still significant limitations. Conventional approaches such as Finite Element Methods (FEMs) and Finite Differential Methods (FDMs) require considerable time and are computationally expensive. In contrast, machine learning-based methods such as neural networks are faster once trained, but tend to be restricted to a specific discretization. This article aims to provide a comprehensive summary of conventional methods and recent machine learning-based methods to approximate PDEs numerically. Furthermore, we highlight several key architectures centered around the neural operator, a novel and fast approach (∼1000x) to learning the solution operator of a PDE. We will note how these new computational approaches can bring immense advantages in tackling many problems in fundamental and applied physics.

show abstract

“…Neural operators have been successfully used for learning the solution spaces of Partial Differential Equations (PDE). FNOs have been used to learn the solutions to the Accustic Wave-equation in two spatial dimensions [Yang et al, 2021]. Operator learning has transformed the field of physics-informed machine learning.…”

Section: Related Workmentioning

confidence: 99%

Generative Adversarial Neural Operators

Rahman¹,

Florez²,

Anandkumar³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

We propose the generative adversarial neural operator (GANO), a generative model paradigm for learning probabilities on infinite-dimensional function spaces. The natural sciences and engineering are known to have many types of data that are sampled from infinite-dimensional function spaces, where classical finite-dimensional deep generative adversarial networks (GANs) may not be directly applicable. GANO generalizes the GAN framework and allows for the sampling of functions by learning push-forward operator maps in infinite-dimensional spaces. GANO consists of two main components, a generator neural operator and a discriminator neural functional. The inputs to the generator are samples of functions from a user-specified probability measure, e.g., Gaussian random field (GRF), and the generator outputs are synthetic data functions. The input to the discriminator is either a real or synthetic data function. In this work, we instantiate GANO using the Wasserstein criterion and show how the Wasserstein loss can be computed in infinite-dimensional spaces. We empirically study GANOs in controlled cases where both input and output functions are samples from GRFs and compare its performance to the finite-dimensional counterpart GAN. We empirically study the efficacy of GANO on real-world function data of volcanic activities and show its superior performance over GAN. Furthermore, we find that for the function-based data considered, GANOs are more stable to train than GANs and require less hyperparameter optimization.

show abstract

Seismic Wave Propagation and Inversion with Neural Operators

Cited by 33 publications

References 51 publications

Imaging and seismic modelling inside volcanoes using machine learning

Imaging and seismic modelling inside volcanoes using machine learning

Fast Resolution Agnostic Neural Techniques to Solve Partial Differential Equations

Generative Adversarial Neural Operators

Contact Info

Product

Resources

About