Corpus ID: 236469545

Numerical wave propagation aided by deep learning

@article{Nguyen2021NumericalWP,
  title={Numerical wave propagation aided by deep learning},
  author={Hieu Nguyen and R. Tsai},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.13184}
}
  • Hieu Nguyen, R. Tsai
  • Published 2021
  • Mathematics, Computer Science
  • ArXiv
We propose a deep learning approach for wave propagation in media with multiscale wave speed, using a second-order linear wave equation model. We use neural networks to enhance the accuracy of a given inaccurate coarse solver, which under-resolves a class of multiscale wave media and wave fields of interest. Our approach involves generating training data by the given computationally efficient coarse solver and another sufficiently accurate solver, applied to a class of wave media (described by… Expand

References

SHOWING 1-10 OF 34 REFERENCES
Neural network augmented wave-equation simulation
TLDR
This work exploits intrinsic one-to-one similarities between timestepping algorithm with Convolutional Neural Networks (CNNs), and proposes to intersperse CNNs between low-fidelity timesteps to limit the numerical dispersion artifact introduced by a poor discretization of the Laplacian. Expand
Solving the wave equation with physics-informed deep learning
We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presentsExpand
Multiscale Methods for Wave Propagation in Heterogeneous Media Over Long Time
Multiscale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales ofExpand
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Abstract We introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinearExpand
A Nonlinear Method for Imaging with Acoustic Waves Via Reduced Order Model Backprojection
TLDR
A novel nonlinear imaging method for the acoustic wave equation based on model order reduction that resolves all the dynamical behavior captured by the data, so the error from the imperfect knowledge of the velocity model is purely kinematic. Expand
A high-order multiscale finite-element method for time-domain elastic wave modeling in strongly heterogeneous media
TLDR
This work develops a novel high-order multiscale finite-element method to model elastic wave propagation in strongly heterogeneous media in the time domain by using high- order multiscaling basis functions to capture the fine-scale heterogeneities on the coarse mesh. Expand
Gaussian beam decomposition of high frequency wave fields
TLDR
The goal is to extract the necessary parameters for a Gaussian beam superposition from this wave field, so that further evolution of the high frequency waves can be computed by the method of Gaussian beams. Expand
A stable parareal-like method for the second order wave equation
TLDR
This work presents a data-driven strategy in which the computed data gathered from each iteration are re-used to stabilize the coupling by minimizing the wave energy residual of the fine and coarse propagated solutions. Expand
Finite Element Heterogeneous Multiscale Method for the Wave Equation
TLDR
Optimal error estimates in the energy norm and the L2 norm and convergence to the homogenized solution are proved, when both the macro and the micro scales are refined simultaneously. Expand
Numerical homogenization of the acoustic wave equations with a continuum of scales
In this paper, we consider numerical homogenization of acoustic wave equations with heterogeneous coefficients, namely, when the bulk modulus and the density of the medium are only bounded. We showExpand
...
1
2
3
4
...