• Corpus ID: 203626777

Neural network augmented wave-equation simulation

@article{Siahkoohi2019NeuralNA,
  title={Neural network augmented wave-equation simulation},
  author={Ali Siahkoohi and Mathias Louboutin and F. Herrmann},
  journal={ArXiv},
  year={2019},
  volume={abs/1910.00925}
}
Accurate forward modeling is important for solving inverse problems. An inaccurate wave-equation simulation, as a forward operator, will offset the results obtained via inversion. In this work, we consider the case where we deal with incomplete physics. One proxy of incomplete physics is an inaccurate discretization of Laplacian in simulation of wave equation via finite-difference method. We exploit intrinsic one-to-one similarities between timestepping algorithm with Convolutional Neural… 
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References

SHOWING 1-10 OF 15 REFERENCES
Fast approximate simulation of seismic waves with deep learning
TLDR
This work simulates the response of acoustic seismic waves in horizontally layered media using a deep neural network that is able to directly approximate the recorded seismic response at multiple receiver locations in a single inference step, resulting in an order of magnitude reduction in simulation time.
Devito: an embedded domain-specific language for finite differences and geophysical exploration
TLDR
Devito, a new domain-specific language for implementing high-performance finite-difference partial differential equation solvers within Python and making heavy use of SymPy, a symbolic mathematics library, is introduced, making it possible to develop finite-Difference simulators quickly using a syntax that strongly resembles the mathematics.
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
  • M. Raissi
  • Computer Science
    J. Mach. Learn. Res.
  • 2018
TLDR
This work puts forth a deep learning approach for discovering nonlinear partial differential equations from scattered and potentially noisy observations in space and time by approximate the unknown solution as well as the nonlinear dynamics by two deep neural networks.
Learned Iterative Solvers for the Helmholtz Equation
TLDR
This work proposes a ‘learned’ iterative solver for the Helmholtz equation, by combining traditional Krylov-based solvers with machine learning, and demonstrates the effectiveness of this approach under a 1.5-D assumption.
Adam: A Method for Stochastic Optimization
TLDR
This work introduces Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments, and provides a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework.
Architecture and Performance of Devito, a System for Automated Stencil Computation
TLDR
The architecture of the Devito compiler, as well as the performance optimizations that are applied when generating code, are presented and the effectiveness of such performance optimizations is demonstrated using operators drawn from seismic imaging applications.
Perceptual Losses for Real-Time Style Transfer and Super-Resolution
TLDR
This work considers image transformation problems, and proposes the use of perceptual loss functions for training feed-forward networks for image transformation tasks, and shows results on image style transfer, where aFeed-forward network is trained to solve the optimization problem proposed by Gatys et al. in real-time.
How transferable are features in deep neural networks?
TLDR
This paper quantifies the generality versus specificity of neurons in each layer of a deep convolutional neural network and reports a few surprising results, including that initializing a network with transferred features from almost any number of layers can produce a boost to generalization that lingers even after fine-tuning to the target dataset.
Generative Adversarial Nets
We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a
Deep Residual Learning for Image Recognition
TLDR
This work presents a residual learning framework to ease the training of networks that are substantially deeper than those used previously, and provides comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth.
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