Related papers: Deep Neural Helmholtz Operators for 3D Elastic Wav…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…
The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the…
A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…
Inversion of electromagnetic data finds applications in many areas of geophysics. The inverse problem is commonly solved with either deterministic optimization methods (such as the nonlinear conjugate gradient or Gauss-Newton) which are…
This paper considers large-scale simulations of wave propagation phenomena. We argue that it is possible to accurately compute a wavefield by decomposing it onto a largely incomplete set of eigenfunctions of the Helmholtz operator, chosen…
Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…
We develop a deep learning approach to extract ray directions at discrete locations by analyzing highly oscillatory wave fields. A deep neural network is trained on a set of local plane-wave fields to predict ray directions at discrete…
The use of neural operators in a digital twin model of an offshore floating structure can provide a paradigm shift in structural response prediction and health monitoring, providing valuable information for real-time control. In this work,…
In the last decade, deep learning has become a major component of artificial intelligence. The workhorse of deep learning is the optimization of loss functions by stochastic gradient descent (SGD). Traditionally in deep learning, neural…
Understanding human activity is very challenging even with the recently developed 3D/depth sensors. To solve this problem, this work investigates a novel deep structured model, which adaptively decomposes an activity instance into temporal…
Reliability analysis is a formidable task, particularly in systems with a large number of stochastic parameters. Conventional methods for quantifying reliability often rely on extensive simulations or experimental data, which can be costly…
Surrogate modeling of wave propagation and scattering (i.e. the wave speed and source to wave field map) in heterogeneous media has significant potential in applications such as seismic imaging and inversion. High-contrast settings, such as…
A fast method is proposed for solving the high frequency Helmholtz equation. The building block of the new fast method is an overlapping source transfer domain decomposition method for layered medium, which is an extension of the source…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
Solving time-harmonic wave propagation problems in the frequency domain and within heterogeneous media brings many mathematical and computational challenges, especially in the high frequency regime. We will focus here on computational…
Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…
Current groundwater models face a significant challenge in their implementation due to heavy computational burdens. To overcome this, our work proposes a cost-effective emulator that efficiently and accurately forecasts the impact of…
Full Waveform Inversion (FWI) is an inverse problem for estimating the wave velocity distribution in a given domain, based on observed data on the boundaries. The inversion is computationally demanding because we are required to solve…
Underwater explosions produce complex fluid phenomena relevant to diverse applications including maritime engineering, medical therapeutics, and inertial confinement fusion. These systems exhibit multiphase flows, chemical kinetics, and…
We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a…