Related papers: Wavefield solutions from machine learned functions
Solving the wave equation is essential to seismic imaging and inversion. The numerical solution of the Helmholtz equation, fundamental to this process, often encounters significant computational and memory challenges. We propose an…
Solving the wave equation is fundamental for geophysical applications. However, numerical solutions of the Helmholtz equation face significant computational and memory challenges. Therefore, we introduce a physics-informed convolutional…
Wavefield reconstruction inversion (WRI) formulates a PDE-constrained optimization problem to reduce cycle skipping in full-waveform inversion (FWI). WRI often requires expensive matrix inversions to reconstruct frequency-domain wavefields.…
We propose a physics-informed neural network as the forward model for tomographic reconstructions of biological samples. We demonstrate that by training this network with the Helmholtz equation as a physical loss, we can predict the…
Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is…
This paper deals with solving the 2D Helmholtz equation on non-parametric domains, leveraging a physics-informed neural operator network based on the DeepONet framework. We consider a 2D square domain with an inclusion of arbitrary boundary…
We develop efficient and high-order accurate solvers for the Helmholtz equation on complex geometry. The schemes are based on the WaveHoltz algorithm which computes solutions of the Helmholtz equation by time-filtering solutions of the wave…
Physics-Informed Neural Networks (PINNs) have gained increasing attention for solving partial differential equations, including the Helmholtz equation, due to their flexibility and mesh-free formulation. However, their low-frequency bias…
Photonic computing has recently become an interesting paradigm for high-speed calculation of computing processes using light-matter interactions. Here, we propose and study an electromagnetic wave-based structure with the ability to…
This paper proposes a plane wave activation based neural network (PWNN) for solving Helmholtz equation, the basic partial differential equation to represent wave propagation, e.g. acoustic wave, electromagnetic wave, and seismic wave.…
In this paper, we propose a phase shift deep neural network (PhaseDNN), which provides a uniform wideband convergence in approximating high frequency functions and solutions of wave equations. The PhaseDNN makes use of the fact that common…
Recently, Physics-Informed Neural Networks (PINNs) have gained significant attention for their versatile interpolation capabilities in solving partial differential equations (PDEs). Despite their potential, the training can be…
Frequency-domain wavefield solutions corresponding to the anisotropic acoustic wave equations can be used to describe the anisotropic nature of the earth. To solve a frequency-domain wave equation, we often need to invert the impedance…
Wavelet theory has been well studied in recent decades. Due to their appealing features such as sparse multiscale representation and fast algorithms, wavelets have enjoyed many tremendous successes in the areas of signal/image processing…
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 presents unique challenges due to the multi-scale,…
For problems of time-harmonic scattering by polygonal obstacles, embedding formulae provide a useful means of computing the far-field coefficient induced by any incident plane wave, given the far-field coefficient of a relatively small set…
Studying physics-informed neural networks (PINNs) for modeling partial differential equations to solve the acoustic wave field has produced promising results for simple geometries in two-dimensional domains. One option is to compute the…
We present a novel neural network architecture for the efficient prediction of sound fields in two and three dimensions. The network is designed to automatically satisfy the Helmholtz equation, ensuring that the outputs are physically…
The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…
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…