相关论文: Windowed Fourier Propagator: A Frequency-Local Neu…
Vision modeling has advanced rapidly with Transformers, whose attention mechanisms capture visual dependencies but lack a principled account of how semantic information propagates spatially. We revisit this problem from a wave-based…
Simulation tools for photoacoustic wave propagation have played a key role in advancing photoacoustic imaging by providing quantitative and qualitative insights into parameters affecting image quality. Classical methods for numerically…
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…
Deterministic neural operators perform well on many PDEs but can struggle with the approximation of high-frequency wave phenomena, where strong input-to-output sensitivity makes operator learning challenging, and spectral bias blurs…
Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…
Ultrashort-pulse propagation in graded-index multimode fibers is a highly nonlinear phenomenon driven by several physical processes. Although conventional numerical solvers can reproduce this behavior with high fidelity, their computational…
Irregular propagation environments with complex scattering effects challenge traditional ray-tracing-based localization. However, the environment's complexity enables solutions based on wave fingerprints (WFPs). Yet, since WFPs rely on the…
Fourier-encoded implicit neural representations (INRs) have shown strong capability in modeling continuous signals from discrete samples. However, conventional Fourier feature mappings use a fixed set of frequencies over the entire spatial…
This paper presents a new approach to modelling wave propagation in random, linearly elastic materials, namely by means of Fourier integral operators (FIOs). The FIO representation of the solution to the equations of motion can be used to…
High-frequency features are critical in multiscale phenomena such as turbulent flows and phase transitions, since they encode essential physical information. The recently proposed Wavelet Neural Operator (WNO) utilizes wavelets'…
The numerical simulation of wave propagation in semiclassical (high-frequency) problems is well known to pose a formidable challenge. In this work, a new phase-space approach for the numerical simulation of semiclassical wave propagation,…
This contribution presents a novel Windowed Green Function (WGF) method for the solution of problems of wave propagation, scattering and radiation for structures which include open (dielectric) waveguides, waveguide junctions, as well as…
Solving cell problems in homogenization is hard, and available deep-learning frameworks fail to match the speed and generality of traditional computational frameworks. More to the point, it is generally unclear what to expect of…
This paper introduces a new Windowed Green Function (WGF) method for the numerical integral-equation solution of problems of electromagnetic scattering by obstacles in presence of dielectric or conducting half-planes. The WGF method, which…
We present a spectrally accurate fast algorithm for evaluating the solution to the scalar wave equation in free space driven by a large collection of point sources in a bounded domain. With $M$ sources temporally discretized by $N_t$ time…
Accurately estimating the refractive environment over multiple frequencies within the marine atmospheric boundary layer is crucial for the effective deployment of radar technologies. Traditional parabolic equation simulations, while…
Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…
Modeling high-frequency information is a critical challenge in scientific machine learning. For instance, fully turbulent flow simulations of the Navier-Stokes equations at Reynolds numbers 3500 and above can generate high-frequency signals…
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…
Deep learning technique has dramatically boosted the performance of face alignment algorithms. However, due to large variability and lack of samples, the alignment problem in unconstrained situations, \emph{e.g}\onedot large head poses,…