相关论文: Windowed Fourier Propagator: A Frequency-Local Neu…

We present a new methodology, based on the WKB approximation and Fast Fourier Transforms, for the evaluation of wave propagation through inhomogeneous media. This method can accurately resolve fields containing caustics, while still…

Within the expansive domain of optical sciences, achieving the precise characterization of light beams stands as a fundamental pursuit, pivotal for various applications, including telecommunications and imaging technologies. This study…

We extend the Weak Adversarial Neural Pushforward Method (WANPM) to fractional Fokker-Planck equations, in which the classical Laplacian diffusion operator is replaced by the fractional Laplacian of order alpha in (0, 2]. The solution…

With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible…

We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…

Neural operators have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). However, standard spectral methods based on Fourier transforms struggle with problems involving discontinuous…

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…

One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric…

Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…

In this paper, we address the problem of efficient execution of a computation pattern, referred to here as the irregular wavefront propagation pattern (IWPP), on hybrid systems with multiple CPUs and GPUs. The IWPP is common in several…

Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations…

Neural operators are becoming the default tools to learn solutions to governing partial differential equations (PDEs) in weather and ocean forecasting applications. Despite early promising achievements, significant challenges remain,…

Solving the wave equation is one of the most (if not the most) fundamental problems we face as we try to illuminate the Earth using recorded seismic data. The Helmholtz equation provides wavefield solutions that are dimensionally reduced,…

Neural operators have gained recognition as potent tools for learning solutions of a family of partial differential equations. The state-of-the-art neural operators excel at approximating the functional relationship between input functions…

We introduce an extension of continuous wavelet theory that enables an efficient implementation of multiplicative operators in the coefficient space. In the new theory, the signal space is embedded in a larger abstract signal space -- the…

Controlling waves by actively changing the material parameters of a medium enables the development of new acoustic and electrical devices. Modulating the material breaks classical properties like reciprocity and the conservation of energy,…

We introduce a new type of Wannier functions (WFs) obtained by minimizing the conventional spread functional with a penalty term proportional to the variance of the spread distribution. This modified Wannierisation scheme is less prone to…

This study explores the use of fractional calculus as a possible tool to model wave propagation in complex, heterogeneous media. We illustrate the methodology by focusing on elastic wave propagation in a one-dimensional periodic rod. The…

Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…

Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions,…