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This article considers the computational (acoustic) wave propagation in strongly heterogeneous structures beyond the assumption of periodicity. A high contrast between the constituents of microstructured multiphase materials can lead to…

Numerical Analysis · Mathematics 2020-01-29 Daniel Peterseim , Barbara Verfürth

We address propagation and entanglement of Gaussian states in optical media characterised by non-trivial spectral densities. In particular, we consider environments with a finite bandwidth and show that in the low temperature regime: i)…

Quantum Physics · Physics 2025-02-18 Berihu Teklu , Matteo Bina , Matteo G. A. Paris

We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…

Numerical Analysis · Mathematics 2022-02-07 A. Martinez-Finkelshtein , D. Ramos-Lopez , D. R. Iskander

We present a general, Gaussian spatial mode propagation formalism for describing the generation of higher order multi-spatial-mode beams generated during nonlinear interactions. Furthermore, to implement the theory, we simulate optical…

In this paper, we consider the strong convergence of the time-space fractional diffusion equation driven by fractional Gaussion noise with Hurst index $H\in(\frac{1}{2},1)$. A sharp regularity estimate of the mild solution and the numerical…

Numerical Analysis · Mathematics 2021-01-07 Daxin Nie , Weihua Deng

We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…

Machine Learning · Computer Science 2020-06-09 Ang Yang , Cheng Li , Santu Rana , Sunil Gupta , Svetha Venkatesh

In estimation theory, the Kushner equation provides the evolution of the probability density of the state of a dynamical system given continuous-time observations. Building upon our recent work, we propose a new way to approximate the…

Machine Learning · Statistics 2023-10-04 Marc Lambert , Silvère Bonnabel , Francis Bach

Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…

Machine Learning · Statistics 2024-08-26 Ayoub Belhadji , Qianyu Julie Zhu , Youssef Marzouk

Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…

Instrumentation and Methods for Astrophysics · Physics 2017-01-26 Yanning Fu , Jacques Laskar

Paraxial diffraction modeling based on the Fourier transform has seen widespread implementation for simulating the response of a diffraction-limited optical system. For systems where the paraxial assumption is not sufficient, a class of…

This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an…

Computational Engineering, Finance, and Science · Computer Science 2026-05-19 Maximilian Nolte , Riccardo Torchio , Sebastian Schöps , Jürgen Dölz , Felix Wolf , Albert E. Ruehli

In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and…

Machine Learning · Computer Science 2024-10-14 Yifan Chen , Daniel Zhengyu Huang , Jiaoyang Huang , Sebastian Reich , Andrew M. Stuart

Semiclassical Gaussian approximations to the Boltzmann operator have become an important tool for the investigation of thermodynamic properties of clusters of atoms at low temperatures. Usually, numerically expensive thawed Gaussian…

Chemical Physics · Physics 2011-01-26 Holger Cartarius , Eli Pollak

A novel 3-D higher-order finite-difference time-domain framework with complex frequency-shifted perfectly matched layer for the modeling of wave propagation in cold plasma is presented. Second- and fourth-order spatial approximations are…

Plasma Physics · Physics 2013-10-25 Konstantinos P. Prokopidis

Using Gaussian integral transform techniques borrowed from functional-integral field theory and the replica trick we derive a version of the coherent-potential approximation (CPA) suited for describing ($i$) the diffusive (hopping) motion…

Disordered Systems and Neural Networks · Physics 2015-06-15 S. Köhler , G. Ruocco , W. Schirmacher

Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…

Numerical Analysis · Mathematics 2022-04-11 Kai Diethelm

We develop and analyze a numerical method for stochastic time-fractional diffusion driven by additive fractionally integrated Gaussian noise. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative of order…

Numerical Analysis · Mathematics 2018-10-04 Bangti Jin , Yubin Yan , Zhi Zhou

In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…

Numerical Analysis · Mathematics 2020-03-24 Da Li , Keran Li , Wenyuan Liao

A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…

Machine Learning · Computer Science 2014-04-30 Michael Mathieu , Yann LeCun

We present a simple method to decompose the Green forms corresponding to a large class of interesting symmetric Dirichlet forms into integrals over symmetric positive semi-definite and finite range (properly supported) forms that are…

Probability · Mathematics 2019-05-10 Roland Bauerschmidt