相关论文: chebgreen: Learning and Interpolating Continuous E…

This paper is a revised version of the original paper of same title--published in Applied Mathematics Letters 89--containing some corrections and clarifications to the original text. We derive non-singular Green's functions for the…

Discovering causal relationship using multivariate functional data has received a significant amount of attention very recently. In this article, we introduce a functional linear structural equation model for causal structure learning when…

In calculating Green functions for interacting quantum systems numerically one often has to resort to finite systems which introduces a finite size level spacing. In order to describe the limit of system size going to infinity correctly,…

Inspired by constraints from physical law, equivariant machine learning restricts the learning to a hypothesis class where all the functions are equivariant with respect to some group action. Irreducible representations or invariant theory…

In this paper, we consider band-structure calculations governed by the Helmholtz or Maxwell equations in piecewise homogeneous periodic materials. Methods based on boundary integral equations are natural in this context, since they…

Controlling nonlinear systems, especially when data are being used to offset uncertainties in the model, is hard. A natural approach when dealing with the challenges of nonlinear control is to reduce the system to a linear one via change of…

We study Green's function and the large time behavior of the one-dimensional Euler-Maxwell System with relaxation. Firstly, we construct the Green's function of linearized system and obtain the optimal time decay rates of its solutions. And…

Recent work on the quantization of Maxwell theory has used a non-covariant class of gauge-averaging functionals which include explicitly the effects of the extrinsic-curvature tensor of the boundary, or covariant gauges which, unlike the…

Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…

This paper describes a new library for learning Bayesian networks from data containing discrete and continuous variables (mixed data). In addition to the classical learning methods on discretized data, this library proposes its algorithm…

We study the quantum-mechanical problem of scattering caused by a localized obstacle that breaks spatial and temporal reversibility. Accordingly, we follow Maxwell's prescription to achieve a violation of the second law of thermodynamics by…

General formula for causal Green's function of linear differential operator of given degree in one variable is given according to coefficient functions of differential operator as a series of integrals. The solution also provides analytic…

Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information…

We present an overview of electronic device modeling using non-equilibrium Green function techniques. The basic approach developed in the early 1970s has become increasingly popular during the last 10 years. The rise in popularity was…

We introduce the projected Green's function technique to study quasi-periodic systems such as the Andre-Aubry-Harper (AAH) model and beyond. In particular, we use projected Green's functions to construct a "rational approximate" sequence of…

Self-supervised representation learning has achieved remarkable success in recent years. By subverting the need for supervised labels, such approaches are able to utilize the numerous unlabeled images that exist on the Internet and in…

This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our…

While there are many applications of ML to scientific problems that look promising, visuals can be deceiving. Using numerical analysis techniques, we rigorously quantify the accuracy, convergence rates, and generalization bounds of certain…

We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…

The modified Poisson-Boltzmann (MPB) equations are often used to describe equilibrium particle distribution of ionic systems. In this paper, we propose a fast algorithm to solve MPB equations with the self Green's function as the self…