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Implicit Neural Representations (INRs) have revolutionized signal representation by leveraging neural networks to provide continuous and smooth representations of complex data. However, existing INRs face limitations in capturing…

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…

In this paper we introduce a novel way of estimating prediction uncertainty in deep networks through the use of uncertainty surrogates. These surrogates are features of the penultimate layer of a deep network that are forced to match…

Machine learning methods are applied to finding the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Different methods of parametrizing the Green's function are…

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,…

Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…

Boundary value problems (BVPs) play a central role in the mathematical analysis of constrained physical systems subjected to external forces. Consequently, BVPs frequently emerge in nearly every engineering discipline and span problem…

We present a machine-learning approach to a long-standing issue in quantum many-body physics, namely, analytic continuation. This notorious ill-conditioned problem of obtaining spectral function from imaginary time Green's function has been…

This paper presents a novel {\em Interpolated Factored Green Function} method (IFGF) for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF…

In this paper, we summarize the technique of using Green functions to solve electrostatic problems. We start by deriving the electric potential in terms of a Green function and a charge distribution. We then provide a variety of example…

This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…

A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of…

In this paper we study some classes of second order non-homogeneous nonlinear differential equations allowing a specific representation for nonlinear Green's function. In particular, we show that if the nonlinear term possesses a special…

Developing surrogates for computer models has become increasingly important for addressing complex problems in science and engineering. This article introduces an artificial intelligent (AI) surrogate, referred to as the DeepSurrogate, for…

An end-to-end strategy for hybrid quantum-classical computations of Green's functions in many-body systems is presented and applied to the pairing model. The scheme makes explicit use of the spectral representation of the Green's function,…

Deep learning methods have been employed in gravitational-wave astronomy to accelerate the construction of surrogate waveforms for the inspiral of spin-aligned black hole binaries, among other applications. We face the challenge of modeling…

We present a method for analytic continuation of retarded Green functions, including Euclidean Green functions computed using lattice QCD. The method is based on conformal maps and construction of an interpolation function which is analytic…

Self-supervised learning can significantly improve the performance of downstream tasks, however, the dimensions of learned representations normally lack explicit physical meanings. In this work, we propose a novel self-supervised approach…

Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…

This paper introduces a probability density estimator based on Green's function identities. A density model is constructed under the sole assumption that the probability density is differentiable. The method is implemented as a binary…