Related papers: Analytic Origin of Green-Function Compression in t…
Discrete Green's functions are the inverses or pseudo-inverses of combinatorial Laplacians. We present compact formulas for discrete Green's functions, in terms of the eigensystems of corresponding Laplacians, for products of regular graphs…
We explore the connections between Green's functions for certain differential equations, covariance functions for Gaussian processes, and the smoothing splines problem. Conventionally, the smoothing spline problem is considered in a setting…
Lossy image compression is one of the most commonly used operators for digital images. Most recently proposed deep-learning-based image compression methods leverage the auto-encoder structure, and reach a series of promising results in this…
The extensive adoption of Deep Neural Networks has led to their increased utilization in challenging scientific visualization tasks. Recent advancements in building compressed data models using implicit neural representations have shown…
Implicit Neural Representations (INR) use multilayer perceptrons to represent high-frequency functions in low-dimensional problem domains. Recently these representations achieved state-of-the-art results on tasks related to complex 3D…
We present a comprehensive quantum many body theory for kq deformed particles, offering a novel framework that relates particle statistics directly to effective interaction strength. Deformed by the parameters k and q, these particles…
In order to simulate open quantum systems, many approaches (such as Hamiltonian-based solvers in dynamical mean-field theory) aim for a reproduction of a desired environment spectral density in terms of a discrete set of bath states,…
The green functions for the heat and Laplace equations with dynamical boundary conditions in a ball are studied. First, the green functions of the Laplace equation with a dynamical boundary condition are given, and the properties of related…
In classical information theory, the information bottleneck method (IBM) can be regarded as a method of lossy data compression which focusses on preserving meaningful (or relevant) information. As such it has recently gained a lot of…
Pretrained molecular encoders have become indispensable in computational chemistry for tasks such as property prediction and molecular generation. However, the standard practice of relying solely on final-layer embeddings for downstream…
Text encoding is one of the most important steps in Natural Language Processing (NLP). It has been done well by the self-attention mechanism in the current state-of-the-art Transformer encoder, which has brought about significant…
In recent years, intelligent reflecting surface (IRS) has emerged as a promising technology for 6G due to its potential/ability to significantly enhance energy- and spectrum-efficiency. To this end, it is crucial to adjust the phases of…
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…
Accurately and efficiently measuring the pressure field is of paramount importance in many fluid mechanics applications. The pressure gradient field of a fluid flow can be determined from the balance of the momentum equation based on the…
The many-body Green's function provides access to electronic properties beyond density functional theory level in ab inito calculations. In this manuscript, we propose a deep learning framework for predicting the finite-temperature Green's…
The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate…
Neural operators, which learn mappings between the function spaces, have been applied to solve boundary value problems in various ways, including learning mappings from the space of the forcing terms to the space of the solutions with the…
The Green's function has been an indispensable tool to study many-body systems that remain one of the biggest challenges in modern quantum physics for decades. The complicated calculation of Green's function impedes the research of…
The correspondence principle states that classical mechanics emerges from quantum mechanics in the appropriate limits. However, beyond this heuristic rule, an information-theoretic perspective reveals that classical mechanics is a…
The Green's function method is recognized to be a very powerful tool for modelling quantum transport in nanoscale electronic devices. As atomistic calculations are generally expensive, numerical methods and related algorithms have been…