相关论文: Variational Estimates using a Discrete Variable Re…

A novel linear classification method that possesses the merits of both the Support Vector Machine (SVM) and the Distance-weighted Discrimination (DWD) is proposed in this article. The proposed Distance-weighted Support Vector Machine method…

Energy spectroscopy is a powerful tool with diverse applications across various disciplines. The advent of programmable digital quantum simulators opens new possibilities for conducting spectroscopy on various models using a single device.…

In this work we design and analyse a Discrete de Rham (DDR) method for the incompressible Navier-Stokes equations. Our focus is, more specifically, on the SDDR variant, where a reduction in the number of unknowns is obtained using…

A variational integrator for ideal magnetohydrodynamics is derived by applying a discrete action principle to a formal Lagrangian. Discrete exterior calculus is used for the discretisation of the field variables in order to preserve their…

In this paper, a stochastic Hamiltonian formulation (SHF) is proposed and applied to dissipative particle dynamics (DPD) simulations. As an extension of Hamiltonian dynamics to stochastic dissipative systems, the SHF provides necessary…

In this paper, we present a comparative analysis of various self-supervised Vision Transformers (ViTs), focusing on their local representative power. Inspired by large language models, we examine the abilities of ViTs to perform various…

Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally…

We show that the DDR method can be interpreted as defining a computable consistent discrete $\mathrm{L}^2$ product on a conforming FES defined by PDEs. Without modifying the numerical method itself, this point of view provides an…

Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…

We propose a new stable variational formulation for the quad-div problem in three dimensions and prove its well-posedness. Using this weak form, we develop and analyze the $\boldsymbol{H}(\operatorname{grad-div})$-conforming virtual element…

In this article, variational state estimation is examined from the dynamic programming perspective. This leads to two different value functional recursions depending on whether backward or forward dynamic programming is employed. The result…

A procedure for obtaining a "minimal" discretization of a partial differential equation, preserving all of its Lie point symmetries is presented. "Minimal" in this case means that the differential equation is replaced by a partial…

A volatility surface is an important tool for pricing and hedging derivatives. The surface shows the volatility that is implied by the market price of an option on an asset as a function of the option's strike price and maturity. Often,…

We propose a new numerical scheme of evolution for the Einstein equations using the discrete variational derivative method (DVDM). We derive the discrete evolution equation of the constraint using this scheme and show the constraint…

Distributed inference/estimation in Bayesian framework in the context of sensor networks has recently received much attention due to its broad applicability. The variational Bayesian (VB) algorithm is a technique for approximating…

The Variational Bayesian method (VB) is used to solve the probability distributions of latent variables with the minimum free energy criterion. This criterion is not easy to understand, and the computation is complex. For these reasons,…

The simulation of many-body open quantum systems is key to solving numerous outstanding problems in physics, chemistry, material science, and in the development of quantum technologies. Near-term quantum computers may bring considerable…

Motivated by the need for communication-efficient distributed learning, we investigate the method for compressing a unit norm vector into the minimum number of bits, while still allowing for some acceptable level of distortion in recovery.…

A direct and exact method for calculating the density of states for systems with localized potentials is presented. The method is based on explicit inversion of the operator $E-H$. The operator is written in the discrete variable…

In this paper, we discuss a virtual element approximation for the modified transmission eigenvalue problem in inverse scattering for natural materials. In this case, due to the positive artificial diffusivity parameter in the considered…