Related papers: On the Discretization Error of the Discrete Genera…

A discretization scheme is introduced for a set of convection-diffusion equations with a non-linear reaction term, where the convection velocity is constant for each reactant. This constancy allows a transformation to new spatial variables,…

In this paper, we present a new space-time Petrov-Galerkin-like method. This method utilizes a mixed formulation of Tensor Train (TT) and Quantized Tensor Train (QTT), designed for the spectral element discretization (Q1-SEM) of the…

We propose a self-consistent generalized quantum master equation (GQME) to describe electron transport through molecular junctions. In a previous study [M.Esposito and M.Galperin. Phys. Rev. B 79, 205303 (2009)], we derived a time-nonlocal…

The time-fractional Black-Scholes equation (TFBSE) is intended to price the options for which the underlying price fluctuates within a correlated fractal transmission system. Although the TFBSE is an influential approach for grasping the…

Consistency Models (CMs) have shown promise for efficient one-step generation. However, most existing CMs rely on manually designed discretization schemes, which can cause repeated adjustments for different noise schedules and datasets. To…

Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention…

Mathematically, the typical difference of Discrete Boltzmann Model (DBM) from the traditional hydrodynamic one is that the Navier-Stokes (NS) equations are replaced by a discrete Boltzmann equation. But physically, this replacement has a…

An implicit Euler--Maruyama method with non-uniform step-size applied to a class of stochastic partial differential equations is studied. A spectral method is used for the spatial discretization and the truncation of the Wiener process. A…

We propose a multilevel tensor-train (TT) framework for solving nonlinear partial differential equations (PDEs) in a global space-time formulation. While space-time TT solvers have demonstrated significant potential for compressed…

We propose a framework for discrete scientific data compression based on the tensor-train (TT) decomposition. Our approach is tailored to handle unstructured output data from discrete element method (DEM) simulations, demonstrating its…

Semi- and quasi-classical (SC) theories can handle arbitrary interatomic interactions and are thus well-suited to predict quantum dynamics in condensed phases that encode energy and charge transport, spectroscopic responses, and chemical…

In this work, the z-transform is presented to analyze time-discrete solutions for Volterra integrodifferential equations (VIDEs) with nonsmooth multi-term kernels in the Hilbert space, and this class of continuous problem was first…

The Diffusion model, a prevalent framework for image generation, encounters significant challenges in terms of broad applicability due to its extended inference times and substantial memory requirements. Efficient Post-training Quantization…

Investigations of quantum and mesoscopic thermodynamics force one to answer two fundamental questions associated with the foundations of statistical mechanics: (i) how does macroscopic irreversibility emerge from microscopic reversibility?…

We develop a general framework for designing conservative numerical methods based on summation by parts operators and split forms in space, combined with relaxation Runge-Kutta methods in time. We apply this framework to create new classes…

Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial…

We consider discrete-time (DT) systems S in which a DT input is first tranformed to a continuous-time (CT) format by phase-amplitude modulation, then modified by a non-linear CT dynamical transformation F, and finally converted back to DT…

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard…

We study majorization-minimization methods for nonnegative tensor decompositions under the $\beta$-divergence family, focusing on nonnegative CP and Tucker models. Our aim is to avoid explicit mode unfoldings and large auxiliary matrices by…

We present a quantum algorithm based on the Generalized Quantum Master Equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the…