相关论文: On the Efficient Implementation of an Implicit Dis…

Among the single-trajectory Gaussian-based methods for solving the time-dependent Schr\"{o}dinger equation, the variational Gaussian approximation is the most accurate one. In contrast to Heller's original thawed Gaussian approximation, it…

In this paper, we propose and analyze an explicit time-stepping scheme for a spatial discretization of stochastic Cahn--Hilliard equation with additive noise. The fully discrete approximation combines a spectral Galerkin method in space…

We study three different time integration methods for a dynamic pore network model for immiscible two-phase flow in porous media. Considered are two explicit methods, the forward Euler and midpoint methods, and a new semi-implicit method…

The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…

We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…

In this work, we consider the development of implicit explicit total variation diminishing (TVD) methods (also termed SSP: strong stability preserving) for the compressible isentropic Euler system in the low Mach number regime. The scheme…

This paper is concerned with developing and analyzing two novel implicit temporal discretization methods for the stochastic semilinear wave equations with multiplicative noise. The proposed methods are natural extensions of well-known…

We propose a new discrete-time online parameter estimation algorithm that combines two different aspects, one that adds momentum, and another that includes a time-varying learning rate. It is well known that recursive least squares based…

The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of…

First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…

In the recent breakthrough paper by Barbulescu, Gaudry, Joux and Thom{\'e}, a quasi-polynomial time algorithm (QPA) is proposed for the discrete logarithm problem over finite fields of small characteristic. The time complexity analysis of…

We present stochastic variants of the exponential time differencing schemes for stiff stochastic differential equations. We derive three explicit schemes that offer better stability compared to Euler-Maruyama and Milstein's method, and…

We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient…

We consider estimating the transition probability matrix of a finite-state finite-observation alphabet hidden Markov model with known observation probabilities. The main contribution is a two-step algorithm; a method of moments estimator…

We present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex…

The Hurst exponent is a significant metric for characterizing time sequences with long-term memory property and it arises in many fields. The available methods for estimating the Hurst exponent can be categorized into time-domain and…

Currently, many machine learning algorithms contain lots of iterations. When it comes to existing large-scale distributed systems, some slave nodes may break down or have lower efficiency. Therefore traditional machine learning algorithm…

Exploiting higher-order derivatives in convex optimization is known at least since 1970's. In each iteration higher-order (also called tensor) methods minimize a regularized Taylor expansion of the objective function, which leads to faster…

We establish optimal order a priori error estimates for implicit-explicit BDF methods for abstract semilinear parabolic equations with time-dependent operators in a complex Banach space settings, under a sharp condition on the…

Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…