相关论文: An explicit splitting SAV scheme for the kinetic L…

The Stochastic Liouville-von Neumann equation provides an exact numerical simulation strategy for quantum systems interacting with Gaussian reservoirs [J.T. Stockburger & H. Grabert, PRL 88, 170407 (2002)]. Its scaling with the extension of…

We propose a new Stein self-repulsive dynamics for obtaining diversified samples from intractable un-normalized distributions. Our idea is to introduce Stein variational gradient as a repulsive force to push the samples of Langevin dynamics…

A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…

In this paper, we show how the It\^o-stochastic Magnus expansion can be used to efficiently solve stochastic partial differential equations (SPDE) with two space variables numerically. To this end, we will first discretize the SPDE in space…

We introduce a novel approach for decomposing and learning every scale of a given multiscale objective function in $\mathbb{R}^d$, where $d\ge 1$. This approach leverages a recently demonstrated implicit bias of the optimization method of…

The problem of sampling a target probability distribution on a constrained domain arises in many applications including machine learning. For constrained sampling, various Langevin algorithms such as projected Langevin Monte Carlo (PLMC),…

We propose an adaptive biasing algorithm aimed at enhancing the sampling of multimodal measures by Langevin dynamics. The underlying idea consists in generalizing the standard adaptive biasing force method commonly used in conjunction with…

Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation…

The dynamics of many systems from physics, economics, chemistry, and biology can be modelled through polynomial functions. In this paper, we provide a computational means to find positively invariant sets of polynomial dynamical systems by…

We propose a single time-scale stochastic subgradient method for constrained optimization of a composition of several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz and differentiable in a generalized…

A wide body of work has applied the concept of critical slowing down to estimate the stability of different Earth system components. Most of them -- such as global vegetation -- are inherently non-stationary, for example due to strong…

Markov chain sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample from a distribution by sampling uniformly from the region under…

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…

In recent years, considerable attention has been devoted to the regularization models due to the presence of high-dimensional data in scientific research. Sparse support vector machine (SVM) are useful tools in high-dimensional data…

Support Vector Machines (SVM), a popular machine learning technique, has been applied to a wide range of domains such as science, finance, and social networks for supervised learning. Whether it is identifying high-risk patients by…

Most existing approximate Thompson Sampling (TS) algorithms for multi-armed bandits use Stochastic Gradient Langevin Dynamics (SGLD) or its variants in each round to sample from the posterior, relaxing the need for conjugacy assumptions…

Bayesian methods of sampling from a posterior distribution are becoming increasingly popular due to their ability to precisely display the uncertainty of a model fit. Classical methods based on iterative random sampling and posterior…

This paper delves into the well-posedness and the numerical approximation of non-autonomous stochastic differential algebraic equations (SDAEs) with nonlinear local Lipschitz coefficients that satisfy the more general monotonicity condition…

We present a framework that allows for the non-asymptotic study of the $2$-Wasserstein distance between the invariant distribution of an ergodic stochastic differential equation and the distribution of its numerical approximation in the…

This paper provides a self-contained ordinary differential equation solver approach for separable convex optimization problems. A novel primal-dual dynamical system with built-in time rescaling factors is introduced, and the exponential…