相关论文: The strong convergence of operator-splitting metho…
Stochastic dynamical systems with continuous symmetries arise commonly in nature and often give rise to coherent spatio-temporal patterns. However, because of their random locations, these patterns are not well captured by current order…
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only.…
In this paper, we propose a novel technique to implement stochastic gradient methods, which are beneficial for learning from large datasets, through accelerated stochastic dynamics. A stochastic gradient method is based on mini-batch…
We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…
We study the mixing properties of an important optimization algorithm of machine learning: the stochastic gradient Langevin dynamics (SGLD) with a fixed step size. The data stream is not assumed to be independent hence the SGLD is not a…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
Formulated is a new systematic method for obtaining higher order corrections in numerical simulation of stochastic differential equations (SDEs), i.e., Langevin equations. Random walk step algorithms within a given order of finite $\Delta…
Stochastic reaction networks governed by Chemical Langevin Equations (CLE) exhibit pronounced multiscale dynamics spanning fast molecular reactions, intermediate transport, and slow cellular regulation, posing significant challenges for…
The Douglas-Rachford splitting method is a classical and widely used algorithm for solving monotone inclusions involving the sum of two maximally monotone operators. It was recently shown to be the unique frugal, no-lifting…
A formulation of Langevin dynamics for discrete systems is derived as a class of generic stochastic processes. The dynamics simplify for a two-state system and suggest a network architecture which is implemented by the Langevin machine. The…
We consider the Vlasov-Poisson equation in a Hamiltonian framework and derive new time splitting methods based on the decomposition of the Hamiltonian functional between the kinetic and electric energy. Assuming smoothness of the solutions,…
Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for a rigid…
This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives…
Euler's elastica model has a wide range of applications in Image Processing and Computer Vision. However, the non-convexity, the non-smoothness and the nonlinearity of the associated energy functional make its minimization a challenging…
Sampling from a high-dimensional probability distribution is a fundamental algorithmic task arising in wide-ranging applications across multiple disciplines, including scientific computing, computational statistics and machine learning.…
A method is described to solve the nonlinear Langevin equations arising from quadratic interactions in quantum mechanics. While, the zeroth order linearization approximation to the operators is normally used, here first and second order…
Neural stochastic differential equation model with a Brownian motion term can capture epistemic uncertainty of deep neural network from the perspective of a dynamical system. The goal of this paper is to improve the convergence rate of the…
We propose and study the weak convergence of a projective splitting algorithm for solving multi-term composite monotone inclusion problems involving the finite sum of $n$ maximal monotone operators, each of which having an inner four-block…