Related papers: Splitting AVF method for generalized Langevin equa…
We evaluate the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations. The methods are based on affine combinations of time-splitting integrators and…
In this paper, we present a high order conservative semi-Lagrangian (SL) Hermite weighted essentially non-oscillatory (HWENO) method for the Vlasov equation based on dimensional splitting [Cheng and Knorr, Journal of Computational Physics,…
Exponentiated gradient descent (EGD), a biologically motivated optimisation algorithm that respects Dale's law, produces log-normally distributed synaptic weights at convergence, in alignment with experimental observations in neuroscience.…
We propose Annealed Langevin Monte Carlo for Flow ODE Sampling (ALMC-ODE), a method for generating samples from unnormalized target distributions, with a particular emphasis on multimodal densities that are challenging for standard Markov…
The generalized Langevin equation (GLE) is a useful framework for analyzing and modeling the dynamics of many-body systems in terms of low-dimensional reaction coordinates, with its specific form determined by the choice of projection…
Large scale Gaussian process (GP) regression is infeasible for larger data sets due to cubic scaling of flops and quadratic storage involved in working with covariance matrices. Remedies in recent literature focus on divide-and-conquer,…
We develop several efficient numerical schemes which preserve exactly the global constraints for constrained gradient flows. Our schemes are based on the SAV approach combined with the Lagrangian multiplier approach. They are as efficient…
Langevin algorithms are gradient descent methods with additive noise. They have been used for decades in Markov chain Monte Carlo (MCMC) sampling, optimization, and learning. Their convergence properties for unconstrained non-convex…
Two local discontinuous Galerkin (LDG) methods using some non-standard numerical fluxes are developed for the Helmholtz equation with the first order absorbing boundary condition in the high frequency regime. It is shown that the proposed…
In this paper, we present two multiple scalar auxiliary variable (MSAV)-based, finite element numerical schemes for the Abels-Garcke-Gr{\"u}n (AGG) model, which is a thermodynamically consistent phase field model of two-phase incompressible…
Adaptive Multilevel Splitting (AMS for short) is a generic Monte Carlo method for Markov processes that simulates rare events and estimates associated probabilities. Despite its practical efficiency, there are almost no theoretical results…
Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical…
Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic…
We consider the image denoising problem using total variation (TV) regularization. This problem can be computationally challenging to solve due to the non-differentiability and non-linearity of the regularization term. We propose an…
In this paper, we consider the generalised (higher order) Langevin equation for the purpose of simulated annealing and optimisation of nonconvex functions. Our approach modifies the underdamped Langevin equation by replacing the Brownian…
In this article we consider a generalized equal width wave (GEW) equation which is a significant nonlinear wave equation as it can be used to model many problems occurring in applied sciences. As the analytic solution of the (GEW) equation…
The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…
The authors propose a new modeling approach based on the impedance field method (IFM) to analyze the general geometric variations in device simulations. Compared with the direct modeling of multiple variational devices, the proposed…
In order to completely separate objects with large sections of occluded boundaries in an image, we devise a new variational level set model for image segmentation combining the Chan-Vese model with elastica and landmark constraints. For…
Reducing communication in training large-scale machine learning applications on distributed platform is still a big challenge. To address this issue, we propose a distributed hierarchical averaging stochastic gradient descent (Hier-AVG)…