Related papers: A Primal-dual Forward-backward Splitting Method fo…

This work is an attempt to transfer to biology the methods developed in physics for formulating and solving the kinetic equations in which the kernel of the integral operator in spatial coordinates is slowly decreasing with increasing…

The time-fractional optimal transport (OT) and mean-field planning (MFP) models are developed to describe the anomalous transport of the agents in a heterogeneous environment such that their densities are transported from the initial…

In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis. For the well-known standard version of the problem: we establish…

The forward-backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward-backward envelope (FBE).…

We present a previously unexplored forward-mode differentiation method for Maxwell's equations, with applications in the field of sensitivity analysis. This approach yields exact gradients and is similar to the popular adjoint variable…

Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…

We extend the methods from Nurbekyan, Saude "Fourier approximation methods for first-order nonlocal mean-field games" [Port. Math. 75 (2018), no. 3-4] and Liu, Jacobs, Li, Nurbekyan, Osher "Computational methods for nonlocal mean field…

We present a framework enabling variational data assimilation for gradient flows in general metric spaces, based on the minimizing movement (or Jordan-Kinderlehrer-Otto) approximation scheme. After discussing stability properties in the…

Diffusion Models (DMs) have achieved remarkable progress in generative modeling. However, the mismatch between the forward terminal distribution and reverse initial distribution introduces prior error, leading to deviations of sampling…

A new approach for integration of motion in many-body systems of interacting polyatomic molecules is proposed. It is based on splitting time propagation of pseudo-variables in a modified phase space, while the real translational and…

We introduce and investigate the convergence properties of an inertial forward-backward-forward splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitzian…

We consider a network of agents, each with its own private cost consisting of the sum of two possibly nonsmooth convex functions, one of which is composed with a linear operator. At every iteration each agent performs local calculations and…

We develop a novel stochastic primal dual splitting method with Bregman distances for solving a structured composite problems involving infimal convolutions in non-Euclidean spaces. The sublinear convergence in expectation of the…

The timely precoding of frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems is a substantial challenge in practice, especially in mobile environments. In order to improve the precoding performance and…

We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two main steps. In the first step, the space variable is…

We present a new efficient method for Monte Carlo simulations of diffusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditional small diffusion hops and propagates the…

In this paper, we study the local linear convergence properties of a versatile class of Primal-Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of…

In this paper, we present splitting algorithms to solve multicomponent transport models with Maxwell-Stefan-diffusion approaches. The multicomponent models are related to transport problems, while we consider plasma processes, in which the…

This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…

Schr\"odinger bridge (SB) has emerged as the go-to method for optimizing transportation plans in diffusion models. However, SB requires estimating the intractable forward score functions, inevitably resulting in the costly implicit training…