相关论文: Second Order Threshold Dynamics Schemes for Two Ph…

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…

The self-consistent method, first introduced by Kuramoto, is a powerful tool for the analysis of the steady states of coupled oscillator networks. For second-order oscillator networks complications to the application of the self-consistent…

Second-order optimality conditions are essential for nonsmooth optimization, where both the objective and constraint functions are Lipschitz continuous and second-order directionally differentiable. This paper provides no-gap second-order…

We consider the problem of minimizing a strongly convex smooth function where the gradients are subject to additive worst-case deterministic errors that are square-summable. We study the trade-offs between the convergence rate and…

A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded…

We study the dynamics of a droplet moving on an inclined rough surface in the absence of inertial and viscous stress effects. In this case, the dynamics of the droplet is a purely geometric motion in terms of the wetting domain and the…

We develop Policy Gradient with Second-Order Momentum (PG-SOM), a lightweight second-order optimisation scheme for reinforcement-learning policies. PG-SOM augments the classical REINFORCE update with two exponentially weighted statistics: a…

Zeroth-order (ZO) methods are widely used when gradients are unavailable or prohibitively expensive, including black-box learning and memory-efficient fine-tuning of large models, yet their optimization dynamics in deep learning remain…

Stochastic MPECs have found increasing relevance for modeling a broad range of settings in engineering and statistics. Yet, there seem to be no efficient first/zeroth-order schemes equipped with non-asymptotic rate guarantees for resolving…

In this paper we study the problem of divergence-free numerical MHD and show that the work done so far still has four key unresolved issues. We resolve those issues in this paper. The problem of reconstructing MHD flow variables with…

This paper extends first-order motion planners to robots governed by second-order dynamics. Two control schemes are proposed based on the knowledge of a scalar function whose negative gradient aligns with a given first-order motion planner.…

In this paper, we present a new Hyperfast Second-Order Method with convergence rate $O(N^{-5})$ up to a logarithmic factor for the convex function with Lipshitz the third derivative. This method based on two ideas. The first comes from the…

Accurate numerical solutions of the equations of hydrodynamics play an ever more important role in many fields of astrophysics. In this work, we reinvestigate the accuracy of the moving-mesh code \textsc{Arepo} and show how its convergence…

We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types…

Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While…

Three non-equilibrium photoionisation algorithms for hydrodynamical grid-based simulation codes are compared in terms of accuracy, timestepping criteria, and parallel scaling. Explicit methods with first-order time accuracy for photon…

We consider here a fully discrete variant of the implicit variational scheme for mean curvature flow [AlmTayWan,LucStu], in a setting where the flow is governed by a crystalline surface tension defined by the limit of pairwise interactions…

Higher-order tensor methods were recently proposed for minimizing smooth convex and nonconvex functions. Higher-order algorithms accelerate the convergence of the classical first-order methods thanks to the higher-order derivatives used in…

In this paper, we present and analyze a linear fully discrete second order scheme with variable time steps for the phase field crystal equation. More precisely, we construct a linear adaptive time stepping scheme based on the second order…

A rotation-two-component Camassa-Holm (R2CH) system was proposed recently to describe the motion of shallow water waves under the influence of gravity. This is a highly nonlinear and strongly coupled system of partial differential…