相关论文: Multigrid reduction-in-time convergence for advect…

In this paper, we study communication efficient distributed algorithms for distributionally robust federated learning via periodic averaging with adaptive sampling. In contrast to standard empirical risk minimization, due to the minimax…

This article is devoted to the construction of a new class of semi-Lagrangian (SL) schemes with implicit-explicit (IMEX) Runge-Kutta (RK) time stepping for PDEs involving multiple space-time scales. The semi-Lagrangian (SL) approach fully…

A hydraulic fracturing system with super-hydrophobic proppants is characterized by a transient triple-porosity Navier-Stokes model. For this complex multiphysics system, particularly in the context of three-dimensional space, a local…

Analytic methods are emerging in solid and configuration modeling, while providing new insights into a variety of shape and motion related problems by exploiting tools from group morphology, convolution algebras, and harmonic analysis.…

As a promising distributed machine learning paradigm, Federated Learning (FL) enables all the involved devices to train a global model collaboratively without exposing their local data privacy. However, for non-IID scenarios, the…

The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…

The paper aims to establish a fully discrete finite element (FE) scheme and provide cost-effective solutions for one-dimensional time-space Caputo-Riesz fractional diffusion equations on a bounded domain $\Omega$. Firstly, we construct a…

Federated learning (FL) enables distributed model training, yet in heterogeneous deployments, Bandwidth-Constrained Clients (BCCs) often contribute inefficiently due to limited uplink bandwidth. In model-heterogeneous FL with fixed small…

We consider strongly convex-concave minimax problems in the federated setting, where the communication constraint is the main bottleneck. When clients are arbitrarily heterogeneous, a simple Minibatch Mirror-prox achieves the best…

This paper considers the analysis of continuous time gradient-based optimization algorithms through the lens of nonlinear contraction theory. It demonstrates that in the case of a time-invariant objective, most elementary results on…

The balancing domain decomposition methods (BDDC) are originally introduced for symmetric positive definite systems and have been extended to the nonsymmetric positive definite system from the linear finite element discretization of…

We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means…

In this paper, we study a constrained minimization problem that arise from materials science to determine the dislocation (line defect) structure of grain boundaries. The problems aims to minimize the energy of the grain boundary with…

Operator splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which all simple pieces of the…

We propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower…

Recent studies have shown that by introducing prior knowledge, multi-scale analysis of complex and non-stationary time series in real environments can achieve good results in the field of long-term forecasting. However, affected by…

In this paper we proposed two new quasi-boundary value methods for regularizing the ill-posed backward heat conduction problems. With a standard finite difference discretization in space and time, the obtained all-at-once nonsymmetric…

We present distributed subgradient methods for min-max problems with agreement constraints on a subset of the arguments of both the convex and concave parts. Applications include constrained minimization problems where each constraint is a…

To address limitations of the graph fractional Fourier transform (GFRFT) Wiener filtering and the traditional joint time-vertex fractional Fourier transform (JFRFT) Wiener filtering, this study proposes a filtering method based on the…

Multifractal Detrended Fluctuation Analysis (MFDFA) is a powerful and widely used technique for characterizing the scaling properties and long-range correlations of complex time series. However, its application often involves significant…