Related papers: Multilevel convergence analysis of multigrid-reduc…
Multirate integration is an increasingly relevant tool that enables scientists to simulate multiphysics systems. Existing multirate methods are designed for equations whose fast and slow variables can be linearly separated using additive or…
A novel and scalable geometric multi-level algorithm is presented for the numerical solution of elliptic partial differential equations, specially designed to run with high occupancy of streaming processors inside Graphics Processing…
The design of fast solvers for isogeometric analysis is receiving a lot of attention due to the challenge that offers to find an algorithm with a robust convergence with respect to the spline degree. Here, we analyze the application of…
We present a new framework for learning Granger causality networks for multivariate categorical time series, based on the mixture transition distribution (MTD) model. Traditionally, MTD is plagued by a nonconvex objective,…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Prompt engineering is crucial for fully leveraging large language models (LLMs), yet most existing optimization methods follow a single trajectory, resulting in limited adaptability, gradient conflicts, and high computational overhead. We…
Large-scale machine learning models are trained on clusters of machines that exhibit heterogeneous performance due to hardware variability, network delays, and system-level instabilities. In such environments, time complexity rather than…
Multi-grade deep learning (MGDL) has been shown to significantly outperform the standard single-grade deep learning (SGDL) across various applications. This work aims to investigate the computational advantages of MGDL focusing on its…
We develop a multigrid solver for the second biharmonic problem in the context of Isogeometric Analysis (IgA), where we also allow a zero-order term. In a previous paper, the authors have developed an analysis for the first biharmonic…
We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…
Averaging scheme has attracted extensive attention in deep learning as well as traditional machine learning. It achieves theoretically optimal convergence and also improves the empirical model performance. However, there is still a lack of…
Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…
Algebraic multigrid (AMG) is known to be an effective solver for many sparse symmetric positive definite (SPD) linear systems. For SPD systems, the convergence theory of AMG is well-understood in terms of the $A$-norm, but in a nonsymmetric…
In this work we present two new families of multirate time step adaptivity controllers, that are designed to work with embedded multirate infinitesimal (MRI) time integration methods for adapting time steps when solving problems with…
Motivated by the growing use of artificial intelligence (AI) tools in control design, this paper analyses the intersection between results from gradient methods for the model-free linear quadratic regulator (LQR), and linear feedforward…
We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid…
A framework is presented to design multirate time stepping algorithms for two dissipative models with coupling across a physical interface. The coupling takes the form of boundary conditions imposed on the interface, relating the solution…
Recent advancements in Generative Reward Models (GRMs) have demonstrated that scaling the length of Chain-of-Thought (CoT) reasoning considerably enhances the reliability of evaluation. However, current works predominantly rely on…
In recent years, Riemannian stochastic gradient descent (R-SGD), Riemannian stochastic variance reduction (R-SVRG) and Riemannian stochastic recursive gradient (R-SRG) have attracted considerable attention on Riemannian optimization. Under…
A robust multilevel preconditioner based on the hybridizable discontinuous Galerkin method for the Helmholtz equation with high wave number is presented in this paper. There are two keys in our algorithm, one is how to choose a suitable…