Related papers: Multilevel convergence analysis of multigrid-reduc…
We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…
Traditional time discretization methods use a single timestep for the entire system of interest and can perform poorly when the dynamics of the system exhibits a wide range of time scales. Multirate infinitesimal step (MIS) methods (Knoth…
The study on the implicit regularization induced by gradient-based optimization is a longstanding pursuit. In the present paper, we characterize the implicit regularization of momentum gradient descent (MGD) with early stopping by comparing…
Recent advancements in table-based reasoning have expanded beyond factoid-level QA to address insight-level tasks, where systems should synthesize implicit knowledge in the table to provide explainable analyses. Although effective, existing…
This paper is devoted to the multigrid convergence analysis for the linear systems arising from the conforming linear finite element discretization of the second order elliptic equations with anisotropic diffusion. The multigrid convergence…
We present the first finite time global convergence analysis of policy gradient in the context of infinite horizon average reward Markov decision processes (MDPs). Specifically, we focus on ergodic tabular MDPs with finite state and action…
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…
Stochastic Gradient Descent (SGD) is a fundamental algorithm in machine learning, representing the optimization backbone for training several classic models, from regression to neural networks. Given the recent practical focus on…
A parallel dynamic overset framework has been developed for the curvilinear immersed boundary (overset-CURVIB) method to enable tackling a wide range of challenging flow problems. The dynamic overset grids are used to locally increase the…
The fast growing capabilities of large-scale deep learning models, such as Bert, GPT and ViT, are revolutionizing the landscape of NLP, CV and many other domains. Training such models, however, poses an unprecedented demand for computing…
We discuss how multi-grid computing schemes can be used to design hierarchical coordination architectures for energy systems. These hierarchical architectures can be used to manage multiple temporal and spatial scales and mitigate…
This paper presents a parallel-in-time multilevel iterative method for solving differential algebraic equation, arising from a discretization of linear time-dependent partial differential equation. The core of the method is the multilevel…
Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…
We propose MCGrad, a novel and scalable multicalibration algorithm. Multicalibration - calibration in subgroups of the data - is an important property for the performance of machine learning-based systems. Existing multicalibration methods…
Distribution system integrated community microgrids (CMGs) can restore loads during extended outages. The CMG is challenged with limited resource availability, absence of a robust grid-support, and demand-supply uncertainty. To address…
Problems arising in Earth's mantle convection involve finding the solution to Stokes systems with large viscosity contrasts. These systems contain localized features which, even with adaptive mesh refinement, result in linear systems that…
In recent years several research efforts focused on the development of high-order discontinuous Galerkin (dG) methods for scale resolving simulations of turbulent flows. Nevertheless, in the context of incompressible flow computations, the…
Parallel-in-time integration has been the focus of intensive research efforts over the past two decades due to the advent of massively parallel computer architectures and the scaling limits of purely spatial parallelization. Various…