Related papers: Multilevel convergence analysis of multigrid-reduc…
In his article "Powerlist: A Structure for Parallel Recursion" Jayadev Misra wrote: "Many data parallel algorithms - Fast Fourier Transform, Batcher's sorting schemes and prefix sum - exhibit recursive structure. We propose a data…
In this paper we consider a class of robust multilevel precontioners for the Helmholtz equation with high wave number. The key idea in this work is to use the continuous interior penalty finite element methods (CIP-FEM) studied in…
We propose a variance reduction framework for variational inference using the Multilevel Monte Carlo (MLMC) method. Our framework is built on reparameterized gradient estimators and "recycles" parameters obtained from past update history in…
Bilevel optimization is a powerful tool for many machine learning problems, such as hyperparameter optimization and meta-learning. Estimating hypergradients (also known as implicit gradients) is crucial for developing gradient-based methods…
Restoring critical loads after extreme events demands adaptive control to maintain distribution-grid resilience, yet uncertainty in renewable generation, limited dispatchable resources, and nonlinear dynamics make effective restoration…
A numerical investigation of grain-boundary (GB) grooving by means of the Level Set (LS) method is carried out. GB grooving is emerging as a key element of electromigration drift in polycrystalline microelectronic interconnects, as…
We consider online convex optimization with time-varying stage costs and additional switching costs. Since the switching costs introduce coupling across all stages, multi-step-ahead (long-term) predictions are incorporated to improve the…
This paper considers the decentralized composite optimization problem. We propose a novel decentralized variance-reduction proximal-gradient algorithmic framework, called PMGT-VR, which is based on a combination of several techniques…
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…
There hardly exists a general solver that is efficient for scheduling problems due to their diversity and complexity. In this study, we develop a two-stage framework, in which reinforcement learning (RL) and traditional operations research…
In this paper, we discuss two grid-quality measures, F- and G-measures, in relation to iterative convergence of an implicit unstructured-grid Navier-Stokes solver. The F-measure is a lower bound of a least-squares gradient, which is a…
A multi-fidelity regression model is proposed for combining multiple datasets with different fidelities, particularly abundant low-fidelity data and scarce high-fidelity observations. The model builds upon recent multi-fidelity frameworks…
Low precision arithmetic, in particular half precision floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
This paper presents estimates of the convergence rate and complexity of an algebraic multilevel preconditioner based on piecewise constant coarse vector spaces applied to the graph Laplacian. A bound is derived on the energy norm of the…
We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…
We propose a highly parallel primal-dual algorithm for the multicut (a.k.a. correlation clustering) problem, a classical graph clustering problem widely used in machine learning and computer vision. Our algorithm consists of three steps…
The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a…
In this work, we consider minimizing the average of a very large number of smooth and possibly non-convex functions, and we focus on two widely used minibatch frameworks to tackle this optimization problem: Incremental Gradient (IG) and…
To effectively leverage user-specific data, retrieval augmented generation (RAG) is employed in multimodal large language model (MLLM) applications. However, conventional retrieval approaches often suffer from limited retrieval accuracy.…