Related papers: From Additive Average Schwarz Methods to Non-overl…
Flows in which the primary features of interest do not rely on high-frequency acoustic effects, but in which long-wavelength acoustics play a nontrivial role, present a computational challenge. Integrating the entire domain with…
In many real-world applications, we often need to handle various deployment scenarios, where the resource constraint and the superclass of interest corresponding to a group of classes are dynamically specified. How to efficiently deploy…
A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being…
We study a class of nonsmooth stochastic optimization problems on Riemannian manifolds. In this work, we propose MARS-ADMM, the first stochastic Riemannian alternating direction method of multipliers with provable near-optimal complexity…
The multilevel Schwarz preconditioner is one of the most popular parallel preconditioners for enhancing convergence and improving parallel efficiency. However, its parallel implementation on arbitrary unstructured triangular/tetrahedral…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
Training deep neural networks at scale can benefit from domain decomposition, where the network is split into subdomains trained in parallel and coupled by a global trust-region mechanism. Building on the Additively Preconditioned…
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
The uniform white noise assumption is one of the basic assumptions in most of the existing directional-of-arrival (DOA) estimation methods. In many applications, however, the non-uniform white noise model is more adequate. Then the noise…
In the current work we present a spectral analysis of the additive and multiplicative Schwarz methods within the framework of domain decomposition techniques, by investigating the spectral properties of these classical Schwarz…
Recent years have seen the emergence of nonlinear methods for solving partial differential equations (PDEs), such as physics-informed neural networks (PINNs). While these approaches often perform well in practice, their theoretical analysis…
Stochastic nested optimization, including stochastic compositional, min-max and bilevel optimization, is gaining popularity in many machine learning applications. While the three problems share the nested structure, existing works often…
Conformal regression provides finite-sample marginal coverage, but it does not by itself determine how interval width should adapt across heterogeneous inputs. Existing locally adaptive methods mainly account for aleatoric noise, leaving…
Coordinate-type subgradient methods for addressing nonsmooth optimization problems are relatively underexplored due to the set-valued nature of the subdifferential. In this work, our study focuses on nonsmooth composite optimization…
The method of fundamental solutions (MFS), also known as the method of auxiliary sources (MAS), is a well-known computational method for the solution of boundary-value problems. The final solution ("MAS solution") is obtained once we have…
Neural architecture search (NAS) enables finding the best-performing architecture from a search space automatically. Most NAS methods exploit an over-parameterized network (i.e., a supernet) containing all possible architectures (i.e.,…
Neural network-based semantic segmentation has achieved remarkable results when large amounts of annotated data are available, that is, in the supervised case. However, such data is expensive to collect and so methods have been developed to…
The additive model is a popular nonparametric regression method due to its ability to retain modeling flexibility while avoiding the curse of dimensionality. The backfitting algorithm is an intuitive and widely used numerical approach for…
Accelerating iterative eigenvalue algorithms is often achieved by employing a spectral shifting strategy. Unfortunately, improved shifting typically leads to a smaller eigenvalue for the resulting shifted operator, which in turn results in…
In ptychography experiments, redundant scanning is usually required to guarantee the stable recovery, such that a huge amount of frames are generated, and thus it poses a great demand of parallel computing in order to solve this large-scale…