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While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…

Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of partial differential equations. In…

This paper considers the problem of distributed estimation in a sensor network, where multiple sensors are deployed to infer the state of a linear time-invariant (LTI) Gaussian system. By proposing a lossless decomposition of Kalman filter,…

When the data is distributed across multiple servers, lowering the communication cost between the servers (or workers) while solving the distributed learning problem is an important problem and is the focus of this paper. In particular, we…

With the rapid growth of large language models (LLMs), a wide range of methods have been developed to distribute computation and memory across hardware devices for efficient training and inference. While existing surveys provide descriptive…

Partitioning a graph into blocks of roughly equal weight while cutting only few edges is a fundamental problem in computer science with numerous practical applications. While shared-memory parallel partitioners have recently matured to…

This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…

Given a graph, a maximal independent set (MIS) is a maximal subset of pairwise non-adjacent vertices. Finding an MIS is a fundamental problem in distributed computing. Although the problem is extensively studied and well understood in…

Motivated by the increasing availability of high-performance parallel computing, we design a distributed parallel algorithm for linearly-coupled block-structured nonconvex constrained optimization problems. Our algorithm performs…

In recent years, there is a growing need to train machine learning models on a huge volume of data. Designing efficient distributed optimization algorithms for empirical risk minimization (ERM) has therefore become an active and challenging…

A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…

Large language models (LLMs) have demonstrated remarkable success across various application domains, but their enormous sizes and computational demands pose significant challenges for deployment on resource-constrained edge devices. To…

Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exist within a PUM scheme for handling problems with zones of…

The current trend of multicore architectures on shared memory systems underscores the need of parallelism. While there are some programming model to express parallelism, thread programming model has become a standard to support these system…

This note constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients. The basis functions are solutions of local problems on vertex patches. The error of the corresponding…

Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…

The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…

This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…

This paper proposes a two-level restricted additive Schwarz (RAS) method for multiscale PDEs, built on top of a multiscale spectral generalized finite element method (MS-GFEM). The method uses coarse spaces constructed from optimal local…