arXiv subjects

Srinivas Eswar

Publications and source records attributed to Srinivas Eswar.

8 recordsLinked to original sources

arXiv2026

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory

Linear systems arise in generating samples and in calculating observables in lattice quantum chromodynamics~(QCD). Solving the Hermitian positive definite systems, which are sparse but ill-conditioned, involves using iterative methods, such as Conjugate Gradient (CG), which are time-consuming and computationally expensive. Preconditioners can effectively accelerate this process, with the state-of-the-art being multigrid preconditioners. However, constructing useful preconditioners can be challenging, adding additional computational overhead, especially in large linear systems. We propose a framework, leveraging operator learning techniques, to construct linear maps as effective preconditioners. The method in this work does \emph{not} rely on explicit matrices from either the original linear systems or the produced preconditioners, allowing efficient model training and application in the CG solver. In the context of the Schwinger model U(1) gauge theory in 1+1 spacetime dimensions with two degenerate-mass fermions), this preconditioning scheme effectively decreases the condition number of the linear systems and approximately halves the number of iterations required for convergence in relevant parameter ranges. We further demonstrate the framework learns a general mapping dependent on the lattice structure which leads to zero-shot learning ability for the Dirac operators constructed from gauge field configurations of different sizes.

hep-lat↗

arXiv2026

High-Performance Star-M SVD for Big Data Compression

In the era of big data, effectively compressing large datasets while performing complex mathematical operations is crucial. Tensor-based decomposition methods have shown superior compression capabilities with minimal loss of accuracy compared to traditional matrix methods. Under the star-M tensor framework, tensors can be decomposed in a matrix-mimetic way, including using the star-M SVD. This tensor SVD has optimality guarantees and has shown exceptional performance on specific types of data, but software implementations have been mostly limited to productivity-oriented languages. In this work, we present our development of a shared-memory parallel, high-performance solution designed to efficiently implement the underlying algorithms. This software will enable optimal compression of extensive scientific datasets, paving the way for enhanced data analysis and insights.

cs.DC↗

arXiv2025

Structured Column Subset Selection for Bayesian Optimal Experimental Design

We consider optimal experimental design (OED) for Bayesian inverse problems, where the experimental design variables have a certain multiway structure. Given $d$ different experimental variables with $m_i$ choices per design variable $1 \le i\le d$, the goal is to select $k_i \le m_i$ experiments per design variable. Previous work has related OED to the column subset selection problem by mapping the design variables to the columns of a matrix $\mathbf{A}$. However, this approach is applicable only to the case $d=1$ in which the columns can be selected independently. We develop an extension to the case where the design variables have a multi-way structure. Our approach is to map the matrix $\mathbf{A}$ to a tensor and perform column subset selection on mode unfoldings of the tensor. We develop an algorithmic framework with three different algorithmic templates, and randomized variants of these algorithms. We analyze the computational cost of all the proposed algorithms and also develop greedy versions to facilitate comparisons. Numerical experiments on four different applications -- time-dependent inverse problems, seismic tomography, X-ray tomography, and flow reconstruction -- demonstrate the effectiveness and scalability of our methods for structured experimental design in Bayesian inverse problems.

math.NA↗

arXiv2025

Bayesian D-Optimal Experimental Designs via Column Subset Selection

This paper tackles optimal sensor placement for Bayesian linear inverse problems, a popular version of the more general Optimal Experimental Design (OED) problem, using the D-optimality criterion. This is done by establishing connections between sensor placement and Column Subset Selection Problem (CSSP), which is a well-studied problem in Numerical Linear Algebra (NLA). In particular, we use the Golub-Klema-Stewart (GKS) approach which involves computing the truncated Singular Value Decomposition (SVD) followed by a pivoted QR factorization on the right singular vectors. The algorithms are further accelerated by using randomization to compute the low-rank approximation as well as for sampling the indices. The resulting algorithms are robust, computationally efficient, amenable to parallelization, require virtually no parameter tuning, and come with strong theoretical guarantees. One of the proposed algorithms is also adjoint-free which is beneficial in situations, where the adjoint is expensive to evaluate or is not available. Additionally, we develop a method for data completion without solving the inverse problem. Numerical experiments on model inverse problems involving the heat equation and seismic tomography in two spatial dimensions demonstrate the performance of our approaches.

math.NA↗

arXiv2020

An Alternating Rank-K Nonnegative Least Squares Framework (ARkNLS) for Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a prominent technique for data dimensionality reduction that has been widely used for text mining, computer vision, pattern discovery, and bioinformatics. In this paper, a framework called ARkNLS (Alternating Rank-k Nonnegativity constrained Least Squares) is proposed for computing NMF. First, a recursive formula for the solution of the rank-k nonnegativity-constrained least squares (NLS) is established. This recursive formula can be used to derive the closed-form solution for the Rank-k NLS problem for any integer k $\ge$ 1. As a result, each subproblem for an alternating rank-k nonnegative least squares framework can be obtained based on this closed form solution. Assuming that all matrices involved in rank-k NLS in the context of NMF computation are of full rank, two of the currently best NMF algorithms HALS (hierarchical alternating least squares) and ANLS-BPP (Alternating NLS based on Block Principal Pivoting) can be considered as special cases of ARkNLS with k = 1 and k = r for rank r NMF, respectively. This paper is then focused on the framework with k = 3, which leads to a new algorithm for NMF via the closed-form solution of the rank-3 NLS problem. Furthermore, a new strategy that efficiently overcomes the potential singularity problem in rank-3 NLS within the context of NMF computation is also presented. Extensive numerical comparisons using real and synthetic data sets demonstrate that the proposed algorithm provides state-of-the-art performance in terms of computational accuracy and cpu time.

math.NA↗

arXiv2019

PLANC: Parallel Low Rank Approximation with Non-negativity Constraints

We consider the problem of low-rank approximation of massive dense non-negative tensor data, for example to discover latent patterns in video and imaging applications. As the size of data sets grows, single workstations are hitting bottlenecks in both computation time and available memory. We propose a distributed-memory parallel computing solution to handle massive data sets, loading the input data across the memories of multiple nodes and performing efficient and scalable parallel algorithms to compute the low-rank approximation. We present a software package called PLANC (Parallel Low Rank Approximation with Non-negativity Constraints), which implements our solution and allows for extension in terms of data (dense or sparse, matrices or tensors of any order), algorithm (e.g., from multiplicative updating techniques to alternating direction method of multipliers), and architecture (we exploit GPUs to accelerate the computation in this work).We describe our parallel distributions and algorithms, which are careful to avoid unnecessary communication and computation, show how to extend the software to include new algorithms and/or constraints, and report efficiency and scalability results for both synthetic and real-world data sets.

math.NA↗

arXiv2019

A Microbenchmark Characterization of the Emu Chick

The Emu Chick is a prototype system designed around the concept of migratory memory-side processing. Rather than transferring large amounts of data across power-hungry, high-latency interconnects, the Emu Chick moves lightweight thread contexts to near-memory cores before the beginning of each memory read. The current prototype hardware uses FPGAs to implement cache-less "Gossamer cores for doing computational work and a stationary core to run basic operating system functions and migrate threads between nodes. In this multi-node characterization of the Emu Chick, we extend an earlier single-node investigation (Hein, et al. AsHES 2018) of the the memory bandwidth characteristics of the system through benchmarks like STREAM, pointer chasing, and sparse matrix-vector multiplication. We compare the Emu Chick hardware to architectural simulation and an Intel Xeon-based platform. Our results demonstrate that for many basic operations the Emu Chick can use available memory bandwidth more efficiently than a more traditional, cache-based architecture although bandwidth usage suffers for computationally intensive workloads like SpMV. Moreover, the Emu Chick provides stable, predictable performance with up to 65% of the peak bandwidth utilization on a random-access pointer chasing benchmark with weak locality.

cs.DC↗

arXiv2018

Programming Strategies for Irregular Algorithms on the Emu Chick

The Emu Chick prototype implements migratory memory-side processing in a novel hardware system. Rather than transferring large amounts of data across the system interconnect, the Emu Chick moves lightweight thread contexts to near-memory cores before the beginning of each remote memory read. Previous work has characterized the performance of the Chick prototype in terms of memory bandwidth and programming differences from more typical, non-migratory platforms, but there has not yet been an analysis of algorithms on this system. This work evaluates irregular algorithms that could benefit from the lightweight, memory-side processing of the Chick and demonstrates techniques and optimization strategies for achieving performance in sparse matrix-vector multiply operation (SpMV), breadth-first search (BFS), and graph alignment across up to eight distributed nodes encompassing 64 nodelets in the Chick system. We also define and justify relative metrics to compare prototype FPGA-based hardware with established ASIC architectures. The Chick currently supports up to 68x scaling for graph alignment, 80 MTEPS for BFS on balanced graphs, and 50\% of measured STREAM bandwidth for SpMV.

cs.DC↗