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Hierarchical matrices are space and time efficient representations of dense matrices that exploit the low rank structure of matrix blocks at different levels of granularity. The hierarchically low rank block partitioning produces…
Time delay estimation has long been an active area of research. In this work, we show that compressive sensing with interpolation may be used to achieve good estimation precision while lowering the sampling frequency. We propose an…
The volume of data and the velocity with which it is being generated by com- putational experiments on high performance computing (HPC) systems is quickly outpacing our ability to effectively store this information in its full fidelity.…
This paper introduces a new pseudodifferential preconditioner for the Helmholtz equation in variable media with absorption. The pseudodifferential operator is associated with the multiplicative inverse to the symbol of the Helmholtz…
Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattered data interpolation in a d-dimensional space, however,…
In this paper, we study numerical homogenization methods based on integral equations. Our work is motivated by materials such as concrete, modeled as composites structured as randomly distributed inclusions imbedded in a matrix. We…
Leveraging matrix sparsity has proven a fruitful strategy for accelerating quantum chemical calculations. Here we present the hierarchical SOS-MP2 algorithm, which uses hierarchical matrix ($\mathcal{H}^{2}$) compression of the electron…
Despite the success of deep neural networks (DNNs), state-of-the-art models are too large to deploy on low-resource devices or common server configurations in which multiple models are held in memory. Model compression methods address this…
Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be alternatively formulated as integral equations that are…
With lowrank approximation the storage requirements for dense data are reduced down to linear complexity and with the addition of hierarchy this also works for data without global lowrank properties. However, the lowrank factors itself are…
We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…
In this paper, we present methods for image compression on the basis of eigenvalue decomposition of normal matrices. The proposed methods are convenient and self-explanatory, requiring fewer and easier computations as compared to some…
We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…
In this work, we study the accuracy and efficiency of hierarchical matrix ($\mathcal{H}$-matrix) based fast methods for solving dense linear systems arising from the discretization of the 3D elastodynamic Green's tensors. It is well known…
This work focuses on reducing neural network size, which is a major driver of neural network execution time, power consumption, bandwidth, and memory footprint. A key challenge is to reduce size in a manner that can be exploited readily for…
Compute-in-memory (CIM) based neural network accelerators offer a promising solution to the Von Neumann bottleneck by computing directly within memory arrays. However, SRAM CIM faces limitations in executing larger models due to its cell…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
Deep neural networks have achieved strong performance in image classification tasks due to their ability to learn complex patterns from high-dimensional data. However, their large computational and memory requirements often limit deployment…
In recent years, commercial HTS superconductors have gained an increasing interest for their use in applications involving large-scale superconductor systems. These systems are typically made from hundreds to thousands of turns of…
We propose and analyze an inexact gradient method based on incremental proper orthogonal decomposition (iPOD) to address the data storage difficulty in time-dependent PDE-constrained optimization, particularly for a data assimilation…