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Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. An efficient algorithm for the…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
We develop and study FPGA implementations of algorithms for charged particle tracking based on graph neural networks. The two complementary FPGA designs are based on OpenCL, a framework for writing programs that execute across heterogeneous…
The polar decomposition of a matrix is a key element in the quantum linear algebra toolbox. We show that the problem of quantum polar decomposition, recently studied in Lloyd et al. [LBP+20], has a simple and concise implementation via the…
In recent years graphical processing units (GPUs) have become a powerful tool in scientific computing. Their potential to speed up highly parallel applications brings the power of high performance computing to a wider range of users.…
Graph algorithms and techniques are increasingly being used in scientific and commercial applications to express relations and explore large data sets. Although conventional or commodity computer architectures, like CPU or GPU, can compute…
To respond to the need of efficient training and inference of deep neural networks, a plethora of domain-specific hardware architectures have been introduced, such as Google Tensor Processing Units and NVIDIA Tensor Cores. A common feature…
Force-directed algorithms are widely used for visualizing graphs. However, these algorithms are computationally expensive in producing good quality layouts for complex graphs. The layout quality is largely influenced by execution time and…
Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which…
Recent advances in multi and many-core processors have led to significant improvements in the performance of scientific computing applications. However, the addition of a large number of complex cores have also increased the overall power…
We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which…
The use of FPGAs for efficient graph processing has attracted significant interest. Recent memory subsystem upgrades including the introduction of HBM in FPGAs promise to further alleviate memory bottlenecks. However, modern multi-channel…
New real structure-preserving decompositions are introduced to develop fast and robust algorithms for the (right) eigenproblem of general quaternion matrices. Under the orthogonally JRS-symplectic transformations, the Francis JRS-QR step…
During the last years, algorithms known as Convolutional Neural Networks (CNNs) had become increasingly popular, expanding its application range to several areas. In particular, the image processing field has experienced a remarkable…
Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…
FPGA technology can offer significantly hi\-gher performance at much lower power consumption than is available from CPUs and GPUs in many computational problems. Unfortunately, programming for FPGA (using ha\-rdware description languages,…
Core decomposition is a classic technique for discovering densely connected regions in a graph with large range of applications. Formally, a $k$-core is a maximal subgraph where each vertex has at least $k$ neighbors. A natural extension of…
Deep Neural Networks (DNNs) have shown significant advantages in a wide variety of domains. However, DNNs are becoming computationally intensive and energy hungry at an exponential pace, while at the same time, there is a vast demand for…
Convolutional Neural Networks (CNNs) are state-of-the-art in numerous computer vision tasks such as object classification and detection. However, the large amount of parameters they contain leads to a high computational complexity and…
Transport map methods offer a powerful statistical learning tool that can couple a target high-dimensional random variable with some reference random variable using invertible transformations. This paper presents new computational…