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Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
The great success of Physics-Informed Neural Networks (PINN) in solving partial differential equations (PDEs) has significantly advanced our simulation and understanding of complex physical systems in science and engineering. However, many…
A novel parallel simulation algorithm on the GPU, implemented in CUDA and C++, is presented for the simulation of Brownian particles that display excluded volume repulsion and interact with long and short range forces. When an explicit…
In this paper, two accelerated divide-and-conquer algorithms are proposed for the symmetric tridiagonal eigenvalue problem, which cost $O(N^2r)$ {flops} in the worst case, where $N$ is the dimension of the matrix and $r$ is a modest number…
The main objective of this paper is to present an efficient structure-preserving scheme, which is based on the idea of the scalar auxiliary variable approach, for solving the space fractional nonlinear Schr\"{o}dinger equation. First, we…
In this paper we implemented the algorithm we developed in [1] called 3DPIFCM in a parallel environment by using CUDA on a GPU. In our previous work we introduced 3DPIFCM which performs segmentation of images in noisy conditions and uses…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
The Partitioning Min-Max Weighted Matching (PMMWM) problem is an NP-hard problem that combines the problem of partitioning a group of vertices of a bipartite graph into disjoint subsets with limited size and the classical Min-Max Weighted…
We develop an efficient parallel algorithm for answering shortest-path queries in planar graphs and implement it on a multi-node CPU/GPU clusters. The algorithm uses a divide-and-conquer approach for decomposing the input graph into small…
The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the…
We present a parallel implementation of a direct solver for the Poisson's equation on extreme-scale supercomputers with accelerators. We introduce a chunked-pencil decomposition as the domain-decomposition strategy to distribute work among…
We study the balanced $k$-way hypergraph partitioning problem, with a special focus on its practical applications to manycore scheduling. Given a hypergraph on $n$ nodes, our goal is to partition the node set into $k$ parts of size at most…
With their constantly increasing peak performance and memory capacity, modern supercomputers offer new perspectives on numerical studies of open many-body quantum systems. These systems are often modeled by using Markovian quantum master…
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…
In this article we design a novel quasi-regression Monte Carlo algorithm in order to approximate the solution of discrete time backward stochastic differential equations (BSDEs), and we analyze the convergence of the proposed method. The…
A new flow solver scalable on multiple Graphics Processing Units (GPUs) for direct numerical simulation of wall-bounded incompressible flow is presented. This solver utilizes a previously reported work (J. Comp. Physics, vol. 352 (2018),…
In this paper, we propose a design methodology to partition and map the neurons and synapses of online learning SNN-based applications to neuromorphic architectures at {run-time}. Our design methodology operates in two steps -- step 1 is a…
The exponential growth of computational workloads is surpassing the capabilities of conventional architectures, which are constrained by fundamental limits. In-memory computing (IMC) with RRAM provides a promising alternative by providing…
Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…
In this article, we present a parallel recursive algorithm based on multi-level domain decomposition that can be used as a precondtioner to a Krylov subspace method to solve sparse linear systems of equations arising from the discretization…