Related papers: Improved Implementation of Approximate Full Mass M…
Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…
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…
Mixed-precision quantization is a promising approach for compressing large language models under tight memory budgets. However, existing mixed-precision methods typically suffer from one of two limitations: they either rely on expensive…
QM/MM hybrid methods employ accurate quantum (QM) models only in regions of interest (defects) and switch to computationally cheaper interatomic potential (MM) models to describe the crystalline bulk. We develop two QM/MM hybrid methods for…
An implicit mass-matrix penalization (IMMP) of Hamiltonian dynamics is proposed, and associated dynamical integrators, as well as sampling Monte-Carlo schemes, are analyzed for systems with multiple time scales. The penalization is based on…
The widespread adoption of machine learning algorithms necessitates hardware acceleration to ensure efficient performance. This acceleration relies on custom matrix engines that operate on full or reduced-precision floating-point…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
The Optimized Gradient Method (OGM), its strongly convex extension, the Information Theoretical Exact Method (ITEM), as well as the related Triple Momentum Method (TMM) have superior convergence guarantees when compared to the Fast Gradient…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…
Learning the closest matrix product state (MPS) representation of a quantum state enables useful tools for quantum machine learning and analysis of complex quantum systems. In this work, we study the problem of learning MPS in the following…
In this work, we present an extension to a linear Model Predictive Control (MPC) scheme that plans external contact forces for the robot when given multiple contact locations and their corresponding friction cone. To this end, we set up a…
Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently,…
We propose a novel scheme that allows MIMO system to modulate a set of permutation matrices to send more information bits, extending our initial work on the topic. This system is called Permutation Matrix Modulation (PMM). The basic idea is…
Pulay's Residual Metric Minimization (RMM) method is one of the standard techniques for achieving self consistency in ab initio electronic structure calculations. We describe a reformulation of Pulay's RMM which guarantees reduction of the…
Quantum mechanics/molecular mechanics (QM/MM) hybrid models allow one to address chemical phenomena in complex molecular environments. Whereas this modeling approach can cope with a large system size at moderate computational costs, the…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Large scale atomistic simulations with suitable interatomic potentials are widely employed by scientists or engineers of different areas. Quick generation of high-quality interatomic potentials is of urgent need under present circumstances,…
Numerous linear and non-linear data-detection and precoding algorithms for wideband massive multi-user (MU) multiple-input multiple-output (MIMO) wireless systems that rely on orthogonal frequency-division multiplexing (OFDM) or…
Numerical approximation of quantum states via convex combinations of states with positive partial transposes (bi-PPT state) in multipartite systems constitutes a fundamental challenge in quantum information science. We reformulate this…
We introduce the use of the Fast Multipole Method (FMM) to speed up gravitational lensing ray tracing calculations. The method allows very fast calculation of ray deflections when a large number of deflectors, $N_*$, is involved, while…