Related papers: A Tutorial and Open Source Software for the Effici…
We propose an effective and flexible way to implement 2D and 3D elastoplastic problems in MATLAB using fully vectorized codes. Our technique is applied to a broad class of the problems including perfect plasticity or plasticity with…
Tight binding (TB) models are one approach to the quantum mechanical many particle problem. An important role in TB models is played by hopping and overlap matrix elements between the orbitals on two atoms, which of course depend on the…
The rapid development of the Transformer-based Large Language Models (LLMs) in recent years has been closely linked to their ever-growing and already enormous sizes. Many LLMs contain hundreds of billions of parameters and require dedicated…
The 3D Discrete Fourier Transform (DFT) is a technique used to solve problems in disparate fields. Nowadays, the commonly adopted implementation of the 3D-DFT is derived from the Fast Fourier Transform (FFT) algorithm. However, evidence…
Training machine learning interatomic potentials that are both computationally and data-efficient is a key challenge for enabling their routine use in atomistic simulations. To this effect, we introduce franken, a scalable and lightweight…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…
Predicting equipment anomalies before they escalate into failures is a critical challenge in industrial facility management. Existing approaches rely either on hand-crafted threshold rules, which lack generalizability, or on large neural…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
We propose an efficient algorithm for the evaluation of the potential and its gradient of gravitational/electrostatic $N$-body systems, which we call particle mesh multipole method (PMMM or PM$^3$). PMMM can be understood both as an…
Low energy barrier magnet (LBM) technology has recently been proposed as a candidate for accelerating algorithms based on energy minimization and probabilistic graphs because their physical characteristics have a one-to-one mapping onto the…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
We introduce a new class of machine learning interatomic potentials - fast General Two- and Three-body Potential (GTTP), which is as fast as conventional empirical potentials and require computational time that remains constant with…
Boolean matrix has been used to represent digital information in many fields, including bank transaction, crime records, natural language processing, protein-protein interaction, etc. Boolean matrix factorization (BMF) aims to find an…
We develop a framework for efficiently transforming certain approximation algorithms into differentially-private variants, in a black-box manner. Specifically, our results focus on algorithms A that output an approximation to a function f…
This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and…
Large kernel convolutions offer a scalable alternative to vision transformers for high-resolution 3D volumetric analysis, yet naively increasing kernel size often leads to optimization instability. Motivated by the spatial bias inherent in…
A major challenge in single particle reconstruction methods using cryo-electron microscopy is to attain a resolution sufficient to interpret fine details in three-dimensional (3D) macromolecular structures. Obtaining high resolution 3D…
Peridynamic (PD) theory is significant and promising in engineering and materials science; however, it imposes challenges owing to the enormous computational cost caused by its nonlocality. Our main contribution, which overcomes the…
We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider…
Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…