Related papers: fmmgen: Automatic Code Generation of Operators for…
The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We…
We describe a methodology for designing efficient parallel and distributed scientific software. This methodology utilizes sequences of mechanizable algebra--based optimizing transformations. In this study, we apply our methodology to the…
Polynomial multiplication is a key algorithm underlying computer algebra systems (CAS) and its efficient implementation is crucial for the performance of CAS. In this paper we design and implement algorithms for polynomial multiplication…
We present the first quantum-hardware implementation of a Hamiltonian simulation algorithm that produces signed vector-field solutions to the time-domain Maxwells equations using a Schrodingerisation-based approach. The electromagnetic…
Quantum algorithms for computational linear algebra promise up to exponential speedups for applications such as simulation and regression, making them prime candidates for hardware realization. But these algorithms execute in a model that…
Large Language Models (LLMs) have shown remarkable capabilities in code generation tasks, yet they face significant limitations in handling complex, long-context programming challenges and demonstrating complex compositional reasoning…
This work introduces a kernel-independent, multilevel, adaptive algorithm for efficiently evaluating a discrete convolution kernel with a given source distribution. The method is based on linear algebraic tools such as low rank…
Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct…
In this paper, we will introduce a new heterogeneous fast multipole method (H-FMM) for 2-D Helmholtz equation in layered media. To illustrate the main algorithm ideas, we focus on the case of two and three layers in this work. The key…
Prompt engineering enables Large Language Models (LLMs) to perform a variety of tasks. However, lengthy prompts significantly increase computational complexity and economic costs. To address this issue, we study six prompt compression…
Valiant showed that Boolean matrix multiplication (BMM) can be used for CFG parsing. We prove a dual result: CFG parsers running in time $O(|G||w|^{3 - \myeps})$ on a grammar $G$ and a string $w$ can be used to multiply $m \times m$ Boolean…
Quantum simulation of the interactions of fermions and bosons -- the fundamental particles of nature -- is essential for modeling complex quantum systems in material science, chemistry and high-energy physics and has been proposed as a…
We present a GPU accelerated CUDA-C implementation of the Barnes Hut (BH) tree code for calculating the gravitational potential on octree adaptive meshes. The tree code algorithm is implemented within the FLASH4 adaptive mesh refinement…
Neural machine translation (NMT) methods developed for natural language processing have been shown to be highly successful in automating translation from one natural language to another. Recently, these NMT methods have been adapted to the…
There are many methods used to compute the classical gravitational field in astrophysical simulation codes. With the exception of the typically impractical method of direct computation, none ensure conservation of angular momentum to…
The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine learning algorithms to develop…
In this paper, we explore how numerical calculations can be accelerated by implementing several numerical methods of fractional-order systems using parallel computing techniques. We investigate the feasibility of parallel computing…
We have newly developed a Parallelized Particle-Particle Particle-tree code for Planet formation, PENTACLE, which is a parallelized hybrid $N$-body integrator executed on a CPU-based (super)computer. PENTACLE uses a 4th-order Hermite…
Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…
Purpose: Previously-developed Voxel Spread Function (VSF) method (Yablonskiy, et al, MRM, 2013;70:1283) provides means to correct artifacts induced by macroscopic magnetic field inhomogeneities in the images obtained by…