Related papers: FFTArray: A Python Library for the Implementation …
Arrays are ubiquitous in the context of software verification. However, effective reasoning over arrays is still rare in CP, as local reasoning is dramatically ill-conditioned for constraints over arrays. In this paper, we propose an…
Understanding fracture in cementitious materials caused by the deposition and growth of corrosion products requires scale-bridging approaches due to the large length-scale difference between the micro-pores, where deposition occurs, and the…
Fourier Ptychographic Microscopy (FPM) is a computational imaging method that is able to super-resolve features beyond the diffraction-limit set by the objective lens of a traditional microscope. This is accomplished by using synthetic…
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…
Density Functional Theory (DFT) is the de facto workhorse for large-scale electronic structure calculations in chemistry and materials science. While plane-wave DFT implementations remain the most widely used, real-space DFT provides…
The Fast Fourier Transform (FFT) over a finite field $\mathbb{F}_q$ computes evaluations of a given polynomial of degree less than $n$ at a specifically chosen set of $n$ distinct evaluation points in $\mathbb{F}_q$. If $q$ or $q-1$ is a…
To represent the biological variability of clinical neuroimaging populations, it is vital to be able to combine data across scanners and studies. However, different MRI scanners produce images with different characteristics, resulting in a…
We present a new library for parallel distributed Fast Fourier Transforms (FFT). The importance of FFT in science and engineering and the advances in high performance computing necessitate further improvements. AccFFT extends existing FFT…
As the large language models (LLMs) grow in size each day, efficient training and fine-tuning has never been as important as nowadays. This resulted in the great interest in parameter efficient fine-tuning (PEFT), and effective methods…
Continuous-depth learning has recently emerged as a novel perspective on deep learning, improving performance in tasks related to dynamical systems and density estimation. Core to these approaches is the neural differential equation, whose…
In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appropriate change of variables, can be rewritten as…
We propose an implementation of the algorithm for the fast Fourier transform (FFT) as a quantum circuit consisting of a combination of some quantum gates. In our implementation, a data sequence is expressed by a tensor product of vector…
All major weather and climate applications are currently developed using languages such as Fortran or C++. This is typical in the domain of high performance computing (HPC), where efficient execution is an important concern. Unfortunately,…
We present an efficient, fast and robust Nonlinear Fourier Transform (NFT) algorithm to detect eigenvalues of the discrete spectrum. It outperforms other known NFT algorithms as it detects the eigenvalues from the continuous spectrum, the…
In this paper, we present an early version of a SYCL-based FFT library, capable of running on all major vendor hardware, including CPUs and GPUs from AMD, ARM, Intel and NVIDIA. Although preliminary, the aim of this work is to seed further…
Multidimensional arrays (NDArrays) are a central abstraction in modern scientific computing environments. Unfortunately, they can make reasoning about programs harder as the number of different array shapes used in an execution of a program…
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…
We introduce Fuzzy PyTorch, a framework for rapid evaluation of numerical variability in deep learning (DL) models. As DL is increasingly applied to diverse tasks, understanding variability from floating-point arithmetic is essential to…
Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each…
The fast Fourier transform (FFT) is a primitive kernel in numerous fields of science and engineering. OpenFFT is an open-source parallel package for 3-D FFTs, built on a communication-optimal domain decomposition method for achieving…