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Machine learning relies on the availability of a vast amount of data for training. However, in reality, most data are scattered across different organizations and cannot be easily integrated under many legal and practical constraints. In…

Edge devices are being deployed at increasing volumes to sense and act on information from the physical world. The discrete Fourier transform (DFT) is often necessary to make this sensed data suitable for further processing -- such as by…

Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…

The marriage of density functional theory (DFT) and deep learning methods has the potential to revolutionize modern computational materials science. Here we develop a deep neural network approach to represent DFT Hamiltonian (DeepH) of…

Understanding the flow of complex media is relevant for a wide range of research fields and industrial applications. Several numerical approaches exist by which approximate solutions can be determined for the Stokes equations that describe…

Photonic computing has emerged as a promising platform for accelerating computational tasks with high degrees of parallelism, such as image processing and neural network. We present meta-DFT (discrete Fourier transform), a single layer…

In this paper we focus on the integration of high-performance numerical libraries in ab initio codes and the portability of performance and scalability. The target of our work is FLEUR, a software for electronic structure calculations…

With many advantageous features, softness and better biocompatibility, flexible electronic devices have developed rapidly and increasingly attracted attention. Many currently applications with flexible devices are sensors and drivers, while…

Cyclotomic fast Fourier transforms (CFFTs) are efficient implementations of discrete Fourier transforms over finite fields, which have widespread applications in cryptography and error control codes. They are of great interest because of…

Computer simulations are becoming an essential tool in many scientific fields from molecular dynamics to aeronautics. In glaciology, future predictions of sea level change require input from ice sheet models. Due to uncertainties in the…

Density-functional perturbation theory (DFPT) is nowadays the method of choice for the accurate computation of linear and non-linear response properties of materials from first principles. A notable advantage of DFPT over alternative…

Most communications systems tend to achieve bandwidth, power and cost efficiencies to capable to describe modulation scheme. Hence for signal modulation, orthogonal frequency division multiplexing (OFDM) transceiver is introduced to cover…

With the rapid growth of deep learning, there is an increasing availability of open-source models for various tasks. However, single fine-tuned models often fall short of meeting the diverse needs of users. Model merging has thus emerged as…

Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…

Training deep neural networks (DNNs) is a computationally expensive job, which can take weeks or months even with high performance GPUs. As a remedy for this challenge, community has started exploring the use of more efficient data…

In deep time series forecasting, the Fourier Transform (FT) is extensively employed for frequency representation learning. However, it often struggles in capturing multi-scale, time-sensitive patterns. Although the Wavelet Transform (WT)…

GPU-based fast Fourier transform (FFT) is extremely important for scientific computing and signal processing. However, we find the inefficiency of existing FFT libraries and the absence of fault tolerance against soft error. To address…

FPGAs are rarely mentioned when discussing the implementation of large machine learning applications, such as Large Language Models (LLMs), in the data center. There has been much evidence showing that single FPGAs can be competitive with…

Resonances in optical systems are useful for many applications, such as frequency comb generation, optical filtering, and biosensing. However, many of these applications are difficult to implement in optical metasurfaces because traditional…