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This work presents a multi-layered methodology for efficiently accelerating multimodal foundation models (MFMs). It combines hardware and software co-design of transformer blocks with an optimization pipeline that reduces computational and…
Multivariate time series imputation is fundamental in applications such as healthcare, traffic forecasting, and biological modeling, where sensor failures and irregular sampling lead to pervasive missing values. However, existing…
The computational efficiency of many neural operators, widely used for learning solutions of PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations. As the FFT is limited to equispaced (rectangular) grids,…
Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…
Accurate simulations of various physical processes on digital computers requires huge computing performance, therefore accelerating these scientific and engineering applications has a great importance. Density of programmable logic devices…
Fourier transforms are an often necessary component in many computational tasks, and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a…
In view of recently demonstrated joint use of novel Fourier-transform techniques and effective high-accuracy frequency domain solvers related to the Method of Moments, it is argued that a set of transformative innovations could be developed…
Computational micromechanics and homogenization require the solution of the mechanical equilibrium of a periodic cell that comprises a (generally complex) microstructure. Techniques that apply the Fast Fourier Transform have attracted much…
Objective: Most deep neural network-based diffusion tensor imaging methods require the diffusion gradients' number and directions in the data to be reconstructed to match those in the training data. This work aims to develop and evaluate a…
Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense…
The Fast Fourier Transform (FFT) is one of the most widely used algorithms in high performance computing, with critical applications in spectral analysis for both signal processing and the numerical solution of partial differential…
Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient…
The fast algorithms in Fourier optics have invigorated multifunctional device design and advanced imaging technologies. However, the necessity for fast computations has led to limitations in the widely used conventional Fourier methods,…
Pseudo-spectral method is one of the most accurate techniques for simulating turbulent flows. Fast Fourier transform (FFT) is an integral part of this method. In this paper, we present a new procedure to compute FFT in which we save…
We give a fairly comprehensive review of wavelets and of their application to density-functional theory (DFT) and to our recent application of a wavelet-based version of linear-response time-dependent DFT (LR-TD-DFT). Our intended audience…
Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of…
High-throughput approximations of quantum mechanics calculations and combinatorial experiments have been traditionally used to reduce the search space of possible molecules, drugs and materials. However, the interplay of structural and…
The non-equidistant fast Fourier transform (NFFT) is an extension of the famous fast Fourier transform (FFT), which can be applied to non-equidistantly sampled data in time/space or frequency domain. It is an approximative algorithm that…
High-performance computing platforms are becoming more and more heterogeneous, which makes it very difficult for researchers and scientific software developers to keep up with the rapid changes on the hardware market. In this paper, the…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…