Related papers: The Fast Slepian Transform
When solving the time-dependent radiative transport equation (RTE), implicit time discretization is often employed for its robustness and stability. This results in a sequence of steady-state RTEs with identical cross-sections but varying…
This is the second part in a series of papers on multi-step schemes for solving coupled forward backward stochastic differential equations (FBSDEs). We extend the basic idea in our former paper [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci.…
The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…
Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94,PF95]. One difficulty in dealing with…
This paper presents an efficient and concise double fast algorithm to solve high dimensional time-space fractional diffusion problems with spectral fractional Laplacian. We first establish semi-discrete scheme of time-space fractional…
Approximate counting via correlation decay is the core algorithmic technique used in the sharp delineation of the computational phase transition that arises in the approximation of the partition function of anti-ferromagnetic two-spin…
Compressed Sensing (CS) takes advantage of signal sparsity or compressibility and allows superb signal reconstruction from relatively few measurements. Based on CS theory, a suitable dictionary for sparse representation of the signal is…
We propose a patchwise local Fourier extension method for approximating smooth functions on general two dimensional domains with curved boundaries. The domain is embedded into a Cartesian background grid and decomposed into rectangular…
We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Lo\`eve transform, and several others along with their continuous counterparts (Fourier transform, Fourier series,…
The dominant paradigm in computational materials discovery relies on heavily parameterized deep architectures, including message-passing graph networks and equivariant models, that require millions of DFT-labeled training structures and…
In this paper we approximate high-dimensional functions $f\colon\mathbb T^d\to\mathbb C$ by sparse trigonometric polynomials based on function evaluations. Recently it was shown that a dimension-incremental sparse Fourier transform (SFT)…
We investigate the S/N of a new incoherent dedispersion algorithm optimized for FPGA-based architectures intended for deployment on ASKAP and other SKA precursors for fast transients surveys. Unlike conventional CPU- and GPU-optimized…
The knowledge of effective masses is a key ingredient to analyze numerous properties of semiconductors, like carrier mobilities, (magneto-)transport properties, or band extrema characteristics yielding carrier densities and density of…
3D Gaussian splatting (3DGS) has shown its detailed expressive ability and highly efficient rendering speed in the novel view synthesis (NVS) task. The application to inverse rendering still faces several challenges, as the discrete nature…
In this paper an approach for decreasing the computational effort required for the split-step Fourier method (SSFM) is introduced. It is shown that using the sparsity property of the simulated signals, the compressive sampling algorithm can…
While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…
Deep learning-based techniques for automatic dysarthric speech detection have recently attracted interest in the research community. State-of-the-art techniques typically learn neurotypical and dysarthric discriminative representations by…
Diffusion Policy (DP) excels in embodied control but suffers from high inference latency and computational cost due to multiple iterative denoising steps. The temporal complexity of embodied tasks demands a dynamic and adaptable computation…
For a sample set of 1024 values, the FFT is 102.4 times faster than the discrete Fourier transform (DFT). The basis for this remarkable speed advantage is the `bit-reversal' scheme of the Cooley-Tukey algorithm. Eliminating the burden of…
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…