Related papers: Automatic Synthesis of Low-Complexity Translation …
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…
Multiphysics simulations play an essential role in accurately modeling complex interactions across diverse scientific and engineering domains Although neural operators especially the Fourier Neural Operator FNO have significantly improved…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
We propose a multipole representation of the Fermi-Dirac function and the Fermi operator, and use this representation to develop algorithms for electronic structure analysis of metallic systems. The new algorithm is quite simple and…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
For the majority of the applications of Reed-Solomon (RS) codes, hard decision decoding is based on syndromes. Recently, there has been renewed interest in decoding RS codes without using syndromes. In this paper, we investigate the…
In this work, we propose a novel low complexity Generalised Frequency Division Multiplexing (GFDM) transceiver design. GFDM modulation matrix is factorized into FFT matrices and a diagonal matrix to design low complexity GFDM transmitter.…
Tensor Train (TT) decompositions provide a powerful framework to compress grid-structured data, such as sampled function values, on regular Cartesian grids. Such high compression, in turn, enables efficient high-dimensional computations.…
In the kernel density estimation (KDE) problem one is given a kernel $K(x, y)$ and a dataset $P$ of points in a Euclidean space, and must prepare a data structure that can quickly answer density queries: given a point $q$, output a…
We propose a high-order FDTD scheme based on the correction function method (CFM) to treat interfaces with complex geometry without increasing the complexity of the numerical approach for constant coefficients. Correction functions are…
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…
We present a numerical method for the analysis of mutual coupling effects in large, dense and irregular arrays with identical antennas. Building on the Method of Moments (MoM), our technique employs a Macro Basis Function (MBF) approach for…
A large part of modern machine learning theory often involves computing the high-dimensional expected trace of a rational expression of large rectangular random matrices. To symbolically compute such quantities using free probability…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
The extended Hubbard model on a two-dimensional lattice captures key physical phenomena, but is challenging to simulate due to the presence of long-range interactions. In this work, we present an efficient quantum algorithm for simulating…
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…
Developments of nonlocal operators for modeling processes that traditionally have been described by local differential operators have been increasingly active during the last few years. One example is peridynamics for brittle materials and…
In this paper, we propose two low-complexity peak to average power ratio(PAPR) reduction algorithms for orthogonal frequency division multiplexing(OFDM) signals. The main content is as follows: First, a non-convex optimization model is…
This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive…
Characteristic mode (CM) analysis poses challenges in computational electromagnetics (CEM) as it calls for efficient solutions of dense generalized eigenvalue problems (GEP). Multilevel fast multipole algorithm (MLFMA) can greatly reduce…