Related papers: A Dual-space Multilevel Kernel-splitting Framework…

The Fast Multipole Method (FMM) is an efficient numerical algorithm for computation of long-ranged forces in $N$-body problems within gravitational and electrostatic fields. This method utilizes multipole expansions of the Green's function…

Deep Metric Learning (DML) methods have been proven relevant for visual similarity learning. However, they sometimes lack generalization properties because they are trained often using an inappropriate sample selection strategy or due to…

This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous…

We present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here the unit cell) with advanced electronic-structure methods, that are computationally too expensive for periodic…

Scale-invariance, good localization and robustness to noise and distortions are the main properties that a local feature detector should possess. Most existing local feature detectors find excessive unstable feature points that increase the…

As telecommunication systems evolve to meet increasing demands, integrating deep neural networks (DNNs) has shown promise in enhancing performance. However, the trade-off between accuracy and flexibility remains challenging when replacing…

Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…

Existing permutation-invariant methods can be divided into two categories according to the aggregation scope, i.e. global aggregation and local one. Although the global aggregation methods, e. g., PointNet and Deep Sets, get involved in…

Knowledge distillation (KD) is known as a promising solution to compress large language models (LLMs) via transferring their knowledge to smaller models. During this process, white-box KD methods usually minimize the distance between the…

We develop a combined machine learning (ML) and quantum mechanics approach that enables data-efficient reconstruction of flexible molecular force fields from high-level ab initio calculations, through the consideration of fundamental…

Affine Frequency Division Multiplexing (AFDM), a new chirp-based multicarrier waveform for high mobility communications, is introduced here. AFDM is based on discrete affine Fourier transform (DAFT), a generalization of discrete Fourier…

We introduce a deep generative framework for high-dimensional Bayesian inference that enables efficient posterior sampling. As telescopes and simulations rapidly expand the volume and resolution of astrophysical data, fast simulation-based…

Dynamic mode (DM) decomposition decomposes spatiotemporal signals into basic oscillatory components (DMs). DMs can improve the accuracy of neural decoding when used with the nonlinear Grassmann kernel, compared to conventional power…

Extreme learning machine (ELM) is a methodology for solving partial differential equations (PDEs) using a single hidden layer feed-forward neural network. It presets the weight/bias coefficients in the hidden layer with random values, which…

Deep neural networks face several challenges in hyperspectral image classification, including complex and sparse ground object distributions, small clustered structures, and elongated multi-branch features that often lead to missing…

Standard infinite-width limits of neural networks sacrifice the ability for intermediate layers to learn representations from data. Recent work (A theory of representation learning gives a deep generalisation of kernel methods, Yang et al.…

We present a unified treatment of the Fourier spectra of spherically symmetric nonlocal diffusion operators. We develop numerical and analytical results for the class of kernels with weak algebraic singularity as the distance between source…

In this paper, we will introduce a new heterogeneous fast multipole method (H-FMM) for 2-D Helmholtz equation in layered media. To illustrate the main algorithm ideas, we focus on the case of two and three layers in this work. The key…

Based on recent advancements in using machine learning for classical density functional theory for systems with one-dimensional, planar inhomogeneities, we propose a machine learning model for application in two dimensions (2D) akin to…

This master thesis introduces the idea of dynamic cutoffs in molecular dynamics simulations, based on the distance between particles and the interface, and presents a solution for detecting interfaces in real-time. Our dynamic cutoff method…