相关论文: The Heterogeneous Multi-Scale Method
Homogenization appeared more than 100 years ago. It is an approach to study the macro-behavior of a medium by its micro-properties. In mathematics, homogenization theory considers the limitations of the sequences of the problems and its…
Hardware heterogeneity across diverse user devices poses new challenges for beam-based communication in 5G and beyond. This heterogeneity limits the applicability of machine learning (ML)-based algorithms. This article highlights the…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
We consider randomized block coordinate stochastic mirror descent (RBSMD) methods for solving high-dimensional stochastic optimization problems with strongly convex objective functions. Our goal is to develop RBSMD schemes that achieve a…
In our work, we propose to represent HTM as a set of flat models, or layers, and a set of topical hierarchies, or edges. We suggest several quality measures for edges of hierarchical models, resembling those proposed for flat models. We…
Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…
Multi-frequency, highly-oscillatory Hamiltonian problems derive from the mathematical modelling of many real life applications. We here propose a variant of Hamiltonian Boundary Value Methods (HBVMs), which is able to efficiently deal with…
In this paper, we construct a hierarchy of hybrid numerical methods for multi-scale kinetic equations based on moment realizability matrices, a concept introduced by Levermore, Morokoff and Nadiga. Following such a criterion, one can…
Sampling-based inference has seen a surge of interest in recent years. Hamiltonian Monte Carlo (HMC) has emerged as a powerful algorithm that leverages concepts from Hamiltonian dynamics to efficiently explore complex target distributions.…
Decays of unstable heavy particles usually involve the coherent sum of several amplitudes, like in a multiple slit experiment. Dedicated amplitude analysis techniques have been widely used to resolve these amplitudes for better…
We show that the properties of the lower part of the spectrum of the Helmholtz equation for an heterogeneous system in a finite region in $d$ dimensions, where the solutions to the homogeneous problems are known, can be systematically…
Hierarchical multi-label classification (HMC) is a challenging classification task extending standard multi-label classification problems by imposing a hierarchy constraint on the classes. In this paper, we propose C-HMCNN(h), a novel…
Multiscale modeling of material properties has emerged as one of the grand challenges in material science and engineering. We provide a comprehensive, though not exhaustive, overview of the current status of multiscale simulations of…
$\Gamma$-convergence techniques are used to give a characterization of the behavior of a family of heterogeneous multiple scale integral functionals. Periodicity, standard growth conditions and nonconvexity are assumed whereas a stronger…
This study introduces a hybrid machine learning-based scale-bridging framework for predicting the permeability of fibrous textile structures. By addressing the computational challenges inherent to multiscale modeling, the proposed approach…
We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together…
Multivariate longitudinal data of mixed-type are increasingly collected in many science domains. However, algorithms to cluster this kind of data remain scarce, due to the challenge to simultaneously model the within- and between-time…
In this paper, we propose a unified framework, the Hessian discretisation method (HDM), which is based on four discrete elements (called altogether a Hessian discretisation) and a few intrinsic indicators of accuracy, independent of the…
Multimodal foundation models that can holistically process text alongside images, video, audio, and other sensory modalities are increasingly used in a variety of real-world applications. However, it is challenging to characterize and study…
This article presents general procedures for constructing, estimating, and testing Hilbert space multi-dimensional (HSM) models, which are based on quantum probability theory. HSM models can be applied to collections of K different…