Results 51 to 60 of about 16,403 (208)
, 2014 In this paper we introduce a reproducing kernel Hilbert space defined on $\mathbb{R}^{d+1}$ as the tensor product of a reproducing kernel defined on the unit sphere $\mathbb{S}^{d}$ in $\mathbb{R}^{d+1}$ and a reproducing kernel defined on $[0,\infty ...
Brauchart, Johann S. +2 more
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Advanced Energy Materials, EarlyView.This perspective highlights how machine learning accelerates sustainable energy materials discovery by integrating quantum‐accurate interatomic potentials with property prediction frameworks. The evolution from statistical methods to physics‐informed neural networks is examined, showcasing applications across batteries, catalysts, and photovoltaics ...
Kwang S. Kim
wiley +1 more source
Boundary Value ProblemsIn this work, we investigate the Klein–Gordon equation, a physical problem, using the reproducing kernel Hilbert space method (RKHSM). The analytical solution is expressed as a series within the reproducing kernel Hilbert space (RKHS).
Hadjer Zerouali +6 more
doaj +1 more source
Toward efficient quantum computation of molecular ground‐state energies
AIChE Journal, EarlyView.Abstract Variational quantum eigensolvers (VQEs) represent a promising approach to computing molecular ground states and energies on modern quantum computers. These approaches use a classical computer to optimize the parameters of a trial wave function, while the quantum computer simulates the energy by preparing and measuring a set of bitstring ...
Farshud Sorourifar +8 more
wiley +1 more source
Density Problem and Approximation Error in Learning Theory
Abstract and Applied Analysis, 2013 We study the density problem and approximation error of reproducing kernel Hilbert spaces for the purpose of learning theory. For a Mercer kernel on a compact metric space (, ), a characterization for the generated reproducing kernel Hilbert space (RKHS)
Ding-Xuan Zhou
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Advanced Intelligent Discovery, EarlyView.Feature selection combined with machine learning and high‐throughput experimentation enables efficient handling of high‐dimensional datasets in emerging photovoltaics. This approach accelerates material discovery, improves process optimization, and strengthens stability prediction, while overcoming challenges in data quality and model scalability to ...
Jiyun Zhang +5 more
wiley +1 more source
Application of Reproducing Kernel Hilbert Space Method for Solving a Class of Nonlinear Integral Equations [PDF]
Mathematical Problems in Engineering, 2017 A new approach based on the Reproducing Kernel Hilbert Space Method is proposed to approximate the solution of the second‐kind nonlinear integral equations. In this case, the Gram‐Schmidt process is substituted by another process so that a satisfactory result is obtained. In this method, the solution is expressed in the form of a series.
Sedigheh Farzaneh Javan +2 more
openaire +1 more source
A probabilistic diagnostic for Laplace approximations: Introduction and experimentation
Canadian Journal of Statistics, EarlyView.Abstract Many models require integrals of high‐dimensional functions: for instance, to obtain marginal likelihoods. Such integrals may be intractable, or too expensive to compute numerically. Instead, we can use the Laplace approximation (LA). The LA is exact if the function is proportional to a normal density; its effectiveness therefore depends on ...
Shaun McDonald, Dave Campbell
wiley +1 more source
Regularized system identification using orthonormal basis functions
, 2015 Most of existing results on regularized system identification focus on regularized impulse response estimation. Since the impulse response model is a special case of orthonormal basis functions, it is interesting to consider if it is possible to tackle ...
Chen, Tianshi, Ljung, Lennart
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Chemistry–Methods, EarlyView.Expanded porphyrins, with their flexible structures and rich redox chemistry, offer a powerful platform to explore how aromaticity shapes molecular properties. This review introduces a multidimensional framework to quantify Hückel and Möbius aromaticity and examines its impact on the spectroscopic behavior across redox‐ and topology‐controlled expanded
Freija De Vleeschouwer +2 more
wiley +1 more source