Related papers: Permutationally Invariant, Reproducing Kernel-Base…
Reproducing kernel Hilbert spaces (RKHSs) are key elements of many non-parametric tools successfully used in signal processing, statistics, and machine learning. In this work, we aim to address three issues of the classical RKHS based…
Two different methods of the covariant relativistic separable kernel construction in the Bethe-Salpeter approach are considered. One of them leads in the center-of-mass system of two particles to the quasipotential equation. The constructed…
Chemical accuracy serves as an important metric for assessing the effectiveness of the numerical method in Kohn--Sham density functional theory. It is found that to achieve chemical accuracy, not only the Kohn--Sham wavefunctions but also…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
Multiscale Models are known to be successful in uncovering and analyzing the structures in data at different resolutions. In the current work we propose a feature driven Reproducing Kernel Hilbert space (RKHS), for which the associated…
Machine learned interatomic potentials (MLIPs) are becoming a standard method for DFT-level accurate molecular dynamics simulation and large-scale studies of crystal energetics. Increasingly popular are universal pre-trained potentials,…
In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R}^d$. For two-dimensional surfaces embedded…
A new method for synthesizing Single-Bit Reconfigurable Passive Electromagnetic Skins (1RP-EMSs) featuring advanced beam shaping capabilities is proposed. By using single-bit unit cells, the multi-scale problem of controlling 1RP-EMSs is…
Reconfigurable electromagnetic structures (REMSs), such as reconfigurable reflectarrays (RRAs) or reconfigurable intelligent surfaces (RISs), hold significant potential to improve the spectral efficiency of wireless communication systems…
We introduce property-independent kernels for machine learning modeling of arbitrarily many molecular properties. The kernels encode molecular structures for training sets of varying size, as well as similarity measures sufficiently diffuse…
The polarizable embedding (PE) model is a fragment-based quantum-classical approach aimed at accurate inclusion of environment effects in quantum-mechanical response property calculations. The aim of this tutorial is to give insight into…
Following recent work in search of a universal function (Van Hooydonk, Eur J Inorg Chem, 1999, 1617), we test symmetric potentials for reproducing molecular potential energy curves (PECs). For a bond, a four-particle system, charge…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
This paper considers the construction of Reproducing Kernel Hilbert Spaces (RKHS) on the sphere as an alternative to the conventional Hilbert space using the inner product that yields the L^2(S^2) function space of finite energy signals. In…
The accurate quantum chemical calculation of excited states is a challenging task, often requiring computationally demanding methods. When entire ground and excited potential energy surfaces (PESs) are desired, e.g., to predict the…
Nonlinearities in piezoelectric systems can arise from internal factors such as nonlinear constitutive laws or external factors like realizations of boundary conditions. It can be difficult or even impossible to derive detailed models from…
The representation of the potential energy surfaces of atom molecule or molecular dimers interactions should account faithfully for the symmetry properties of the systems, preserving at the same time a compact analytical form. To this aim,…
Isomerization, i.e. the rearrangement between distinct molecular configurations, is a fundamental process in chemistry. Here we demonstrate that two-dimensional Coulomb crystals can emulate molecular isomerization and be used to…
A central problem of materials science is to determine whether a hypothetical material is stable without being synthesized, which is mathematically equivalent to a global optimization problem on a highly non-linear and multi-modal potential…
The rich phenomenology of quantum many-body systems such as atomic nuclei is complex to interpret. Often, the behaviour (e.g. evolution with the number of constituents) of measurable/observable quantities such as binding or excitation…