Related papers: Permutationally Invariant, Reproducing Kernel-Base…
A new analytical potential energy surface (PES) has been constructed for H$_2^+$-He using a reproducing kernel Hilbert space (RKHS) representation from an extensive number of $ab initio$ energies computed at the multi-reference and full…
Kernel methods such as kernel ridge regression and Gaussian process regressions with Matern type kernels have been increasingly used, in particular, to fit potential energy surfaces (PES) and density functionals, and for materials…
The methanol molecule is a sensitive probe of astrochemistry, astrophysics, and fundamental physics. The first-principles elucidation and prediction of its rotation-torsional-vibrational motions are enabled in this work by the computation…
Two new nine-dimensional potential energy surfaces (PESs) have been generated using high-level \textit{ab initio} theory for the two main isotopologues of methyl chloride, CH$_{3}{}^{35}$Cl and CH$_{3}{}^{37}$Cl. The respective PESs,…
The role of numerical accuracy in training and evaluating neural network-based potential energy surfaces is examined for different experimental observables. For observables that require third- and fourth-order derivatives of the total…
Modeling non-empirical and highly flexible interatomic potential energy surfaces (PES) using machine learning (ML) approaches is becoming popular in molecular and materials research. Training an ML-PES is typically performed in two stages:…
In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
The newly developed machine learning (ML) empirical pseudopotential (EP) method overcomes the poor transferability of the traditional EP method with the help of ML techniques while preserving its formal simplicity and computational…
Hierarchical data pervades diverse machine learning applications, including natural language processing, computer vision, and social network analysis. Hyperbolic space, characterized by its negative curvature, has demonstrated strong…
We introduce an accurate and efficient algebraic technique for the computation of the vibrational spectra of triatomic molecules, of both linear and bent equilibrium geometry. The full three-dimensional potential energy surface (PES), which…
We propose a simple scheme to estimate potential energy surface (PES) with which the accuracy can be easily controlled and improved up to the level of the density functional theory (DFT) calculations. It is based on a model selection within…
This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the theoretical and numerical foundations on positive-definite…
We discuss a theoretical approach that employs machine learning potential energy surfaces (ML-PESs) in the nonadiabatic dynamics simulation of polyatomic systems by taking 6-aminopyrimidine as a typical example. The Zhu-Nakamura theory is…
Highly accurate force fields are a mandatory requirement to generate predictive simulations. Here we present the path for the construction of machine learned molecular force fields by discussing the hierarchical pathway from generating the…
In this work, we present a new fitting of the Na+HF potential energy surface (PES) utilizing a new optmization method based in Genetic Algorithm. Topology studies, such as isoenergetic contours and Minimum Energy Path(MEP), show that the…
A kernel-based method (kernelized minimal distributed charge model - kMDCM) to represent the molecular electrostatic potential (ESP) in terms of off-center point charges whose positions adapts to the molecular geometry. Using Gaussian…
Electromagnetic structure (EMS) design plays a critical role in developing advanced antennas and materials, but remains challenging due to high-dimensional design spaces and expensive evaluations. While existing methods commonly employ…
Motivated by applications to the study of stochastic processes, we introduce a new analysis of positive definite kernels $K$, their reproducing kernel Hilbert spaces (RKHS), and an associated family of feature spaces that may be chosen in…
This paper presents two new adiabatic, global potential energy surfaces (PESs) for the two lowest $^3A'$ and $^3A''$ electronic states of the O($^3P$)+H$_2$ system. For each of these states, ab initio electronic energies were calculated for…