Related papers: Kernel-based Minimal Distributed Charges: A Confor…
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed…
Accurate simulations of atomistic systems from first principles are limited by computational cost. In high-throughput settings, machine learning can reduce these costs significantly by accurately interpolating between reference…
In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…
The Koopman operator is a linear, infinite-dimensional operator that governs the dynamics of system observables; Extended Dynamic Mode Decomposition (EDMD) is a data-driven method for approximating the Koopman operator using functions…
Extended dynamic mode decomposition (EDMD) is a popular data-driven method to predict the action of the Koopman operator, i.e., the evolution of an observable function along the flow of a dynamical system. In this paper, we leverage a…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
The interaction of condensed phase systems with external electric fields is crucial in myriad processes in nature and technology ranging from the field-directed motion of cells (galvanotaxis), to energy storage and conversion systems…
A multiscale QM/classical approach is presented, that is able to model the optical properties of complex nanostructures composed of a molecular system adsorbed on metal nanoparticles. The latter are described by a combined…
Understanding electron energy dynamics in low-temperature plasmas such as capacitively coupled plasmas (CCPs), including energy absorption, conversion, transport, and dissipation, is essential for interpreting discharge physics and process…
Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with…
The analysis of the damage on plasma facing materials (PFM), due to its direct interaction with the plasma environment, is needed to build the next generation of nuclear machines, where tungsten has been proposed as a candidate. In this…
This review describes recent advances by the authors and others on the topic of incorporating experimental data into molecular simulations through maximum entropy methods. Methods which incorporate experimental data improve accuracy in…
In order to rigorously evaluate the energy and dipole moment of a certain configuration of molecules one needs to solve the Schr\"odinger equation. Repeating this for many different configurations allows one to determine the potential…
A crucial aspect in the simulation of electrochemical interfaces consists in treating the distribution of electronic charge of electrode materials that are put in contact with an electrolyte solution. Recently, it has been shown how a…
We present a quasi-conforming embedded reproducing kernel particle method (QCE-RKPM) for modeling heterogeneous materials that makes use of techniques not available to mesh-based methods such as the finite element method (FEM) and avoids…
The Kernel Polynomial Method (KPM) is a well-established scheme in quantum physics and quantum chemistry to determine the eigenvalue density and spectral properties of large sparse matrices. In this work we demonstrate the high optimization…
Energy decomposition analysis (EDA) based on absolutely localized molecular orbitals provides detailed insights into intermolecular bonding by decomposing the total molecular binding energy into physically meaningful components. Here, we…
The paper describes the coupling of the MercuryDPM discrete element method (DEM) code and the implementation of the kernel-independent fast multipole method (KIFMM). The combined simulation framework allows addressing the large class of…
The consistency of a learning method is usually established under the assumption that the observations are a realization of an independent and identically distributed (i.i.d.) or mixing process. Yet, kernel methods such as support vector…
We study spectral algorithms in the setting where kernels are learned from data. We introduce the effective span dimension (ESD), an alignment-sensitive complexity measure that depends jointly on the signal, spectrum, and noise level…