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Empirical Dynamic Modeling (EDM) is a state-of-the-art non-linear time-series analysis framework. Despite its wide applicability, EDM was not scalable to large datasets due to its expensive computational cost. To overcome this obstacle,…

Mapping the electrostatic potential (ESP) distribution around ions in electrolyte solution is crucial for the establishment of a microscopic understanding of electrolyte solution properties. For solutions in the bulk phase, it has not been…

The trending integrations of Battery Energy Storage System (BESS, stationary battery) and Electric Vehicles (EV, mobile battery) to distribution grids call for advanced Demand Side Management (DSM) technique that addresses the scalability…

A current challenge in atomistic machine learning is that of efficiently predicting the response of the electron density under electric fields. We address this challenge with symmetry-adapted kernel functions that are specifically derived…

The impact of targeted replacement of individual terms in empirical force fields is quantitatively assessed for pure water, dichloromethane (DCM), and solvated K$^+$ and Cl$^-$ ions. For the electrostatics, point charges (PCs) and machine…

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…

The kernel polynomial method (KPM) is a powerful numerical method for approximating spectral densities. Typical implementations of the KPM require an a prior estimate for an interval containing the support of the target spectral density,…

Classical molecular dynamics simulations have recently become a standard tool for the study of electrochemical systems. State-of-the-art approaches represent the electrodes as perfect conductors, modelling their responses to the charge…

Atomic partial charges appear in the Coulomb term of many force-field models and can be derived from electronic structure calculations with a myriad of atoms-in-molecules (AIM) methods. More advanced models have also been proposed, using…

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…

Fundamental mechanisms of energy storage, corrosion, sensing, and multiple biological functionalities are directly coupled to electrical processes and ionic dynamics at solid-liquid interfaces. In many cases, these processes are spatially…

Accurate, yet computationally efficient energy functions are essential for state-of-the art molecular dynamics (MD) studies of condensed phase systems. Here, a generic workflow based on a combination of machine learning-based and empirical…

Characterizing conformational transitions in physical systems remains a fundamental challenge, as traditional sampling methods struggle with the high-dimensional nature of molecular systems and high-energy barriers between stable states.…

To further develop accurate and large-scale simulations of electrochemical interfaces, we propose a unified explicit electric potential framework to simultaneously predict atomic forces and electron density distributions. The framework…

Computing ground-state properties of molecules is a promising application for quantum computers operating in concert with classical high-performance computing resources. Quantum embedding methods are a family of algorithms particularly…

We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. This MMD, which is also known as energy distance, has several advantageous…

The algebraic reformulation of molecular Quantum Electrodynamics (mQED) at finite temperatures is applied to Nuclear Magnetic Resonance (NMR) in order to provide a foundation for the reconstruction of much more detailed molecular…

In recent years, molecular dynamics (MD) simulations have emerged as a pivotal tool for understanding the structure, dynamics, and phase behavior in charged soft matter systems. To explore phenomena across greater length and time scales in…

This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…

In recent years, significant progress has been made in the development of machine learning potentials (MLPs) for atomistic simulations with applications in many fields from chemistry to materials science. While most current MLPs are based…