Related papers: Dimension-free path-integral molecular dynamics wi…
In this work, a novel ring polymer representation for multi-level quantum system is proposed for thermal average calculations. The proposed presentation keeps the discreteness of the electronic states: besides position and momentum, each…
Conventional molecular dynamics (MD) simulation approaches, such as $\textit{ab initio}$ MD (AIMD) and empirical force field MD (EFFMD), face significant trade-offs between physical accuracy and computational efficiency. This work presents…
A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics…
When the Channel State Information (CSI) is known by both the transmitter and the receiver, beamforming techniques employing Singular Value Decomposition (SVD) are commonly used in Multiple-Input Multiple-Output (MIMO) systems. Without…
The impact of polymer-polymer interactions of various types on the thermodynamics, structure, and accommodation of topological constraints is addressed for systems comprising many directed polymers in two spatial dimensions. The approach is…
Convergence analysis of Markov chain Monte Carlo methods in high-dimensional statistical applications is increasingly recognized. In this paper, we develop general mixing time bounds for Metropolis-Hastings algorithms on discrete spaces by…
Full-wave 3D electromagnetic simulations of complex planar devices, multilayer interconnects, and chip packages are presented for wide-band frequency-domain analysis using the finite difference integration technique developed in the PETSc…
Molecular dynamics (MD) simulations provide atomistic insights into the structure, dynamics, and function of biomolecules by generating time-resolved, high-dimensional trajectories. Analyzing such data benefits from estimating the minimal…
Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations…
We are interested in mesh-free formulas based on the Monte-Carlo methodology for the approximation of multi-dimensional integrals, and we investigate their accuracy when the functions belong to a reproducing-kernel space. A kernel typically…
Path integral molecular dynamics (PIMD), which maps a quantum particle onto a fictitious classical system of ring polymers and propagates the "beads" of this extended classical system using molecular dynamics, is widely used to capture…
The exact formulation of the path integral centroid dynamics is extended to include composites of the position and momentum operators. We present the generalized centroid dynamics (GCD), which provides a basis to calculate Kubo-transformed…
This work develops advanced numerical methods for free-surface simulations of polymer mixing processes, integrating a Volume of Fluid (VOF) interface-capturing approach with a non-conforming Immersed Boundary (IB) method to model two-phase…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
We present a Data-Driven (DD) paradigm that enables molecular dynamics calculations to be performed directly from sampled force-field data such as obtained, e.g., from ab initio calculations, thereby eschewing the conventional step of…
We study the relaxation dynamics of a coarse-grained polymer chain at different degrees of stretching by both analytical means and numerical simulations. The macromolecule is modelled as a string of beads, connected by anharmonic springs,…
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement,…
Dynamic Programming (DP) suffers from the well-known ``curse of dimensionality'', further exacerbated by the need to compute expectations over process noise in stochastic models. This paper presents a Monte Carlo-based sampling approach for…
We develop a path-integral dynamics method for water that resembles centroid molecular dynamics (CMD), except that the centroids are averages of curvilinear, rather than cartesian, bead coordinates. The curvilinear coordinates are used…
The theoretical justification of the Hybrid Monte Carlo algorithm depends upon the molecular dynamics trajectories within it being exactly reversible. If computations were carried out with exact arithmetic then it would be easy to ensure…