Related papers: A Surface Hopping Gaussian Beam Method for High-Di…
Surface hopping algorithms are popular tools to study dynamics of the quantum-classical mixed systems. In this paper, we propose a surface hopping algorithm in diabatic representations, based on time dependent perturbation theory and…
Recently, the mapping approach to surface hopping (MASH) was proposed as a method to simulate the non-adiabatic dynamics of two-level systems. It was shown that the method possesses many desirable qualities, both theoretically and through…
The quantum-classical Liouville equation offers a rigorous approach to nonadiabatic quantum dynamics based on surface hopping type trajectories. However, in practice the applicability of this approach has been limited to short times owing…
Inspired by the Boltzmann kinetics, we propose a collision-based dynamics with a Monte Carlo solution algorithm that approximates the solution of the multi-marginal optimal transport problem via randomized pairwise swapping of sample…
Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single…
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…
We develop a surface hopping algorithm based on frozen Gaussian approximation for semiclassical matrix Schr\"odinger equations, in the spirit of Tully's fewest switches surface hopping method. The algorithm is asymptotically derived from…
The rapid growth of 3D Gaussian Splatting (3DGS) has revolutionized neural rendering, enabling real-time production of high-quality renderings. However, the previous 3DGS-based methods have limitations in urban scenes due to reliance on…
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\em in both space and time}.Such PDE…
Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single…
Nonlinear stochastic motion presents significant challenges for Bayesian particle tracking. To address this challenge, this paper proposes a framework to construct an invertible transformation that maps the nonlinear state-space model (SSM)…
We propose an optimization algorithm called Frictionless Hamiltonian Descent, which is a direct counterpart of classical Hamiltonian Monte Carlo in sampling. We analyze Frictionless Hamiltonian Descent for strongly convex quadratic…
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…
Hopping transport in a one-dimensional system is studied numerically. A fast algorithm is devised to find the lowest-resistance path at arbitrary electric field. Probability distribution functions of individual resistances on the path and…
In this article, we propose a Frozen Gaussian Sampling (FGS) algorithm for simulating nonadiabatic quantum dynamics at metal surfaces with a continuous spectrum. This method consists of a Monte-Carlo algorithm for sampling the initial wave…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
We present a nonadiabatic classical-trajectory approach that offers the best of both worlds between fewest-switches surface hopping (FSSH) and quasiclassical mapping dynamics. This mapping approach to surface hopping (MASH) propagates the…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
This paper generalizes stochastic collocation methods to handle correlated non-Gaussian random parameters. The key challenge is to perform a multivariate numerical integration in a correlated parameter space when computing the coefficient…
Autonomous vehicles are expected to navigate in complex traffic scenarios with multiple surrounding vehicles. The correlations between road users vary over time, the degree of which, in theory, could be infinitely large, thus posing a great…