相关论文: Variational Adaptive Gaussian Decomposition: Scala…

We study the time-sliced thawed Gaussian propagation method, which was recently proposed for solving the time-dependent Schr\"odinger equation. We introduce a triplet of quadrature-based analysis, synthesis and re-initialization operators…

We propose a Standing Wave Decomposition (SWD) approximation to Gaussian Process regression (GP). GP involves a costly matrix inversion operation, which limits applicability to large data analysis. For an input space that can be…

The ultimate semiclassical wave packet propagation technique is a complex, time-dependent WBK method known as generalized Gaussian wave packet dynamics (GGWPD). It requires overcoming many technical difficulties in order to be carried out…

We consider modeling of angular or directional data viewed as a linear variable wrapped onto a unit circle. In particular, we focus on the spatio-temporal context, motivated by a collection of wave directions obtained as computer model…

A method for performing variable-width (thawed) Gaussian wavepacket (GWP) variational dynamics on machine-learned potentials is presented. Instead of fitting the potential energy surface (PES), the anharmonic correction to the global…

The free expansion of a Gaussian wavepacket is a problem commonly discussed in undergraduate quantum classes by directly solving the time-dependent Schrodinger equation as a differential equation. In this work, we provide an alternative way…

Gaussian wave packets (GWPs) are well suited as basis functions to describe the time evolution of arbitrary wave functions in systems with nonsingular smooth potentials. They are less so in atomic systems on account of the singular behavior…

3D Gaussian Splatting has emerged as an alternative 3D representation for novel view synthesis, benefiting from its high-quality rendering results and real-time rendering speed. However, the 3D Gaussians learned by 3D-GS have ambiguous…

Stein Variational Gradient Descent (SVGD) is a nonparametric particle-based deterministic sampling algorithm. Despite its wide usage, understanding the theoretical properties of SVGD has remained a challenging problem. For sampling from a…

Gaussian wavepackets are a popular tool for semiclassical analyses of classically chaotic systems. We demonstrate that they are extremely powerful in the semiquantal analysis of such systems, too, where their dynamics can be recast in an…

We develop a non-linear distributional renormalisation algebra for Gaussian Quantum Foam, built from sequences of scaled Gaussians on spacelike hypersurfaces of homotopic, globally hyperbolic spacetimes and their distributional limits. The…

We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…

We assessed three schemes for propagating a variable-width (thawed) Gaussian wave packet moving under the influence of Morse or double-well potentials with parameters that are chemically representative. The most rigorous scheme is based on…

Many approximate solutions of the time-dependent Schr\"odinger equation can be formulated as exact solutions of a nonlinear Schr\"odinger equation with an effective Hamiltonian operator depending on the state of the system. We show that…

The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be…

Scalable spatial GPs for massive datasets can be built via sparse Directed Acyclic Graphs (DAGs) where a small number of directed edges is sufficient to flexibly characterize spatial dependence. The DAG can be used to devise fast algorithms…

An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of…

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model…

Video tokenization procedure is critical for a wide range of video processing tasks. Most existing approaches directly transform video into fixed-grid and patch-wise tokens, which exhibit limited versatility. Spatially, uniformly allocating…