Variational Adaptive Gaussian Decomposition: Scalable Quadrature-Free Time-Sliced Thawed Gaussian Dynamics

TL;DR

This paper introduces VAGD, a neural network-based variational method for decomposing quantum wave functions into Gaussian packets, enabling scalable, quadrature-free semiclassical quantum dynamics simulations.

Contribution

It presents a novel variational adaptive Gaussian decomposition framework that optimizes GWP parameters using neural networks, improving semiclassical quantum dynamics modeling.

Findings

VAGD produces compact Gaussian expansions for wave functions.

The method enhances semiclassical approximations towards full quantum accuracy.

VAGD is scalable and adaptable during wave function propagation.

Abstract

Time-slicing has emerged as a strategy for incorporating semiclassical propagation into real-time path integral formulation and recovering full quantum dynamics. A central step is the decomposition of a time-evolved wave function into a superposition of Gaussian wave packets (GWPs). Here we introduce a quadrature-free variational framework for GWP decomposition, reformulating it as an optimization problem in which the GWP parameters are chosen to maximize the overlap with the time-evolving wave function. An autoencoder-decoder neural network is used for this optimization, with the representation being adaptively reoptimized during propagation. Each wave packet in this decomposition represents a localized patch of the underlying semiclassical manifold, while retaining full correlations between all degrees of freedom. This variational adaptive Gaussian decomposition (VAGD) approach yields a compact Gaussian expansion, providing a scalable route to time-sliced semiclassical quantum dynamics. While general, applying VAGD to facilitate time-slicing of thawed Gaussian approximation (TGA) allows a route to improving the semiclassical treatment to the full quantum mechanical result in a systematic manner.