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

Abstract: Time-slicing has emerged as a strategy for incorporating semiclassical propagation into real-time path integral formulation and recovering full quantum mechanical dynamics. A central step is the decomposition of a time-evolved wave function into a superposition of Gaussian wave packets. Here we introduce a quadrature-free variational framework for Gaussian wave packet decomposition, reformulating it as an optimization problem in which the parameters of Gaussian wave packets 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) simulation allows a route to improving the semiclassical result to the full quantum mechanical result in a systematic manner.