Applied & Computational Mathematics seminar: QH-GEM: Quantum-Hydrodynamic Generative Modeling

Speaker:  Sarswati Shah, George Mason University

Title:  QH-GEM: Quantum-Hydrodynamic Generative Modeling

Abstract:   Generative models can be interpreted as transporting a simple reference probability distribution toward a target distribution. In many modern approaches, the transport map, velocity field, or score function is learned from data. This talk presents a different perspective in which the transport mechanism is prescribed by a physical PDE. We introduce QH-GEM, a deterministic, physics-constrained generative framework based on the Madelung formulation of the free-particle Schrödinger equation. A reference probability density is evolved together with a controllable initial phase, whose gradient determines the hydrodynamic velocity field and hence the characteristic flow that transports samples. Once the initial phase is fixed, randomness enters only through the initial sampling; the subsequent evolution is deterministic. This viewpoint leads naturally to a PDE-constrained phase-identification problem for matching a prescribed target distribution. The talk discusses the underlying transport structure, exact reachability results for Gaussian distributions, a short-time connection with classical transport maps, and numerical examples demonstrating phase identification for non-Gaussian targets. These results provide a mathematical proof of concept for phase-controlled quantum hydrodynamics as a deterministic framework for generative modeling.

Time:  Friday, September 18, 1:30pm – 2:30pm
Place:  Exploratory Hall, room 4106 or Zoom