Quantum Dynamics via Score Matching on Bohmian Trajectories

• URL: http://arxiv.org/abs/2604.25137v1
• Date: Tue, 28 Apr 2026 02:25:48 GMT
• Title: Quantum Dynamics via Score Matching on Bohmian Trajectories
• Abstract summary: We solve the time-dependent Schrdinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories.<n>By recasting real-time quantum dynamics as a self-consistent score-driven normalizing flow, this framework opens the time-dependent Schrdinger equation to the rapidly advancing toolkit of modern generative modeling.
• Score: 2.8019312134731233
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We solve the time-dependent Schrödinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under the classical potential supplemented by a quantum potential depending on the score function of the evolving density. These non-crossing Bohmian trajectories form a continuous normalizing flow governed by the score. We parametrize the score with a neural network and minimize a self-consistent Fisher divergence between the network and the score of the resulting density. We prove that the zero-loss minimizer of this self-consistent objective recovers Schrödinger dynamics for nodeless wave functions, a condition naturally met in quantum vibrations of atoms. We demonstrate the approach on wavepacket splitting in a double-well potential and anharmonic vibrations of a Morse chain. By recasting real-time quantum dynamics as a self-consistent score-driven normalizing flow, this framework opens the time-dependent Schrödinger equation to the rapidly advancing toolkit of modern generative modeling.

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