Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations

• URL: http://arxiv.org/abs/2512.13913v1
• Date: Mon, 15 Dec 2025 21:48:10 GMT
• Title: Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations
• Authors: Patrick Egenlauf, Iva Březinová, Sabine Andergassen, Miriam Klopotek,
• Abstract summary: We show that a neural ODE model trained on exact 2RDM data can reproduce its dynamics without any explicit three-particle information.<n>The magnitude of the time-averaged three-particle-correlation buildup appears to be the primary predictor of success.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Out-of-equilibrium quantum many-body systems exhibit rapid correlation buildup that underlies many emerging phenomena. Exact wave-function methods to describe this scale exponentially with particle number; simpler mean-field approaches neglect essential two-particle correlations. The time-dependent two-particle reduced density matrix (TD2RDM) formalism offers a middle ground by propagating the two-particle reduced density matrix (2RDM) and closing the BBGKY hierarchy with a reconstruction of the three-particle cumulant. But the validity and existence of time-local reconstruction functionals ignoring memory effects remain unclear across different dynamical regimes. We show that a neural ODE model trained on exact 2RDM data (no dimensionality reduction) can reproduce its dynamics without any explicit three-particle information -- but only in parameter regions where the Pearson correlation between the two- and three-particle cumulants is large. In the anti-correlated or uncorrelated regime, the neural ODE fails, indicating that no simple time-local functional of the instantaneous two-particle cumulant can capture the evolution. The magnitude of the time-averaged three-particle-correlation buildup appears to be the primary predictor of success: For a moderate correlation buildup, both neural ODE predictions and existing TD2RDM reconstructions are accurate, whereas stronger values lead to systematic breakdowns. These findings pinpoint the need for memory-dependent kernels in the three-particle cumulant reconstruction for the latter regime. Our results place the neural ODE as a model-agnostic diagnostic tool that maps the regime of applicability of cumulant expansion methods and guides the development of non-local closure schemes. More broadly, the ability to learn high-dimensional RDM dynamics from limited data opens a pathway to fast, data-driven simulation of correlated quantum matter.

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