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.
| Subjects: | Machine Learning (cs.LG); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph) |
| Cite as: | arXiv:2512.13913 [cs.LG] |
| (or arXiv:2512.13913v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2512.13913 arXiv-issued DOI via DataCite |
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| Journal reference: | Mach. Learn.: Sci. Technol. 7 (2026) 025062 |
| Related DOI: | https://doi.org/10.1088/2632-2153/ae57f8
DOI(s) linking to related resources |
From: Patrick Egenlauf [view email]
[v1]
Mon, 15 Dec 2025 21:48:10 UTC (220 KB)
[v2]
Thu, 19 Mar 2026 15:41:09 UTC (250 KB)
[v3]
Tue, 5 May 2026 08:13:48 UTC (250 KB)
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