Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914529608204288 |
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| author | Egenlauf, Patrick Březinová, Iva Andergassen, Sabine Klopotek, Miriam |
| author_facet | Egenlauf, Patrick Březinová, Iva Andergassen, Sabine Klopotek, Miriam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13913 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations Egenlauf, Patrick Březinová, Iva Andergassen, Sabine Klopotek, Miriam Machine Learning Statistical Mechanics Quantum Physics 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. |
| title | Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations |
| topic | Machine Learning Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2512.13913 |