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Peer-reviewedCC BYJournal of scientific computing

High-Order BUG Dynamical Low-Rank Integrators Based on Explicit Runge-Kutta Methods.

  • Fabio Nobile1
  • Sébastien Riffaud1
  1. 1CSQI Chair, École Polytechnique Fédérale de Lausanne, Lausanne, 1015 Switzerland
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Abstract

In this work, we introduce high-order Basis-Update & Galerkin (BUG) integrators based on explicit Runge-Kutta methods for large-scale matrix differential equations. These dynamical low-rank integrators extend the BUG integrator [1] to arbitrary explicit Runge-Kutta schemes by performing a BUG step at each stage of the method. The resulting Runge-Kutta BUG (RK-BUG) integrators are robust with respect to small singular values, fully forward in time, and high-order accurate, while enabling conservation and rank adaptivity. We prove that RK-BUG integrators retain the order of convergence of the underlying Runge-Kutta method until the error reaches a plateau corresponding to the low-rank truncation error, which vanishes as the rank becomes full. This theoretical analysis is supported by several numerical experiments. The results demonstrate the high-order convergence of the RK-BUG integrator and its superior accuracy compared to other existing dynamical low-rank integrators.

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Cite

BibTeXRIS
BibTeX
@article{nobile2026highorder,
  title = {{High-Order BUG Dynamical Low-Rank Integrators Based on Explicit Runge-Kutta Methods.}},
  author = {Fabio Nobile and Sébastien Riffaud},
  journal = {Journal of scientific computing},
  year = {2026},
  month = may,
  doi = {10.1007/s10915-026-03317-5},
  url = {https://europepmc.org/article/MED/42898398},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - High-Order BUG Dynamical Low-Rank Integrators Based on Explicit Runge-Kutta Methods.
AU  - Fabio Nobile
AU  - Sébastien Riffaud
PY  - 2026
DA  - 2026/05/13
JO  - Journal of scientific computing
DO  - 10.1007/s10915-026-03317-5
UR  - https://europepmc.org/article/MED/42898398
AB  - In this work, we introduce high-order Basis-Update & Galerkin (BUG) integrators based on explicit Runge-Kutta methods for large-scale matrix differential equations. These dynamical low-rank integrators extend the BUG integrator [1] to arbitrary explicit Runge-Kutta schemes by performing a BUG step at each stage of the method. The resulting Runge-Kutta BUG (RK-BUG) integrators are robust with respect to small singular values, fully forward in time, and high-order accurate, while enabling conservation and rank adaptivity. We prove that RK-BUG integrators retain the order of convergence of the underlying Runge-Kutta method until the error reaches a plateau corresponding to the low-rank truncation error, which vanishes as the rank becomes full. This theoretical analysis is supported by several numerical experiments. The results demonstrate the high-order convergence of the RK-BUG integrator and its superior accuracy compared to other existing dynamical low-rank integrators.
SN  - 0885-7474
SN  - 1573-7691
ER  -