Optimization of fluid mixing by reinforcement learning using limit cycles of a dynamical system
Abstract
We propose a method to overcome the difficulties encountered when applying reinforcement learning to fluid mixing processes. The proposed method has two main features: (i) it does not require detailed measurements of the flow state, and (ii) by effectively exploiting a stable limit cycle of a two-dimensional dynamical system (the Li'enard system), it can stably perform optimization without imposing explicit constraints on the control parameters. As an illustrative example, we optimize a process in which a fluid contained in a cylindrical vessel is mixed by periodically rotating the vessel. The resulting optimal vessel motion is physically reasonable: it reverses its direction of rotation before a solid-body rotation state is established. Furthermore, even when the fluid viscosity increases with time during the mixing process, the method can continuously adapt the control parameters to the changing viscosity.
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BibTeX
@misc{shimizu2026optimization,
title = {{Optimization of fluid mixing by reinforcement learning using limit cycles of a dynamical system}},
author = {Masaki Shimizu and Daiki Watanabe and Takumi Aoyagi and Susumu Goto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21405},
eprint = {2609.21405},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21405},
}
RIS
TY - UNPB
TI - Optimization of fluid mixing by reinforcement learning using limit cycles of a dynamical system
AU - Masaki Shimizu
AU - Daiki Watanabe
AU - Takumi Aoyagi
AU - Susumu Goto
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21405
UR - https://arxiv.org/abs/2609.21405
AB - We propose a method to overcome the difficulties encountered when applying reinforcement learning to fluid mixing processes. The proposed method has two main features: (i) it does not require detailed measurements of the flow state, and (ii) by effectively exploiting a stable limit cycle of a two-dimensional dynamical system (the Li'enard system), it can stably perform optimization without imposing explicit constraints on the control parameters. As an illustrative example, we optimize a process in which a fluid contained in a cylindrical vessel is mixed by periodically rotating the vessel. The resulting optimal vessel motion is physically reasonable: it reverses its direction of rotation before a solid-body rotation state is established. Furthermore, even when the fluid viscosity increases with time during the mixing process, the method can continuously adapt the control parameters to the changing viscosity.
ER -