Reduced-order modeling of two-dimensional turbulent Rayleigh-Bénard flow by hybrid quantum-classical reservoir computing
P. Pfefer, F. Heyder, J. Schumacher · 2023 · Phys. Rev. Research 5, 043242
| 编号 QC060 | 主题 数据驱动方法 | 链接 arXiv:2307.03053 |
摘要
摘要保留原文（英文）
摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。
Two hybrid quantum-classical reservoir computing models are presented to reproduce low-order statistical properties of a two-dimensional turbulent Rayleigh-Bénard convection flow at a Rayleigh number and a Prandtl number . These properties comprise the mean vertical profiles of the root mean square velocity and temperature and the turbulent convective heat flux. The latter is composed of vertical velocity and temperature and measures the global turbulent heat transfer across the convection layer; it manifests locally in coherent hot and cold thermal plumes that rise from the bottom and fall from the top boundaries. Both quantum algorithms differ by the arrangement of the circuit layers of the quantum reservoir, in particular the entanglement layers. The second of the two quantum circuit architectures, denoted as H2, enables a complete execution of the reservoir update inside the quantum circuit without the usage of external memory. Their performance is compared with that of a classical reservoir computing model. Therefore, all three models have to learn the nonlinear and chaotic dynamics of the turbulent flow at hand in a lowerdimensional latent data space which is spanned by the time-dependent expansion coefficients of the 16 most energetic Proper Orthogonal Decomposition (POD) modes. These training data are generated by a POD snapshot analysis from direct numerical simulations of the original turbulent flow. All reservoir computing models are operated in the reconstruction or open-loop mode, i.e., they receive 3 POD modes as an input at each step and reconstruct the missing 13 ones. We analyse different measures of the reconstruction error in dependence on the hyperparameters which are specific for the quantum cases or shared with the classical counterpart, such as the reservoir size and the leaking rate. We show that both quantum algorithms are able to reconstruct the essential statistical properties of the turbulent convection flow successfully with similar performance compared to the classical reservoir network. Most importantly, the quantum reservoirs are by a factor of 4 to 8 smaller in comparison to the classical case.
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