arXiv subjects

Florian Heyder

Publications and source records attributed to Florian Heyder.

5 recordsLinked to original sources

arXiv2023

Reduced-order modeling of two-dimensional turbulent Rayleigh-Bénard flow by hybrid quantum-classical reservoir computing

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 Ra=1e+5 and a Prandtl number Pr=10. These properties comprise the mean vertical profiles of the root mean square velocity and temperature and the turbulent convective heat flux. 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 lower-dimensional 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 mode. 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.

physics.flu-dyn↗

arXiv2023

Generative convective parametrization of dry atmospheric boundary layer

Turbulence parametrizations will remain a necessary building block in kilometer-scale Earth system models. In convective boundary layers, where the mean vertical gradients of conserved properties such as potential temperature and moisture are approximately zero, the standard ansatz which relates turbulent fluxes to mean vertical gradients via an eddy diffusivity has to be extended by mass flux parametrizations for the typically asymmetric up- and downdrafts in the atmospheric boundary layer. In this work, we present a parametrization for a dry convective boundary layer based on a generative adversarial network. The model incorporates the physics of self-similar layer growth following from the classical mixed layer theory by Deardorff. This enhances the training data base of the generative machine learning algorithm and thus significantly improves the predicted statistics of the synthetically generated turbulence fields at different heights inside the boundary layer. The algorithm training is based on fully three-dimensional direct numerical simulation data. Differently to stochastic parametrizations, our model is able to predict the highly non-Gaussian transient statistics of buoyancy fluctuations, vertical velocity, and buoyancy flux at different heights thus also capturing the fastest thermals penetrating into the stabilized top region. The results of our generative algorithm agree with standard two-equation or multi-plume stochastic mass-flux schemes. The present parametrization provides additionally the granule-type horizontal organization of the turbulent convection which cannot be obtained in any of the other model closures. Our work paves the way to efficient data-driven convective parametrizations in other natural flows, such as moist convection, upper ocean mixing, or convection in stellar interiors.

physics.flu-dyn↗

arXiv2022

Hybrid quantum-classical reservoir computing of thermal convection flow

We simulate the nonlinear chaotic dynamics of Lorenz-type models for a classical two-dimensional thermal convection flow with 3 and 8 degrees of freedom by a hybrid quantum--classical reservoir computing model. The high-dimensional quantum reservoir dynamics are established by universal quantum gates that rotate and entangle the individual qubits of the tensor product quantum state. A comparison of the quantum reservoir computing model with its classical counterpart shows that the same prediction and reconstruction capabilities of classical reservoirs with thousands of perceptrons can be obtained by a few strongly entangled qubits. We demonstrate that the mean squared error between model output and ground truth in the test phase of the quantum reservoir computing algorithm increases when the reservoir is decomposed into separable subsets of qubits. Furthermore, the quantum reservoir computing model is implemented on a real noisy IBM quantum computer for up to 7 qubits. Our work thus opens the door to model the dynamics of classical complex systems in a high-dimensional phase space effectively with an algorithm that requires a small number of qubits.

quant-ph↗

arXiv2022

Generalizability of reservoir computing for flux-driven two-dimensional convection

We explore the generalization properties of an echo state network applied as a reduced dynamical model to predict flux-driven two-dimensional turbulent convection. To this end, we consider a convection domain at fixed height with a variable ratio of buoyancy fluxes at the top and bottom boundaries, which break the top-down symmetry in comparison to the standard Rayleigh-Bénard case thus leading to highly asymmetric mean and fluctuation profiles across the layer. Our direct numerical simulation model describes a convective boundary layer in a simple way. The data are used to train and test a recurrent neural network in the form of an echo state network. The input to the echo state networks is obtained in two different ways, either by a proper orthogonal decomposition or by a convolutional autoencoder. In both cases, the echo state network reproduces the turbulence dynamics and the statistical properties of the buoyancy flux, and is able to model unseen data records with different flux ratios.

physics.flu-dyn↗

arXiv2021

Echo State Network for two-dimensional turbulent moist Rayleigh-Bénard convection

Recurrent neural networks are machine learning algorithms which are suited well to predict time series. Echo state networks are one specific implementation of such neural networks that can describe the evolution of dynamical systems by supervised machine learning without solving the underlying nonlinear mathematical equations. In this work, we apply an echo state network to approximate the evolution of two-dimensional moist Rayleigh-Bénard convection and the resulting low-order turbulence statistics. We conduct long-term direct numerical simulations in order to obtain training and test data for the algorithm. Both sets are pre-processed by a Proper Orthogonal Decomposition (POD) using the snapshot method to reduce the amount of data. The training data comprise long time series of the first 150 most energetic POD coefficients. The reservoir is subsequently fed by the data and results in predictions of future flow states. The predictions are thoroughly validated by the data of the original simulation. Our results show good agreement of the low-order statistics. This incorporates also derived statistical moments such as the cloud cover close to the top of the convection layer and the flux of liquid water across the domain. We conclude that our model is capable of learning complex dynamics which is introduced here by the tight interaction of turbulence with the nonlinear thermodynamics of phase changes between vapor and liquid water. Our work opens new ways for the dynamic parametrization of subgrid-scale transport in larger-scale circulation models.

physics.flu-dyn↗