Alejandro Güemes, Carlos Sanmiguel Vila, Stefano Discetti
Reconstruction of field quantities from sparse measurements is a problem arising in a broad spectrum of applications. This task is particularly challenging when the mapping between sparse measurements and field quantities is performed in an unsupervised manner. Further complexity is added for moving sensors and/or random on-off status. Under such conditions, the most straightforward solution is to interpolate the scattered data onto a regular grid. However, the spatial resolution achieved with this approach is ultimately limited by the mean spacing between the sparse measurements. In this work, we propose a super-resolution generative adversarial network (GAN) framework to estimate field quantities from random sparse sensors without needing any full-field high-resolution training. The algorithm exploits random sampling to provide incomplete views of the {high-resolution} underlying distributions. It is hereby referred to as RAndomly-SEEDed super-resolution GAN (RaSeedGAN). The proposed technique is tested on synthetic databases of fluid flow simulations, ocean surface temperature distributions measurements, and particle image velocimetry data of a zero-pressure-gradient turbulent boundary layer. The results show excellent performance even in cases with high sparsity or with levels of noise. To our knowledge, this is the first GAN algorithm for full-field high-resolution estimation from randomly-seeded fields with no need of full-field high-resolution representations.
A. G. Balasubramanian, L. Guastoni, A. Güemes et al.
Modelling the near-wall region of wall-bounded turbulent flows is a widespread practice to reduce the computational cost of large-eddy simulations (LESs) at high Reynolds number. As a first step towards a data-driven wall-model, a neural-network-based approach to predict the near-wall behaviour in a turbulent open channel flow is investigated. The fully-convolutional network (FCN) proposed by Guastoni et al. [preprint, arXiv:2006.12483] is trained to predict the two-dimensional velocity-fluctuation fields at $y^{+}_{\rm target}$, using the sampled fluctuations in wall-parallel planes located farther from the wall, at $y^{+}_{\rm input}$. The data for training and testing is obtained from a direct numerical simulation (DNS) at friction Reynolds numbers $Re_τ = 180$ and $550$. The turbulent velocity-fluctuation fields are sampled at various wall-normal locations, i.e. $y^{+} = \{15, 30, 50, 80, 100, 120, 150\}$. At $Re_τ=550$, the FCN can take advantage of the self-similarity in the logarithmic region of the flow and predict the velocity-fluctuation fields at $y^{+} = 50$ using the velocity-fluctuation fields at $y^{+} = 100$ as input with less than 20% error in prediction of streamwise-fluctuations intensity. These results are an encouraging starting point to develop a neural-network based approach for modelling turbulence at the wall in numerical simulations.
Two models based on convolutional neural networks are trained to predict the two-dimensional velocity-fluctuation fields at different wall-normal locations in a turbulent open channel flow, using the wall-shear-stress components and the wall pressure as inputs. The first model is a fully-convolutional neural network (FCN) which directly predicts the fluctuations, while the second one reconstructs the flow fields using a linear combination of orthonormal basis functions, obtained through proper orthogonal decomposition (POD), hence named FCN-POD. Both models are trained using data from two direct numerical simulations (DNS) at friction Reynolds numbers $Re_τ = 180$ and $550$. Thanks to their ability to predict the nonlinear interactions in the flow, both models show a better prediction performance than the extended proper orthogonal decomposition (EPOD), which establishes a linear relation between input and output fields. The performance of the various models is compared based on predictions of the instantaneous fluctuation fields, turbulence statistics and power-spectral densities. The FCN exhibits the best predictions closer to the wall, whereas the FCN-POD model provides better predictions at larger wall-normal distances. We also assessed the feasibility of performing transfer learning for the FCN model, using the weights from $Re_τ=180$ to initialize those of the $Re_τ=550$ case. Our results indicate that it is possible to obtain a performance similar to that of the reference model up to $y^{+}=50$, with $50\%$ and $25\%$ of the original training data. These non-intrusive sensing models will play an important role in applications related to closed-loop control of wall-bounded turbulence.