Modeling subgrid-scale forces by spatial artificial neural networks in large eddy simulation of turbulence

Toward neural-network-based large eddy simulation: application to turbulent channel flow

“…2019; Xie et al. 2019 a , b , c , 2020 a , b ) hidden layers, and Gamahara & Hattori (2017) showed that 100 neurons per hidden layer were sufficient for the accurate predictions of for a turbulent channel flow in a priori test. We also tested NN with three hidden layers, but more hidden layers than two did not further improve the performance both in a priori and a posteriori tests (see the Appendix).…”

“…(2019) reported that using the filter size as well as the velocity gradient tensor as the input variables was beneficial to predict the SGS stresses for the flow having a filter size different from that of trained data. Xie, Wang & E (2020 a ) used an FCNN to predict the SGS force with the input of at multiple grid points, and this FCNN performed better than DSM for the prediction of energy spectrum. In the case of three-dimensional decaying isotropic turbulence, Wang et al.…”

A perspective on machine learning methods in turbulence modeling

“…The direct prediction of the closure terms instead of their modeling offers an alternative to the parameter estimation task in the previous section. Here, the unknown terms in Equation () are directly approximated by the ML algorithm—either as fluxes or as the forces themselves [5,21,79‐81,84,86,90]. Important to stress, however, is that the mapping from the coarse to the fine field is nonunique, and thus, each coarse field is associated with a distribution of corresponding closure terms.…”

“…Said inconsistency is caused by the interaction of the model predictions and numerical errors, which induces shifting data statistics and is amplified by error accumulation and self‐driving error growth at high wavenumbers. This can either be tackled by removal of this energy through a dissipative mechanism [86] (essentially an additional model term) or the projection of the closure term onto a stable basis with the desired properties [5].…”

“…In general, the results for the closure term approximation based on ML methods are highly encouraging. In [86], the authors used a spatial MLP with approx. 500 000 parameters to predict the three components of the subgrid forces of the incompressible momentum equations independently.…”