A Self-Learning Model for Cylinder Wakes Using Neural Networks

Coupled map lattice models (CML) that combine a series of low-dimensional circle maps with a diffusion model have predicted qualitative features of the wake behind vibrating flexible cables. However, there are always unmodelled dynamics if a quantitative comparison is made with wake patterns obtained from laboratory or simulated wake flows. To overcome this limitation, self-learning features can be incorporated into the simple CML model to capture the unmodelled dynamics. The self-learning CML uses radial basis function neural networks as online approximators of the unmodelled dynamics. The neural network weights are adaptively varied using a combination of a multivariable least squares algorithm and a projection algorithm. The adaptive estimation scheme, derived from a new convective diffusive CML, seeks to precisely estimate the neural network weights at each timestep by mimimizing the error between the simulated and measured wake patterns. Studies of this approach are conducted using wake patterns from spectral element based NEKTAR simulations of freely vibrating cable wakes at Re = 100. It is shown that the neural network based self-learning CML precisely estimates the simulated wake patterns within several shedding cycles. The self-learning CML is also shown to be computationally efficient.