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This work presents a novel methodology for analysis and control of nonlinearfluid systems using neural networks. The approach is demonstrated on fourdifferent study cases being the Lorenz system, a modified version of theKuramoto-Sivashinsky equation, a streamwise-periodic 2D channel flow, and aconfined cylinder flow. Neural networks are trained as models to capture thecomplex system dynamics and estimate equilibrium points through a Newtonmethod, enabled by backpropagation. These neural network surrogate models(NNSMs) are leveraged to train a second neural network, which is designed toact as a stabilizing closed-loop controller. The training process employs arecurrent approach, whereby the NNSM and the neural network controller (NNC)are chained in closed loop along a finite time horizon. By cycling throughphases of combined random open-loop actuation and closed-loop control, aniterative training process is introduced to overcome the lack of data nearequilibrium points. This approach improves the accuracy of the models in themost critical region for achieving stabilization. Through the use of L1regularization within loss functions, the NNSMs can also guide optimal sensorplacement, reducing the number of sensors from an initial candidate set. Thedatasets produced during the iterative training process are also leveraged forconducting a linear stability analysis through a modified dynamic modedecomposition approach. The results demonstrate the effectiveness ofcomputationally inexpensive neural networks in modeling, controlling, andenabling stability analysis of nonlinear systems, providing insights into thesystem behaviour and offering potential for stabilization of complex fluidsystems.

Neural networks in feedback for flow analysis, sensor placement and control