Machine Learning Control – Taming Nonlinear Dynamics and Turbulence

Abstract

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Model identification of reduced order fluid dynamics systems using deep learning

“…Machine learning methods have tremendous potential in data‐driven engineering problems. Genetic programming is especially promising since it optimises both the parameters and structure associated with the system . Neural network method is capable of approximating most input‐output functions, but it is prone to overfitting.…”

“…Genetic programming is especially promising since it optimises both the parameters and structure associated with the system. 2 Neural network method is capable of approximating most input-output functions, but it is prone to overfitting. The neural network method needs tremendous amounts of training data if better solutions are expected.…”

“…Thus, even with moderate complexity problems, the computation cost can still be prohibitive. A number of model identification methods have been presented to improve the capabilities of the mathematical models such as state calibration with 4D Var, 1 neural networks, 2 dynamics with radial basis functions, 3 genetic programming, 2,4,5 and the traditional Galerkin method. 1,6 Reduced order modelling, one of model identification methods, has proven to be a powerful tool to reduce the complexity and large dimensional size of the full discretised dynamical system.…”

Drag reduction of a car model by linear genetic programming control

“…Following Duriez et al (2016), the control design is formulated as a regression problem: find the control law which optimizes a given cost function. We employ linear genetic programming as powerful and general regression method for nonlinear functions and for potential multiple extrema of the cost function.…”

Metric for attractor overlap

“…The forcing is exerted by rotation of the cylinders with circumferential velocities b 1 = U 1 = U F , b 2 = U 2 = U B and b 3 = U 3 = U T for the front, bottom and top cylinder, respectively. The actuation command b = (b 1 , b 2 , b 3 ) = (U 1 , U 2 , U 3 ) is preferably used for control theory purposes (Brunton & Noack 2015;Duriez et al 2016) while (U F , U B , U T ) are more natural for a discussion of physical mechanisms. The actuation is conveniently expressed with the vector cross product '×': u = 2U i x × e z on the ith cylinder.…”