Taming Nonlinear Dynamics with MLC

Duriez, Thomas; Brunton, Steven L.; Noack, Bernd R.

doi:10.1007/978-3-319-40624-4_5

Cited by 19 publications

(33 citation statements)

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“…The sub-selected set of models can then each be evaluated using information criteria to select the correct dynamical system. The connection between information criteria and automatic model selection can also be integrated with genetic algorithms for selecting the structure and parameters of dynamical systems [ 6 , 24 – 26 ]. The process can be semi-automated for data-driven discovery of physical principles and laws of motion, which is now often referred to as the 4th paradigm of science [ 41 ].…”

Section: Discussionmentioning

confidence: 99%

“…Indeed, simultaneous identification of both the structure and the parameters of a model generally requires an intractable search through combinatorially many candidate models. Genetic programming has been recently used to determine the structure and parameters of dynamical systems [ 6 , 24 , 25 ] and control laws [ 26 ], enabling the efficient search of complex function spaces. Sparsity-promoting techniques have also been employed to simultaneously identify the structure and parameters of a dynamical system model.…”

Section: Introductionmentioning

confidence: 99%

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Model selection for dynamical systems via sparse regression and information criteria

et al. 2017

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We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which typically limits the number of candidate models considered due to the intractability of computing information criteria. Using a recently developed sparse identification of nonlinear dynamics algorithm, the sub-selection of candidate models near the Pareto frontier allows feasible computation of Akaike information criteria (AIC) or Bayes information criteria scores for the remaining candidate models. The information criteria hierarchically ranks the most informative models, enabling the automatic and principled selection of the model with the strongest support in relation to the time-series data. Specifically, we show that AIC scores place each candidate model in the strong support, weak support or no support category. The method correctly recovers several canonical dynamical systems, including a susceptible-exposed-infectious-recovered disease model, Burgers’ equation and the Lorenz equations, identifying the correct dynamical system as the only candidate model with strong support.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Model selection for dynamical systems via sparse regression and information criteria

et al. 2017

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“…In the same manner, machine learning techniques [189] will very likely gain more and more attention, both in multiobjective optimization as well as optimal control. There are already many papers on this topic or related ones and the number is growing quickly.…”

Section: Future Directionsmentioning

confidence: 99%

A Survey of Recent Trends in Multiobjective Optimization – Surrogate Models, Feedback Control and Objective Reduction

Peitz¹,

Dellnitz²

2018

Preprint

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Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto optimal solutions have led to a wide range of new applications related to optimal and feedback control which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview over recent developments in accelerating multiobjective optimization for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. In the latter case, various promising model predictive control approaches have been proposed. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

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“…An alternate model-free approach employs downhill simplex optimization to estimate the control parameters for maximizing the time-averaged lift-to-drag ratio of an airfoil (Cattafesta, Tian & Mittal 2009). More recently, methods from machine learning have been employed in flow control, in which the control design is framed as a regression problem and solved by genetic algorithms without explicit knowledge of the dynamics (Duriez, Brunton & Noack 2017; Li et al. 2017; Wu 2018).…”

Section: Introductionmentioning

confidence: 99%

Adaptive separation control of a laminar boundary layer using online dynamic mode decomposition

et al. 2020

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Taming Nonlinear Dynamics with MLC

Cited by 19 publications

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Model selection for dynamical systems via sparse regression and information criteria

Model selection for dynamical systems via sparse regression and information criteria

A Survey of Recent Trends in Multiobjective Optimization – Surrogate Models, Feedback Control and Objective Reduction

Adaptive separation control of a laminar boundary layer using online dynamic mode decomposition

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Taming Nonlinear Dynamics with MLC

Cited by 19 publications

References 0 publications

Model selection for dynamical systems via sparse regression and information criteria

Model selection for dynamical systems via sparse regression and information criteria

A Survey of Recent Trends in Multiobjective Optimization&nbsp;&ndash; Surrogate Models, Feedback Control and Objective Reduction

Adaptive separation control of a laminar boundary layer using online dynamic mode decomposition

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A Survey of Recent Trends in Multiobjective Optimization – Surrogate Models, Feedback Control and Objective Reduction