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• W3092479414 abstract "Various processes in nature can be modelled as dynamical systems. These systems range from climate and ocean circulation to cells and organisms, from non-linear optics to turbulent and reactive flows. Many systems involve high intrinsic dimensionality and complex dynamics extending over multiple spatio-temporal scales. Furthermore, extreme events may appear. Extreme events are characterized by rare transitions that are several standard deviations away from the mean value of the state variables. Regarding the before mentioned dynamical systems, examples of extreme events are tsunamis, tornadoes, volcanoes, floodings and droughts, earthquakes etc.A lot of effort is put into understanding these systems and different forecasting approaches are used. The three main methods are large scale simulations, dimension reduction techniques and multiple data driven forecasting techniques. Successful methods involve the highly nonlinear energy transfer between modes.Large scale simulations are based on the complete description of the system through governing equations. These equations may be computationally difficult to solve and make these methods more expensive. In order to reduce complexity, models can be used, but they themselves can have a certain model error.Classical dimension reduction methods are based on projection. If the underlying set of equations possesses high intrinsic dimensionality, problems often arise as the truncated degrees of freedom are essential for an effective description of the system.In this context, machine learning methods can help. Some studies have proven that recurrent neural networks are able to learn the dynamics of chaotic systems and are therefore universal approximators of dynamical systems. However, due to the intrinsic property of chaos, that small deviations get amplified exponentially, prediction time is limited.The idea of this work is to combine a projection method with a data driven method to improve accuracy and to extend the prediction time. We use a Proper Orthogonal Decomposition as projection method and combine it with an Echo State (ESN). The key concept is that the recurrent neuronal network assists the reduced order model which lost some information due to the reduction. We introduce three hybrid methods, assess their performance of the Lorenz system, the Platt system, the Charney-DeVore system and the Kuramoto Sivashinsky (KS) equation and compare the results with the pure machine learning method. We start with the Lorenz system, which is a well known low-dimensional chaotic system and continue to increase complexity and dimensionality and end with the KS equation which is a high-dimensional chaotic system in the discretized version. The first hybrid method uses the ESN to predict the truncated dynamics and reconstructs the solution in the reduced space. The second hybrid method uses the ESN to predict the truncated dynamics as well, however, the solution is reconstructed in full solution space. In the third hybrid method, the ESN not only predicts the next time step of the solution but is also able to let in information from the ROM.We apply a parameter search routine to find good parameters for each method, test the prediction performance for different reservoir sizes as well as investigate the behavior of the ROM and the methods for different levels of information loss.The results show that hybrid method 1 and 2 can only be used successfully in certain areas. Hybrid method 1 demands accurate ROMs and the reconstruction of the solution in reduced space is too restrictive with low-dimensional systems. Hybrid method 2 tries to correct this and reconstructs the solution in full space. However, this method does not produce consistent results. Hybrid method 3 is superior to the pure data-driven method in all cases. The ability to decide between ROM and ESN information is the key to success." @default.
• W3092479414 created "2020-10-15" @default.
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• W3092479414 date "2020-01-01" @default.
• W3092479414 modified "2023-10-16" @default.
• W3092479414 title "Prediction of Chaotic Systems with Physics - Enhanced Machine Learning Models" @default.
• W3092479414 hasPublicationYear "2020" @default.
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