Abstrakti
Prediction and analysis of nonlinear systems is highly important in natural sciences, medicine, and engineering. In realworld complex systems of nonlinear dynamics the analysis relies largely on surrogate models. Reservoir computers (RC) have proven useful in replicating the climate of chaotic dynamics. The quality of surrogate models based on RCs is crucially dependent on judiciously determined optimal implementation that involves optimising both the reservoir network topology and the used hyperparameters.
In this work, we explore how the topology of reservoir computers reflects in their performance in replicating and predicting systems of chaotic or merely nonlinear dynamics. We show that connectedness of the topology is significant to performance only when reproducing and predicting chaotic systems of sufficient complexity. This is done by systematically applying Bayesian optimisation to produce optimal reservoirs for each topology and using large ensembles of reservoirs. The dynamical systems used are Lorenz 63, coupled WilsonCowan oscillators and KuramotoSivashinsky system. By applying RCs of different topologies to these systems, we show that reservoirs of unconnected nodes (RUN) outperform reservoirs of connected nodes for target systems whose estimated fractal dimension is d_f < 5.5 and that linked reservoirs are better for systems with d_f > 5.5.
Inspection of KuramotoSivashinsky systems up to dimension d_f = 13.5 did not show any difference between the performance of recursively and simply connected reservoir topologies. However, we anticipate that there may be another transition at a higher value of d_f, beyond which recursive neural networks (RNN) outperform nonrecurrent connected reservoirs. Lastly, we show that judicious hyperparameter optimisation is crucial for obtaining reliable results.
In this work, we explore how the topology of reservoir computers reflects in their performance in replicating and predicting systems of chaotic or merely nonlinear dynamics. We show that connectedness of the topology is significant to performance only when reproducing and predicting chaotic systems of sufficient complexity. This is done by systematically applying Bayesian optimisation to produce optimal reservoirs for each topology and using large ensembles of reservoirs. The dynamical systems used are Lorenz 63, coupled WilsonCowan oscillators and KuramotoSivashinsky system. By applying RCs of different topologies to these systems, we show that reservoirs of unconnected nodes (RUN) outperform reservoirs of connected nodes for target systems whose estimated fractal dimension is d_f < 5.5 and that linked reservoirs are better for systems with d_f > 5.5.
Inspection of KuramotoSivashinsky systems up to dimension d_f = 13.5 did not show any difference between the performance of recursively and simply connected reservoir topologies. However, we anticipate that there may be another transition at a higher value of d_f, beyond which recursive neural networks (RNN) outperform nonrecurrent connected reservoirs. Lastly, we show that judicious hyperparameter optimisation is crucial for obtaining reliable results.
Alkuperäiskieli  Englanti 

Pätevyys  Lisensiaatintutkinto 
Myöntävä instituutio 

Valvoja/neuvonantaja 

Myöntöpäivämäärä  23 elok. 2023 
Kustantaja  
Tila  Julkaistu  23 elok. 2023 
OKMjulkaisutyyppi  G3 Lisensiaatintyö 