The overly general title of the thesis, defined at the beginning of the journey, would be better reformulated to "Automatic system identification of large-scale brain activity models", which more precisely describes the scope of this work. Our brain orchestrates the various functions that we need to effectively meet (basic) life needs. This is possible only through precise coordination between individual brain regions. One of the proposed coordination mechanisms is coupling or a temporal synchronization of brain rhythms between local populations of neurons, which can be most simply modeled by a network of coupled oscillators. In the diploma thesis, we were interested in how accurately can we discover both the structure and the parameters of the selected oscillator models with the methods of automatic system identification (ProGED and SINDy). We selected ten dynamical systems, five single oscillators and five pairs of coupled oscillators. By simulating the systems, we obtained synthetic input data, further modified with different levels of noise and observability. Both methods were successful in reconstructing a single oscillator as long as there was less than 1 % noise in the data. ProGED shows good model reconstruction even at 10 % noise, while SINDy fails due to the use of more noise-sensitive numerical derivation. For the same reason, SINDy cannot detect models with only partially observable data, while ProGED can, but in practice with a larger reconstruction error. Even with the cleanest and most complete data, both methods had great difficulty in identifying a pair of coupled oscillators, which was mostly influenced by a large number of state variables and unknown parameters. Overall, we conclude that current implementations of classical automated identification methods for dynamic systems are insufficiently scalable to be useful for modeling more complex M/EEG data involving dozens or hundreds of coupled oscillators with a relatively high level of noise.
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