Latent space modelling of whole-brain dynamics: a Koopman-theoretical approach

Koopman theory offers a powerful framework for transitioning from complex, finite-dimensional and non-linear representation of physical systems to infinite-dimensional but linear ones. Over the last few decades, this theory has gained renewed attention and interest with the possibility to linearize physical systems by identifying key modes of the Koopman operator by training Deep Neural Networks. In this work, Koopman linear-based embeddings are developed through auto-encoders to achieve coordinate transformations and dimensionality reductions that enable linear approximations of non-linear dynamics. Several Neural Network architectures have been tested on both discrete and continuous spectrum problems, proving the versatility of this paradigm. Finally, a real-world fMRI dataset of stroke patients is analysed to evaluate the model’s robustness to noise and variability, as well as its ability to predict future system states.