Before revision:  In this paper, we focus on brain imaging data, including both calcium imaging and functional MRI data. Standard vector-autoregressive models are limited by their linearity assumptions, while nonlinear general-purpose, large-scale temporal models, such as LSTM networks, typically require large amounts of training data, not always readily available in biological applications; furthermore, such models have limited interpretability. We introduce here a novel approach for learning a nonlinear differential equation model aimed at capturing brain dynamics . Specifically, we propose a variable-projection optimization approach to estimate the parameters of the multivariate (coupled ) van der Pol oscillator, and demonstrate that such a model can accurately represent nonlinear dynamics of the brain data.
After revision:  In this paper, we focus on brain calcium imaging (CaI) of URLanisms (zebrafish and rat), aiming to build a model of joint activation dynamics in large neuronal populations, including the whole brain of zebrafish. We propose a new approach for capturing dynamics of temporal SVD components that uses the coupled (multivariate ) van der Pol oscillator, and demonstrate that such a model can accurately represent nonlinear dynamics of the brain data.