Learning Brain Dynamics With Coupled Low-Dimensional Nonlinear Oscillators and Deep Recurrent Networks.

Area of Science:

• Computational neuroscience
• Dynamical systems theory
• Neuroimaging analysis

Background:

• Biological systems exhibit complex nonlinear dynamics difficult for linear models.
• Deep learning models require extensive data and lack interpretability in neuroimaging.
• Integrating domain knowledge, like dynamical systems, can improve data-driven approaches.

Purpose of the Study:

• To evaluate van der Pol (VDP) oscillators for modeling neural activity from brain imaging data.
• To develop an efficient parameter estimation method for coupled dynamical systems.
• To assess VDP models' accuracy, interpretability, and predictive power compared to existing methods.

Main Methods:

• Applied van der Pol (VDP) oscillator models to neural activity data (calcium imaging, fMRI) from zebrafish, rats, and humans.
• Developed a novel parameter estimation technique for networks of coupled ODEs.
• Compared VDP model performance against linear autoregressive models (VAR) and recurrent neural networks (LSTMs).

Main Results:

• VDP models accurately captured low-dimensional neural activity and provided interpretable coupling matrices showing neural interactions.
• VDP models outperformed VAR in data fit and interpretability, and generalized better to unseen data.
• VDP models showed comparable or superior performance to LSTMs and served as effective data augmentation tools.

Conclusions:

• Van der Pol oscillators offer a powerful, interpretable, and data-efficient approach for analyzing complex neural dynamics in neuroimaging.
• This method advances scientific insight into brain function and improves predictive modeling for clinical and technological applications.