"The mind is the music that neural networks play." This quote from computational neurobiologist T.J. Sejnowski underscores a growing scientific consensus that studying the structure and function of vast networks of connections between brain regions is essential to understanding cognitive and affective state maintenance, sensorimotor information processing and control, etiologies and remedies for numerous neuropathologies, as well as a host of other facets of our conscious (and non-conscious) experience. Towards this goal, an ongoing challenge lies in identifying - in vivo in humans - spatiotemporal cortical network dynamics, at the level of individuals and groups, across experimental task conditions, and at the level of single trials.

In the opening chapter of this dissertation, I introduce the Source Information Flow Toolbox (SIFT), a novel open-source software package for identification of neuronal dynamics and causal interactions in electrophysiological source and sensor data. The software integrates with the widely used EEGLAB analysis suite, addressing a need for robust tools for identifying single- and multi-trial multivariate brain network dynamics across time, frequency, anatomical source location, and subjects. I then introduce and assess two new methods (Measure Projection Analysis and Multi-view Hierarchical Bayesian Learning) for statistical analysis of source-level dynamics (including connectivity) across groups of subjects in the presence of missing data. The remaining chapters focus on applications of dynamical modeling approaches in SIFT to open problems within the fields of cognitive neuroscience, clinical neuroscience and neuroengineering. I first present three studies examining single-trial time-varying spatiotemporal network dynamics underlying generation and maintenance of epileptic seizures. Next I present a case study examining the effect of visual feedback on an occipito-parietal-motor network in freezing-of-gait in patients with Parkinson's disease. The final chapters focus on new directions in neuroengineering and brain-computer interfaces (BCI) leveraging neural dynamical system identification. We first review the history and state of the BCI field and summarize important new directions in BCI design. I then present a novel system for real-time mobile brain imaging, artifact rejection, neuronal system identification, and cognitive state prediction, and demonstrate its application in predicting response error commission from cortical network dynamics using a new high-density mobile dry EEG system.

In this work, we explore the topic of forecasting the neural time series using machine-learning based techniques on electroencephalography (EEG) data. Forecasting EEG has a number of potential applications in brain-computer interfaces (BCI), such as ahead-of-time event classification, cognitive response prediction, and preemptive intervention therapy. However, previous work in EEG forecasting has failed to accurately predict the time series more than a few steps into the future. Simple linear models lack the capacity to model the high-dimensional dynamics of EEG activity, while complex nonlinear models are difficult to specify and implement. However, recent deep neural networks have effectively modeled high-dimensional systems in a variety of domains. In this work, we hope to bridge the gap between previous work in EEG forecasting and current techniques in deep learning. In particular, we explore forecasting the EEG patterns that occur after the presentation of a time-locked visual stimulus. We implement a deep neural network that extracts features from pre-event data in order to predict single-trial event-locked EEG data. To capture the variation of a single trial, the network constructs the post-event waveform in two parts: 1) generating ongoing neural activity and 2) generating evoked event-related responses. We evaluate our model by forecasting 500 milliseconds of single channel post-event data from a Rapid Serial Visual Presentation (RSVP) task. Our results indicate a significant increase in forecasting performance compared to baseline methods, suggesting that deep neural networks can extract informative features from EEG data in order to generate a prediction of the post-event waveform.