Understanding Brain Functional Dynamics Through Neural Koopman Operator with Control Mechanism

One of the fundamental scientific problems in neuroscience is to have a good understanding of how cognition and behavior emerge from brain function. Since the neuroscience concept of cognitive control parallels the notion of system control in engineering, many computational models formulate the dynamics neural process into a dynamical system, where the hidden states of the complex neural system are modulated by energetic simulations. However, the human brain is a quintessential complex biological system. Current computation models either use neural networks to approximate the underlying dynamics, which makes it difficult to fully understand the system mechanics, or compromise to simplified linear models with very limited power to characterize non-linear and self-organized dynamics along with complex neural activities. To address this challenge, we devise an end-to-end deep model to identify the underlying brain dynamics based on Koopman operator theory, which allows us to model a complex non-linear system in an infinite-dimensional linear space. In the context of reverse engineering, we further propose a biology-inspired control module that adjusts the input (neural activity data) based on feedback to align brain dynamics with the underlying cognitive task. We have applied our deep model to predict cognitive states from a large scale of existing neuroimaging data by identifying the latent dynamic system of functional fluctuations. Promising results demonstrate the potential of establishing a system-level understanding of the intricate relationship between brain function and cognition through the landscape of explainable deep models.