Date of Award
Spring 2023
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Neuroscience
First Advisor
van Dijk, David
Abstract
Understanding the intricate workings of the brain remains one of science's grand challenges. At its core, the brain operates as a dynamic system, with neural oscillations and coordinated activity patterns enabling integrated cognition. However, modeling these complex dynamics computationally has proven difficult. Traditional models often rely on restrictive assumptions about brain activity properties, limiting their utility. This thesis introduces innovative machine learning frameworks, utilizing neural operator techniques specifically designed for neural data, to model brain dynamics more effectively. Neural operators function as mappings between infinite-dimensional spaces, offering a flexible, data-driven approach to capture the complex spatiotemporal relationships in neural dynamics. This work presents four novel machine learning frameworks. The Neural Integro-Differential Equations (NIDEs) integrate instantaneous and temporal components, providing enhanced accuracy for complex systems like the brain. Attentional Neural Integral Equations ((A)NIEs) harness self-attention mechanisms to learn and compute unknown integral operators from data. The Continuous Spatiotemporal Transformers (CSTs) leverage a new Transformer architecture to model continuous systems directly from data, overcoming the limitations of traditional methods. Brain Language Models (BrainLMs) utilize extensive fMRI dataset pretraining and fine-tuning, offering unmatched versatility in modeling brain dynamics. Analyses of synthetic and real-world data validate these models' superior performance. NIDEs reveal the local and non-local effects of substances like ketamine on fMRI dynamics. (A)NIEs and CSTs demonstrate superior predictive capabilities in modeling fMRI and wide-field recordings, outperforming existing methods for learning dynamics. BrainLM efficiently identifies intrinsic functional networks and, through in-silico perturbation analysis, showcases its ability to differentiate subject states using accumulated knowledge. Collectively, these advancements not only broaden the horizons of modeling diverse neural modalities and data types but also break free from the constraints of previous methodologies. The frameworks extend their utility to various dynamic modeling domains, enhancing flexibility. This thesis highlights the immense potential of AI in offering comprehensive insights and unraveling the organizational principles of complex systems, marking a significant stride in technology-driven neuroscience research.
Recommended Citation
de Oliveira Fonseca, Antonio Henrique, "Learning Brain Dynamics with Neural Operators" (2023). Yale Graduate School of Arts and Sciences Dissertations. 1458.
https://elischolar.library.yale.edu/gsas_dissertations/1458
