NEUR Subgroup Contributed Talks

Brandon Imstepf

University of California, Merced

"Accelerating Solutions of Nonlinear PDEs Using Machine Learning: A Case Study with the Network Transport Model"

Alzheimer’s Disease (AD) is a progressive neurodegenerative disorder affecting approximately 10% of Americans over age 65, leading to memory loss, cognitive decline, and impaired daily function. Disease progression correlates with the spread of tau and amyloid-beta proteins, which aggregate into neurofibrillary tangles. While macroscopic whole-brain network models predict large-scale protein deposition patterns, they lack the specificity to capture individual disease progression. Conversely, microscale neuron-neuron models offer highly detailed biochemical aggregation and transport simulations but are computationally prohibitive for whole-brain parameter inference. In this work, we explore using machine learning to accelerate whole-brain simulations by approximating explicit solutions to the microscopic Two-Neuron Transport Model (TNTM), a partial differential equation describing tau flux along a neuron, incorporating biochemical aggregation, fragmentation, and transport. We simulate a single-edge model across physiological ranges of biochemical parameters and boundary conditions, then compare regression methods with varying levels of interpretability, from neural networks (low) to symbolic regression via PySR (high). Neural networks achieve the lowest error but lack biological insight. Linear and polynomial regression compute rapidly but yield high errors with limited interpretability. Symbolic regression achieves a balance between accuracy and transparency. This work demonstrates the potential of machine learning for computationally scalable AD modeling, opening avenues for patient-specific parameterization using AD data repositories.

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Youngmin Park

University of Florida

"Phase Reduction of Heterogeneous Coupled Oscillators"

We introduce a method to identify phase equations for heterogeneous oscillators beyond the weak coupling regime. This strategy is an extension of the theory from [Y. Park and D. Wilson, SIAM J. Appl. Dyn. Syst., 20 (2021), pp. 1464--1484] and yields coupling functions for N general limit-cycle oscillators with arbitrary types of coupling, with similar benefits as the classic theory of weakly coupled oscillators. These coupling functions enable the study of oscillator networks in terms of phase-locked states, whose stability can be determined using straightforward linear stability arguments. We demonstrate the utility of this approach by reducing and analyzing conductance-based thalamic neuron model. The reduction correctly predicts the emergence of new phase-locked states as a function of coupling strength and heterogeneity. We conclude with a brief remark on recent extensions to n:m phase-locking and N-body interactions.

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