A Data-Driven Computational Framework for Identifiability and Nonlinear Dynamics Discovery in Complex Systems – Wenrui Hao

Data-driven modeling is essential for deciphering complex biological systems, yet its utility is often constrained by two fundamental hurdles: the inability to guarantee parameter identifiability and the high computational cost of learning nonlinear dynamics. This talk introduces a unified computational framework designed to overcome these challenges, bridging theoretical rigor with scalable machine learning.

The first component of the framework establishes a computational foundation for practical identifiability. By leveraging the Fisher Information Matrix and its theoretical links to coordinate identifiability, we propose an efficient method for identifiability assessment. We further introduce regularization-based strategies to manage non-identifiable parameters, thereby enhancing model reliability and facilitating robust uncertainty quantification.

To address the discovery of nonlinear dynamics, we present the Laplacian Eigenfunction-Based Neural Operator (LE-NO). This operator learning framework is specifically engineered for modeling reaction–diffusion equations. By projecting nonlinear operators onto Laplacian eigenfunctions, LE-NO achieves superior computational efficiency and generalization across varying boundary conditions, effectively bypassing the limitations of large-scale architectures and data scarcity.

Finally, we demonstrate the framework’s utility in the context of Alzheimer’s disease modeling. We show that this integrated approach ensures reliable parameter inference while capturing the intricate nonlinear dynamics of disease progression, providing a critical step toward the development of high-fidelity digital twins for neurodegenerative pathology.