Unveiling Scaling Laws of Parameter Identifiability and Uncertainty Quantification in Data-Driven Biological Modeling

TL;DR

This paper develops a computational framework that uncovers fundamental scaling laws for parameter identifiability and uncertainty quantification in data-driven biological models, validated on real-world biological data.

Contribution

It introduces a hierarchical approach combining Fisher information and perturbed Hessians to analyze practical identifiability across different model subspaces.

Findings

Framework reveals scaling laws for identifiability.

Validated on HIV-host and amyloid-beta models.

Enhances interpretability of biological data-driven models.

Abstract

Integrating high-dimensional biological data into data-driven mechanistic modeling requires rigorous practical identifiability to ensure interpretability and generalizability. However, coordinate identifiability analysis often suffers from numerical instabilities near singular local minimizers. We present a computational framework that uncovers fundamental scaling laws governing practical identifiability through asymptotic analysis. By synthesizing Fisher information with perturbed Hessian matrices, we establish a hierarchical approach to quantify coordinate identifiability and inform uncertainty quantification within non-identifiable subspaces across different orders. Supported by rigorous mathematical analysis and validated on synthetic and real-world data, our framework was applied to HIV-host dynamics and spatiotemporal amyloid-beta propagation. These applications demonstrate the framework's efficiency in elucidating critical mechanisms underlying HIV diagnostics and Alzheimer's disease progression. In the era of large-scale mechanistic digital twins, our framework provides the scaling laws for data-driven modeling in terms of both parameter identifiability and uncertainty, ensuring that data-driven inferences are grounded in verifiable biological reality.