Unveiling Scaling Laws of Parameter Identifiability and Uncertainty Quantification in Data-Driven Biological Modeling
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914346820435968 |
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| author | Wang, Shun Hao, Wenrui |
| author_facet | Wang, Shun Hao, Wenrui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20495 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unveiling Scaling Laws of Parameter Identifiability and Uncertainty Quantification in Data-Driven Biological Modeling Wang, Shun Hao, Wenrui Quantitative Methods 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. |
| title | Unveiling Scaling Laws of Parameter Identifiability and Uncertainty Quantification in Data-Driven Biological Modeling |
| topic | Quantitative Methods |
| url | https://arxiv.org/abs/2602.20495 |