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This paper describes a geometric approach to parameter identifiability analysis in models of power systems dynamics. When a model of a power system is to be compared with measurements taken at discrete times, it can be interpreted as a mapping from parameter space into a data or prediction space. Generically, model mappings can be interpreted as manifolds with dimensionality equal to the number of structurally identifiable parameters. Empirically it is observed that model mappings often correspond to bounded manifolds. We propose a new definition of practical identifiability based the topological definition of a manifold with boundary. In many ways, our proposed definition extends the properties of structural identifiability. We construct numerical approximations to geodesics on the model manifold and use the results, combined with insights derived from the mathematical form of the equations, to identify combinations of practically identifiable and unidentifiable parameters. We give several examples of application to dynamic power systems models.
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This content will become publicly available on April 2, 2026
InVAErt networks for amortized inference and identifiability analysis of lumped‐parameter haemodynamic models
Estimation of cardiovascular model parameters from electronic health records (EHRs) poses a significant challenge primarily due to lack of identifiability. Structural non-identifiability arises when a manifold in the space of parameters is mapped to a common output, while practical non-identifiability can result due to limited data, model misspecification or noise corruption. To address the resulting ill-posed inverse problem, optimization-based or Bayesian inference approaches typically use regularization, thereby limiting the possibility of discovering multiple solutions. In this study, we use inVAErt networks, a neural network-based, data-driven framework for enhanced digital twin analysis of stiff dynamical systems. We demonstrate the flexibility and effectiveness of inVAErt networks in the context of physiological inversion of a six-compartment lumped‐parameter haemodynamic model from synthetic data to real data with missing components. This article is part of the theme issue ‘Uncertainty quantification for healthcare and biological systems (Part 2)’.
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- Award ID(s):
- 1942662
- PAR ID:
- 10632882
- Publisher / Repository:
- The Royal Society
- Date Published:
- Journal Name:
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 383
- Issue:
- 2293
- ISSN:
- 1364-503X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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