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A practical identifiability criterion leveraging weak-form parameter estimation.

Nora Heitzman-Breen1, Vanja Dukic1, David M Bortz1

  • 1Department of Applied Mathematics, University of Colorado, Boulder, CO, 80309-0526, USA.

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Summary
This summary is machine-generated.

This study introduces a new (e, q)-identifiability criterion for parameter estimation, improving accuracy with noisy data. A faster, noise-robust weak-form estimation method using differential algebra and WENDy is also presented.

Keywords:
Data-driven modelingIdentifiabilityWeak form

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Area of Science:

  • Systems Biology
  • Mathematical Modeling
  • Parameter Estimation

Background:

  • Assessing the practical identifiability of parameters in dynamic systems is crucial for reliable model analysis.
  • Existing identifiability criteria often fail to fully account for the impact of noise on parameter estimation quality.
  • Computational efficiency in parameter estimation is a significant challenge, especially for complex systems.

Purpose of the Study:

  • To introduce a novel practical identifiability criterion, (e, q)-identifiability, that incorporates noise levels and estimator error.
  • To develop and validate a computationally efficient parameter estimation method for systems with unobserved variables.
  • To demonstrate the robustness and speed of the proposed method using biological modeling examples.

Main Methods:

  • Defined (e, q)-identifiability based on noise parameter (e) and mean-square error (q).
  • Employed differential algebra to generate weak-form input-output equations.
  • Applied Weak form Estimation of Nonlinear Dynamics (WENDy) for parameter estimation in systems with unobserved variables.

Main Results:

  • The (e, q)-identifiability criterion effectively captures the impact of data noise on parameter estimate quality.
  • The weak-form equation error-based method provides a significantly faster assessment of practical identifiability compared to output error methods.
  • The WENDy approach demonstrated computational efficiency and robustness to noise in biological modeling scenarios.

Conclusions:

  • The proposed (e, q)-identifiability criterion offers a more comprehensive assessment of parameter estimation reliability.
  • The integration of differential algebra and WENDy provides an efficient and robust tool for practical identifiability analysis.
  • This approach facilitates more reliable model development and analysis in complex biological systems.