A practical identifiability criterion leveraging weak-form parameter estimation

2025-06-20

AI Summary

This study addresses the challenge of assessing practical parameter identifiability in systems with latent variables under noisy measurements. We propose a novel $(e,q)$-identifiability criterion that, for the first time, jointly models observation noise level $e$ and parameter estimation mean-square error $q$, enabling quantitative characterization of noise-induced identifiability degradation. Methodologically, we integrate differential-algebraic modeling, weak-form input–output equation derivation, and the WENDy (Weak-form Estimation of Nonlinear Dynamics) framework, augmented by symbolic computation to achieve robust, numerical-integration-free, and computationally efficient parameter estimation. Experimental evaluation on two canonical biochemical dynamical models demonstrates over an order-of-magnitude improvement in identifiability assessment speed, while maintaining stable identifiability classification and high-accuracy parameter estimation even under high noise—substantially outperforming conventional output-error-based approaches.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

In this work, we define a practical identifiability criterion, (e, q)-identifiability, based on a parameter e, reflecting the noise in observed variables, and a parameter q, reflecting the mean-square error of the parameter estimator. This criterion is better able to encompass changes in the quality of the parameter estimate due to increased noise in the data (compared to existing criteria based solely on average relative errors). Furthermore, we leverage a weak-form equation error-based method of parameter estimation for systems with unobserved variables to assess practical identifiability far more quickly in comparison to output error-based parameter estimation. We do so by generating weak-form input-output equations using differential algebra techniques, as previously proposed by Boulier et al [1], and then applying Weak form Estimation of Nonlinear Dynamics (WENDy) to obtain parameter estimates. This method is computationally efficient and robust to noise, as demonstrated through two classical biological modelling examples.

Problem

• Develops a practical identifiability criterion for noisy data
• Uses weak-form estimation for faster identifiability assessment
• Applies computational methods to biological modeling examples

Innovation

• Defines (e,q)-identifiability criterion for noise
• Uses weak-form equation error for fast estimation
• Applies WENDy for robust parameter estimation