# On structural and practical identifiability

arXiv: https://arxiv.org/abs/2102.05100 · HTML: https://mlsanity.com/paper/2102.05100/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2021.

## Built on by (most cited first, 19 of 19)

- [Posterior Collapse and Latent Variable Non-identifiability](https://mlsanity.com/paper/2301.00537/) (2023)
- [Marrying Causal Representation Learning with Dynamical Systems for Science](https://mlsanity.com/paper/2405.13888/) (2024)
- [Structure is information: structural identifiability mappings for machine learning with partially observed dynamical systems](https://mlsanity.com/paper/2502.04131/) (2025)
- [BO4IO: A Bayesian optimization approach to inverse optimization with uncertainty quantification](https://mlsanity.com/paper/2405.17875/) (2024)
- [Regularized Nonlinear Regression for Simultaneously Selecting and Estimating Key Model Parameters](https://mlsanity.com/paper/2104.11426/) (2021)
- [Interpretability of Epidemiological Models : The Curse of Non-Identifiability](https://mlsanity.com/paper/2104.14821/) (2021)
- [InVAErt networks for amortized inference and identifiability analysis of lumped parameter hemodynamic models](https://mlsanity.com/paper/2408.08264/) (2024)
- [Bias and Identifiability in the Bounded Confidence Model](https://mlsanity.com/paper/2506.11751/) (2025)
- [Debiased maximum-likelihood estimators for hazard ratios under kernel-based machine-learning adjustment](https://mlsanity.com/paper/2507.17686/) (2025)
- [FieldFormer: Locality-Aware Transformers for Spatio-Temporal Modeling on Sparse Sensor Networks](https://mlsanity.com/paper/2510.03589/) (2025)
- [Achieving Occam's Razor: Deep Learning for Optimal Model Reduction](https://mlsanity.com/paper/2303.13746/) (2023)
- [Sharpness-Aware Hybrid Model Learning for Architecture-Agnostic Parameter Estimation](https://mlsanity.com/paper/2602.06837/) (2026)
- [Learning functional components of PDEs from data using neural networks](https://mlsanity.com/paper/2602.13174/) (2026)
- [Learning What Matters: Adaptive Information-Theoretic Objectives for Robot Exploration](https://mlsanity.com/paper/2605.12084/) (2026)
- [From inverse problems to neural operators: prediction, mechanism, and generalization of data-driven models](https://mlsanity.com/paper/2606.08956/) (2026)
- [HAPI-EP: Towards Hybrid, Adaptive, and Predictive Digital Twins of Cardiac Electrophysiology](https://mlsanity.com/paper/2606.15637/) (2026)
- [A Physics-Chemistry-Informed Neural Network (PCINN) for Real-Time Spatial-ALD Coverage Prediction and Reliable Kinetics Inversion](https://mlsanity.com/paper/2608.00212/) (2026)
- [Wrong Operator or Blind Design? A Post-Training Diagnostic for Physics-Informed Coefficient Learning](https://mlsanity.com/paper/2608.16925/) (2026)
- [Differentiable Hybrid Modelling for Learning and Optimising Chemical Transport Processes from Experimental Data](https://mlsanity.com/paper/2609.04011/) (2026)

## Abstract (arXiv)

We discuss issues of structural and practical identifiability of partially observed differential equations which are often applied in systems biology. The development of mathematical methods to investigate structural non-identifiability has a long tradition. Computationally efficient methods to detect and cure it have been developed recently. Practical non-identifiability on the other hand has not been investigated at the same conceptually clear level. We argue that practical identifiability is more challenging than structural identifiability when it comes to modelling experimental data. We discuss that the classical approach based on the Fisher information matrix has severe shortcomings. As an alternative, we propose using the profile likelihood, which is a powerful approach to detect and resolve practical non-identifiability.