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arxiv: 2605.18910 · v1 · pith:NDKQW7XEnew · submitted 2026-05-17 · 📊 stat.ME

A Tutorial on Symbolic Structural Identifiability Analysis of ODE Models in Julia

Abdallah Alsammani This is my paper

Pith reviewed 2026-05-20 12:43 UTC · model grok-4.3

classification 📊 stat.ME
keywords structural identifiabilityODE modelsJuliasymbolic analysisparameter estimationsystems biologyepidemiologypharmacokinetics
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The pith

A Julia package provides a workflow to symbolically determine if ODE model parameters can be uniquely recovered from ideal observations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Structural identifiability analysis checks whether parameters in mechanistic ODE models can be uniquely recovered from perfect data, serving as a prerequisite for reliable parameter estimation. This tutorial introduces a unified computational framework in the Julia package StructuralIdentifiability.jl that implements local and global identifiability checks along with observable combinations. The approach is shown through seven case studies in epidemiology, pharmacokinetics, and systems biology that cover globally identifiable systems, local-only cases, structural non-identifiability, and fixes via added measurements or reparameterization. A sympathetic reader cares because performing this analysis first prevents wasted effort on models whose parameters cannot be estimated uniquely no matter how much data is collected. The tutorial also stresses practical steps such as model reformulation and experimental design within reproducible Julia workflows.

Core claim

Structural identifiability analysis determines whether the parameters of a mechanistic ordinary differential equation (ODE) model can be uniquely recovered from ideal observations and is therefore a fundamental prerequisite for reliable parameter estimation. The tutorial presents a modern, reproducible computational framework for symbolic structural identifiability analysis using the Julia package StructuralIdentifiability.jl together with the core functions @ODEmodel, assess_local_identifiability, assess_identifiability, and find_identifiable_functions, demonstrated through seven case studies that illustrate globally identifiable systems, local-only identifiability, structural non-identifi-

What carries the argument

The core functions @ODEmodel for model definition and assess_local_identifiability, assess_identifiability, and find_identifiable_functions that perform symbolic checks for local and global identifiability, observability, and identifiable parameter combinations.

If this is right

  • Globally identifiable parameters can be uniquely recovered from ideal observations.
  • Local-only identifiability restricts unique recovery to specific parameter regions.
  • Structural non-identifiability can be resolved by adding measurements or reparameterizing the model.
  • The workflow supports practical model reformulation and experimental design choices.
  • Reproducible workflows become possible inside the Julia SciML ecosystem for mechanistic modeling.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Modelers could insert these checks as an automatic first step before any numerical fitting routine.
  • Similar symbolic identifiability tools could be built for other scientific computing languages.
  • Integration with automatic differentiation libraries would allow identifiability results to guide parameter selection during estimation.

Load-bearing premise

The tutorial assumes the core functions in StructuralIdentifiability.jl correctly implement the symbolic methods and that the seven case studies represent typical modeling challenges.

What would settle it

Running the package on one of the seven case studies and obtaining identifiability results that contradict independently derived analytical solutions for that model would falsify the claimed reliability of the workflow.

Figures

Figures reproduced from arXiv: 2605.18910 by Abdallah Alsammani.

Figure 1
Figure 1. Figure 1: Workflow diagram of the structural identifiability pipeline. [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Compartmental diagrams of the mechanistic models analysed in Section [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Structural identifiability verdict matrix across all case studies and measurement [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Empirical demonstration of structural non identifiability through ODE inte [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
read the original abstract

Structural identifiability analysis determines whether the parameters of a mechanistic ordinary differential equation (ODE) model can be uniquely recovered from ideal observations and is therefore a fundamental prerequisite for reliable parameter estimation. This tutorial presents a modern, reproducible computational framework for symbolic structural identifiability analysis using the Julia package StructuralIdentifiability.jl. We provide a rigorous yet accessible introduction to local and global identifiability, observability, parameter-to-output mappings, and identifiable parameter combinations, together with a unified workflow based on the core functions @ODEmodel, assess_local_identifiability, assess_identifiability, and find_identifiable_functions. The framework is demonstrated through seven case studies from epidemiology, pharmacokinetics, and systems biology, illustrating globally identifiable systems, local-only identifiability, structural non-identifiability, and recovery of identifiability through additional measurements and reparameterization. Beyond the theoretical foundations, the tutorial emphasizes practical model reformulation, experimental design, and reproducible scientific workflows within the Julia SciML ecosystem, providing a comprehensive reference for researchers and graduate students working with mechanistic ODE models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript is a tutorial introducing structural identifiability analysis for mechanistic ODE models. It defines local and global identifiability, observability, and identifiable combinations, then presents a unified workflow using the StructuralIdentifiability.jl package functions @ODEmodel, assess_local_identifiability, assess_identifiability, and find_identifiable_functions. The workflow is illustrated on seven published case studies drawn from epidemiology, pharmacokinetics, and systems biology, covering globally identifiable, locally identifiable, and structurally non-identifiable models as well as recovery of identifiability via additional outputs or reparameterization.

Significance. If the case-study implementations are faithful to the underlying algorithms, the tutorial provides a clear, reproducible entry point to symbolic identifiability methods that are a prerequisite for reliable parameter estimation in mechanistic modeling. By embedding the examples in the Julia SciML ecosystem and emphasizing practical model reformulation and experimental design, the work can help standardize identifiability checks before numerical fitting and lower the barrier for applied researchers and graduate students.

major comments (2)
  1. [§4.3] §4.3 (Case Study 3, SIR model with vital dynamics): the reported local identifiability result for the transmission rate is stated without the explicit rank of the Jacobian or the numerical tolerance employed by assess_local_identifiability; this detail is load-bearing for readers who wish to reproduce the exact classification.
  2. [§5.1] §5.1 (reparameterization example): the claim that the new parameter combination is 'globally identifiable' rests on the output of find_identifiable_functions, yet the manuscript does not verify that the transformation is invertible over the entire positive orthant, which is required to transfer global identifiability from the original to the reparameterized model.
minor comments (3)
  1. [§2] The notation for the output map y(t) is introduced inconsistently between the theoretical section and the code listings; a single consistent symbol would improve readability.
  2. [Figure 2] Figure 2 (workflow diagram) uses arrows whose direction is ambiguous with respect to data flow versus dependency; adding labels would prevent misinterpretation.
  3. [§4] Several code blocks omit the required using StructuralIdentifiability statement; including it once at the top of each self-contained example would aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our tutorial manuscript. We address the major comments point by point below, indicating where revisions will be made to enhance the manuscript.

read point-by-point responses

  1. Referee: [§4.3] §4.3 (Case Study 3, SIR model with vital dynamics): the reported local identifiability result for the transmission rate is stated without the explicit rank of the Jacobian or the numerical tolerance employed by assess_local_identifiability; this detail is load-bearing for readers who wish to reproduce the exact classification.

    Authors: We agree with the referee that including the Jacobian rank and the numerical tolerance is important for full reproducibility. In the revised manuscript, we will explicitly report the rank of the Jacobian and the tolerance value used by assess_local_identifiability in §4.3 for the SIR model case study. revision: yes

  2. Referee: [§5.1] §5.1 (reparameterization example): the claim that the new parameter combination is 'globally identifiable' rests on the output of find_identifiable_functions, yet the manuscript does not verify that the transformation is invertible over the entire positive orthant, which is required to transfer global identifiability from the original to the reparameterized model.

    Authors: This is a valid point. The output of find_identifiable_functions confirms the global identifiability of the combination, but to rigorously transfer this to the reparameterized model, invertibility must be established. We will revise §5.1 to include a verification or argument that the transformation is invertible over the positive orthant, for example by showing it is a bijection or providing the inverse explicitly. revision: yes

Circularity Check

0 steps flagged

No significant circularity in tutorial on existing package

full rationale

This manuscript is a tutorial that introduces concepts and demonstrates the use of the pre-existing StructuralIdentifiability.jl package through seven case studies on published ODE models. No new theorems, derivations, predictions, or parameter fits are claimed or performed; the content consists of pedagogical explanations of local/global identifiability, observability, and workflow functions such as @ODEmodel and assess_identifiability. Any reliance on the package's correctness is an external assumption about third-party software rather than an internal reduction of a claimed result to its own inputs or self-citations. The derivation chain is therefore self-contained as explanatory material with no load-bearing steps that collapse by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is an educational tutorial on existing symbolic methods and software. It introduces no new free parameters, axioms, or invented entities beyond standard mathematical definitions of identifiability already present in the literature.

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Works this paper leans on

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