A fast algorithm to assess local structural identifiability

Stigter, J.D.; Molenaar, Jaap

doi:10.1016/j.automatica.2015.05.004

Cited by 61 publications

(54 citation statements)

References 28 publications

(39 reference statements)

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“…In addition, a wealth of information can be deduced by first looking at the singular vectors { v i , i = k , …, q } for which σ i = 0, i.e. the basis of the nullspace of S ( t 0 , …, t N , θ ) 18 , 23 . We demonstrate that using this information leads to a tremendous simplification and allows a tractable symbolic computation to be performed that further tests the SVD-detected lack of observability and validates these results.…”

Section: Resultsmentioning

confidence: 99%

Observability of Complex Systems: Finding the Gap

Stigter

Joubert

Molenaar

2017

Sci Rep

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For a reconstruction of state and parameter values in a dynamic system model, first the question whether these values can be uniquely determined from the data must be answered. This structural model property is known as observability or, in case of parameter calibration only, identifiability. Testing a given model for observability is a well studied problem in the systems and control sciences. However, it is increasingly difficult, if not impossible, to address this property for large size models that, nowadays, are frequently used. We demonstrate the application of a recently developed algorithm that overcomes this problem and is remarkably efficient. As an illustration we show how an observability analysis for a Chinese Hamster Ovary Cell model (34 states, 117 parameters), a JAKSTAT signalling model (31 states, 51 parameters), and a MAP Kinase model (100 states, 88 parameters) can be established in a very short time.

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Section: Resultsmentioning

confidence: 99%

Observability of Complex Systems: Finding the Gap

Stigter

Joubert

Molenaar

2017

Sci Rep

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“…An example is COMBOS [41, 42], which is based on differential algebra. Here we suggest an approach based on ideas presented in [43, 44] and on the method for finding symmetries proposed by [38]; related work has been recently presented in [45]. …”

Section: Methodsmentioning

confidence: 99%

Structural Identifiability of Dynamic Systems Biology Models

2016

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A powerful way of gaining insight into biological systems is by creating a nonlinear differential equation model, which usually contains many unknown parameters. Such a model is called structurally identifiable if it is possible to determine the values of its parameters from measurements of the model outputs. Structural identifiability is a prerequisite for parameter estimation, and should be assessed before exploiting a model. However, this analysis is seldom performed due to the high computational cost involved in the necessary symbolic calculations, which quickly becomes prohibitive as the problem size increases. In this paper we show how to analyse the structural identifiability of a very general class of nonlinear models by extending methods originally developed for studying observability. We present results about models whose identifiability had not been previously determined, report unidentifiabilities that had not been found before, and show how to modify those unidentifiable models to make them identifiable. This method helps prevent problems caused by lack of identifiability analysis, which can compromise the success of tasks such as experiment design, parameter estimation, and model-based optimization. The procedure is called STRIKE-GOLDD (STRuctural Identifiability taKen as Extended-Generalized Observability with Lie Derivatives and Decomposition), and it is implemented in a MATLAB toolbox which is available as open source software. The broad applicability of this approach facilitates the analysis of the increasingly complex models used in systems biology and other areas.

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“…Other approaches, such as those based on power series [17], differential algebra [4], [15], implicit functions [31], or differential geometry [27], can be applied to systems with external inputs. Additionally, it is possible to assess identifiability for a fully defined experiment (i.e., with specific values for initial conditions and inputs) with numerical approaches based on profile likelihoods [18] or the sensitivity matrix [23]. There are a number of software tools implementing some of the aforementioned methodologies.…”

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confidence: 99%

Input-Dependent Structural Identifiability of Nonlinear Systems

Villaverde

Evans

Chappell

et al. 2019

IEEE Control Syst. Lett.

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A dynamic model is structurally identifiable if it is possible to infer its unknown parameters by observing its output. Structural identifiability depends on the system dynamics, output, and input, as well as on the specific values of initial conditions and parameters. Here we present a symbolic method that characterizes the input that a model requires to be structurally identifiable. It determines which derivatives must be non-zero in order to have a sufficiently exciting input. Our approach considers structural identifiability as a generalization of nonlinear observability and incorporates extended Lie derivatives. The methodology assesses structural identifiability for time-varying inputs and, additionally, it can be used to determine the input profile that is required to make the parameters structurally locally identifiable. Furthermore, it is sometimes possible to replace an experiment with time-varying input with multiple experiments with constant inputs. We implement the resulting method as a MATLAB toolbox named STRIKE-GOLDD2. This tool can assist in the design of new experiments for the purpose of parameter estimation.

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A fast algorithm to assess local structural identifiability

Cited by 61 publications

References 28 publications

Observability of Complex Systems: Finding the Gap

Observability of Complex Systems: Finding the Gap

Structural Identifiability of Dynamic Systems Biology Models

Input-Dependent Structural Identifiability of Nonlinear Systems

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