Abstract
Parameter estimation in ordinary differential equations (ODEs) has manifold applications not only in physics but also in the life sciences. When estimating the ODE parameters from experimentally observed data, the modeler is frequently concerned with the question of parameter identifiability. The source of parameter nonidentifiability is tightly related to Lie group symmetries. In the present work, we establish a direct search algorithm for the determination of admitted Lie group symmetries. We clarify the relationship between admitted symmetries and parameter nonidentifiability. The proposed algorithm is applied to illustrative toy models as well as a data-based ODE model of the NFκB signaling pathway. We find that besides translations and scaling transformations also higher-order transformations play a role. Enabled by the knowledge about the explicit underlying symmetry transformations, we show how models with nonidentifiable parameters can still be employed to make reliable predictions.
Highlights
Modeling of dynamic systems by ordinary differential equations (ODEs) has always been concerned with the problem of unknown parameters in the model equations
The modeler is frequently confronted with the problem of nonidentifiable parameters, i.e., given the observed data there exists a submanifold in parameter space describing, in terms of an objective value, the data or almost well: these cases are denoted as structural or practical nonidentifiability [1]
The system of ordinary differential equations (4) admits a Lie group of transformations defined by the infinitesimal generator X =
Summary
Modeling of dynamic systems by ordinary differential equations (ODEs) has always been concerned with the problem of unknown parameters in the model equations. The authors of [3,4] introduced two methods which can be applied to study the identifiability of ODE models These do not yield algorithms to automatically detect structural nonidentifiabilities. The sampling is employed to investigate the rank of the variational system of the ODEs in order to identify the set of nonidentifiable parameters. This identification is computationally efficient as it is polynomial in time. In this context, we study a data-based ODE model of the NFκB signaling pathway. Besides determining and discussing the intrinsic symmetries of the dynamic system, we infer quantities which can be reliably predicted despite the structural nonidentifiabilities in the model
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