Observable functions of rational ODE models and how to find them
Abstract
Consider a parametric ODE control model. A function of the states and parameters is called observable if its value can in principle be reconstructed from input-output data. The observable functions form a field, called the observation field, represented naturally by a set of generators. Even when the model is not fully observable, this field captures the information still accessible from input-output data. We present an algorithm for computing a concise generating set for the observation field of a model with rational dynamics. The algorithm relies on two new results: one allows observable functions to be extracted from the coefficients of repeated Lie derivatives of the outputs, while the other reduces the required orders of differentiation by exploiting identifiable parameter combinations. We implement the resulting algorithm in StructuralIdentifiability$.$jl (https://github.com/SciML/StructuralIdentifiability.jl). For computational efficiency, we employ recent techniques for differential elimination and rational function field simplification. Using models from epidemiology, chemical kinetics, and cancer modeling, we show that the algorithm produces generators with domain-specific interpretations that can inform model analysis and development.
Related
- Exact barycentric rational interpolation of analytic functions with an application to the Bessel functions
- Rational and integral values of rational functions at rational points
- Real rational Herglotz-Nevanlinna functions in two variables and a class of extremals
- Representation of arbitrary rational functions and polynomials by non-Foster resistor-capacitor-inductor networks
- Higher-dimensional singularities of rational inner functions
BibTeX
@misc{demin2026observable,
title = {{Observable functions of rational ODE models and how to find them}},
author = {Alexander Demin and Gleb Pogudin and Christopher Rackauckas},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06134},
eprint = {2609.06134},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06134},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Observable functions of rational ODE models and how to find them
AU - Alexander Demin
AU - Gleb Pogudin
AU - Christopher Rackauckas
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.06134
UR - https://arxiv.org/abs/2609.06134
AB - Consider a parametric ODE control model. A function of the states and parameters is called observable if its value can in principle be reconstructed from input-output data. The observable functions form a field, called the observation field, represented naturally by a set of generators. Even when the model is not fully observable, this field captures the information still accessible from input-output data. We present an algorithm for computing a concise generating set for the observation field of a model with rational dynamics. The algorithm relies on two new results: one allows observable functions to be extracted from the coefficients of repeated Lie derivatives of the outputs, while the other reduces the required orders of differentiation by exploiting identifiable parameter combinations. We implement the resulting algorithm in StructuralIdentifiability$.$jl (https://github.com/SciML/StructuralIdentifiability.jl). For computational efficiency, we employ recent techniques for differential elimination and rational function field simplification. Using models from epidemiology, chemical kinetics, and cancer modeling, we show that the algorithm produces generators with domain-specific interpretations that can inform model analysis and development.
ER -