## Abstract

Systems of ordinary differential equations (ODEs) are commonly used for mathematical modeling of the rate of change of dynamic processes in areas such as mathematical biology (Edelstein-Keshet, 2005), biochemistry (Voit, 2000) and compartmental models in epidemiology (Anderson & May, 1992), to mention a few. Inference of ODEs involves the ‘standard’ statistical problems such as studying the identifiability of a model, estimating model parameters, predicting future states of the system, testing hypotheses, and choosing the ‘best’ model.

However, dynamical systems are typically very complex: nonlinear, high dimensional and only partialy measured. Moreover, data may be sparse and noisy. Thus, statistical learning (inference, prediction) of dynamical systems is not a trivial task in practice. In particular, numerical

application of standard estimators, like maximum-likelihood or least-squares, may be difficult or computationally costly. It typically requires solving the system numerically for a large set of potential parameters values, and choosing the optimal values using some nonlinear optimization technique. Starting from a random initial guess, the optimization can take a long time

to converge to the optimal solution. Furthermore, there is no guarantee the optimization will converge to the optimal solution at all.

However, dynamical systems are typically very complex: nonlinear, high dimensional and only partialy measured. Moreover, data may be sparse and noisy. Thus, statistical learning (inference, prediction) of dynamical systems is not a trivial task in practice. In particular, numerical

application of standard estimators, like maximum-likelihood or least-squares, may be difficult or computationally costly. It typically requires solving the system numerically for a large set of potential parameters values, and choosing the optimal values using some nonlinear optimization technique. Starting from a random initial guess, the optimization can take a long time

to converge to the optimal solution. Furthermore, there is no guarantee the optimization will converge to the optimal solution at all.

Original language | English |
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Number of pages | 6 |

Journal | Journal of Open Source Software |

Volume | 4 |

Issue number | 44 |

DOIs | |

State | Published - 2019 |