simode: R Package for Statistical Inference of Ordinary Differential Equations using Separable Integral-Matching

Rami Yaari, Itai Dattner

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Number of pages6
JournalJournal of Open Source Software
Issue number44
StatePublished - 2019


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