Robust Parameter Estimation for Rational Ordinary Differential Equations

We present a new approach for estimating parameters in rational ODE models from given (measured) time series data. In typical existing approaches, an initial guess for the parameter values is made from a given search interval. Then, in a loop, the corresponding outputs are computed by solving the ODE numerically, followed by computing the error from the given time series data. If the error is small, the loop terminates and the parameter values are returned. Otherwise, heuristics/theories are used to possibly improve the guess and continue the loop. These approaches tend to be non-robust in the sense that their accuracy depend on the search interval and the true parameter values; furthermore, they cannot handle the case where the parameters are locally identifiable. In this paper, we propose a new approach, which does not suffer from the above non-robustness. In particular, it does not require making good initial guesses for the parameter values or specifying search intervals. Instead, it uses differential algebra, interpolation of the data using rational functions, and multivariate polynomial system solving. We also compare the performance of the resulting software with several other estimation software packages.