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 a typical existing approach, one first tries to make a good initial guess for the parameter values. 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. A downside of this approach is non-robustness, as there are no guarantees for the result of the loop iterations to be predictably close to the true parameter values. 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. Instead, it uses differential algebra, interpolation of the data using rational functions, and multivariate polynomial system solving, and has a potential for a complete user control over the error of the estimation (the actual error analysis is left for the future research). We also compare the performance of the resulting software with several other estimation software packages.