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.

翻译：我们提出了一种新方法，用于从给定的（测量）时间序列数据中估计有理常微分方程模型的参数。在典型的现有方法中，首先尝试对参数值进行良好的初始猜测，然后在循环中通过数值求解常微分方程计算相应输出，并计算与给定时间序列数据的误差。若误差较小，则循环终止并返回参数值；否则，利用启发式方法或理论改进猜测并继续循环。此类方法的缺点在于非鲁棒性，因为无法保证循环迭代的结果能够可预测地接近真实参数值。本文提出的新方法避免了上述非鲁棒性问题。特别地，它无需对参数值进行良好的初始猜测，而是利用微分代数、有理函数数据插值以及多元多项式系统求解，并具有完全用户可控估计误差的潜力（实际误差分析留待未来研究）。我们还将其实现软件与多个其他估计软件包进行了性能比较。