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.

翻译：本文提出一种新方法，用于从给定的（测量）时间序列数据中估计有理ODE模型的参数。现有典型方法通常从给定搜索区间内对参数值进行初始猜测，随后在循环中通过数值求解ODE计算对应输出，继而计算与给定时间序列数据的误差。若误差较小则终止循环并返回参数值；否则利用启发式方法或理论改进猜测值并继续循环。这类方法往往缺乏鲁棒性——其精度依赖于搜索区间与真实参数值，且无法处理参数局部可辨识的情况。本文提出一种不受上述非鲁棒性影响的新方法：无需对参数值进行良好初始猜测或指定搜索区间，而是利用微分代数、有理函数数据插值与多元多项式系统求解。最后将所开发软件与多种参数估计软件包进行了性能对比。