Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on basis functions or Gaussian processes to approximate the ODE solution and its derivatives. Due to the sensitivity of the ODE solution to its derivatives, these methods can be hindered by estimation error, especially when only sparse time-course observations are available. We present a Bayesian collocation framework that operates on the integrated form of the ODEs and also avoids the expensive use of numerical solvers. Our methodology has the capability to handle general nonlinear ODE systems. We demonstrate the accuracy of the proposed method through a simulation study, where the estimated parameters and recovered system trajectories are compared with other recent methods. A real data example is also provided.

翻译：从含噪声观测值中推断常微分方程（ODE）的参数是众多科学领域的重要问题。当前，大多数绕过数值积分的参数估计方法往往依赖基函数或高斯过程来近似ODE解及其导数。由于ODE解对其导数的敏感性，这些方法可能受限于估计误差，尤其在仅有稀疏时间过程观测值时更为显著。本文提出一种基于ODE积分形式的贝叶斯配点框架，同时避免使用昂贵的数值求解器。该方法能够处理一般非线性ODE系统。通过仿真研究验证了所提方法的准确性，其中估计参数和恢复的系统轨迹与其他近期方法进行了比较。此外还给出了一个真实数据示例。