Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this article, an approach for data-based model improvement is described which exploits the geometric constraints imposed by the system observations to estimate these unmodeled terms. The nominal model is augmented using these extra forcing terms to make predictions. This approach is applied to navigational satellite orbit prediction to bring down the error to approximately 12% of the error when using the nominal force model for a 2-hour prediction. In another example improved temperature predictions over the nominal heat equation are obtained for one-dimensional conduction.

中文翻译：

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使用观测施加的几何约束预测动力系统

动力系统的常微分方程 (ODE) 模型的解可能与其观测值不一致。通常，这种差异可归因于动力系统演化规则中的未建模强迫。在本文中，描述了一种基于数据的模型改进方法，该方法利用系统观测施加的几何约束来估计这些未建模项。使用这些额外的强制项来增强名义模型以进行预测。这种方法应用于导航卫星轨道预测，将误差降低到使用标称力模型进行 2 小时预测时的误差的 12% 左右。在另一个示例中，针对一维传导获得了对标称热方程的改进温度预测。