Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the calculation of local sensitivities, i.e. derivatives of the loss function with respect to the estimated parameters, which often necessitates several numerical solves of the underlying system of partial or ordinary differential equations. In this paper we present a new probabilistic approach to computing local sensitivities. The proposed method has several advantages over classical methods. Firstly, it operates within a constrained computational budget and provides a probabilistic quantification of uncertainty incurred in the sensitivities from this constraint. Secondly, information from previous sensitivity estimates can be recycled in subsequent computations, reducing the overall computational effort for iterative gradient-based calibration methods. The methodology presented is applied to two challenging test problems and compared against classical methods.

翻译：在整个应用科学和工程中,大规模差异方程式模型与观测或实验数据之间的校准是一个广泛的挑战。在最先进的校准方法中,一个关键的瓶颈是当地敏感度的计算,即与估计参数有关的损失函数衍生物,这往往需要部分或普通差异方程式基础系统的若干数字解决方案。在本文件中,我们提出了计算当地敏感度的新的概率方法。拟议方法比传统方法具有若干优势。首先,它是在有限的计算预算范围内运作,并且提供了在这一制约的敏感度中产生的不确定性的概率性量化。第二,从先前的敏感度估计数得到的信息可以在以后的计算中回收,从而减少迭代梯度校准方法的总体计算努力。所提出的方法适用于两个具有挑战性的测试问题,并与传统方法进行比较。