论文标题
快速校准微分方程模型的概率梯度
Probabilistic Gradients for Fast Calibration of Differential Equation Models
论文作者
论文摘要
对观察或实验数据进行大规模微分方程模型的校准是整个应用科学和工程的广泛挑战。最先进的校准方法中的关键瓶颈是局部灵敏度的计算，即相对于估计参数的损失函数的导数，这通常需要几个基础或普通微分方程的基础系统的数值解决方案。在本文中，我们提出了一种计算局部敏感性的新概率方法。所提出的方法比经典方法具有多个优点。首先，它在约束的计算预算中运行，并提供了由于此约束而产生的敏感性不确定性的概率量化。其次，可以在随后的计算中回收先前灵敏度估计的信息，从而减少基于迭代梯度的校准方法的总体计算工作。提出的方法应用于两个具有挑战性的测试问题，并与经典方法进行了比较。
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.
