The goal of this paper is to provide a simple approach to perform local sensitivity analysis using Physics-informed neural networks (PINN). The main idea lies in adding a new term in the loss function that regularizes the solution in a small neighborhood near the nominal value of the parameter of interest. The added term represents the derivative of the loss function with respect to the parameter of interest. The result of this modification is a solution to the problem along with the derivative of the solution with respect to the parameter of interest (the sensitivity). We call the new technique SA-PNN which stands for sensitivity analysis in PINN. The effectiveness of the technique is shown using four examples: the first one is a simple one-dimensional advection-diffusion problem to show the methodology, the second is a two-dimensional Poisson's problem with nine parameters of interest, and the third and fourth examples are one and two-dimensional transient two-phase flow in porous media problem.

翻译：本文旨在提供一种利用物理信息神经网络（PINN）进行局部灵敏度分析的简便方法。其核心思想是在损失函数中新增一项，用于在感兴趣参数名义值附近的小邻域内对解进行正则化。新增项代表损失函数关于该感兴趣参数的导数。该改进的结果是同时获得问题解以及解关于感兴趣参数的导数（即灵敏度）。我们将这一新技术称为SA-PNN，即PINN中的灵敏度分析。通过四个算例验证了该技术的有效性：第一个算例是一维对流扩散问题，用于演示方法原理；第二个算例是具有九个感兴趣参数的二维泊松问题；第三和第四个算例分别是一维和二维多孔介质瞬态两相流问题。