The paper's goal is to provide a simple unified approach to perform 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 to perform sensitivity analysis within this context SA-PINN. We show the effectiveness of the technique using 3 examples: the first one is a simple 1D advection-diffusion problem to show the methodology, the second is a 2D Poisson's problem with 9 parameters of interest and the last one is a 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）进行灵敏度分析的统一简化方法。核心思想是在损失函数中添加一个新项，该正则项在感兴趣参数标称值附近的小邻域内约束解。所添加的项表示损失函数关于感兴趣参数的导数。这种修正的结果是同时获得问题的解以及解关于感兴趣参数的导数（即灵敏度）。我们将这种在PINN框架下进行灵敏度分析的新技术称为SA-PINN。通过三个算例验证该方法的有效性：第一个算例是一个简单的一维对流扩散问题以说明方法原理，第二个是包含9个感兴趣参数的二维泊松问题，最后一个算例是多孔介质中瞬态两相流问题。