Sensitivity analysis using Physics-informed neural networks

TL;DR

This paper introduces SA-PINN, a novel method for local sensitivity analysis using Physics-informed neural networks by adding a regularization term to compute derivatives of solutions with respect to parameters.

Contribution

The paper proposes a new technique, SA-PINN, that enables local sensitivity analysis within PINNs by incorporating a derivative-based regularization term in the loss function.

Findings

Effective in simple advection-diffusion problem

Successfully applied to multi-parameter Poisson's problem

Demonstrated on transient flow in porous media

Abstract

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.