Physics-Informed Neural Networks (PINNs) are Neural Network architectures trained to emulate solutions of differential equations without the necessity of solution data. They are currently ubiquitous in the scientific literature due to their flexible and promising settings. However, very little of the available research provides practical studies that aim for a better quantitative understanding of such architecture and its functioning. In this paper, we perform an empirical analysis of the behavior of PINN predictions outside their training domain. The primary goal is to investigate the scenarios in which a PINN can provide consistent predictions outside the training area. Thereinafter, we assess whether the algorithmic setup of PINNs can influence their potential for generalization and showcase the respective effect on the prediction. The results obtained in this study returns insightful and at times counterintuitive perspectives which can be highly relevant for architectures which combines PINNs with domain decomposition and/or adaptive training strategies.

Here the human intelligence in charge is telling the AI model to have a look at these sections of the image. At this stage, only the human knows what is in the selected spots --sheep on a background in full shadow, sheep on the grass, and sheep on the bare ground. Defining areas where you know there are not examples of your object of interest helps the algorithm by enabling it to understand what you are NOT looking for looks like. The AI model will use these sections of your image as counterexamples. It is particularly helpful to draw the attention of the algorithm to areas where you have objects that look similar to your object of interest, but which are not that for which you are looking.