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Physics-Informed Neural Networks (PINNs) are Neural Network architecturestrained to emulate solutions of differential equations without the necessity ofsolution data. They are currently ubiquitous in the scientific literature dueto their flexible and promising settings. However, very little of the availableresearch provides practical studies that aim for a better quantitativeunderstanding of such architecture and its functioning. In this paper, weperform an empirical analysis of the behavior of PINN predictions outside theirtraining domain. The primary goal is to investigate the scenarios in which aPINN can provide consistent predictions outside the training area.Thereinafter, we assess whether the algorithmic setup of PINNs can influencetheir potential for generalization and showcase the respective effect on theprediction. The results obtained in this study returns insightful and at timescounterintuitive perspectives which can be highly relevant for architectureswhich combines PINNs with domain decomposition and/or adaptive trainingstrategies.

On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it