Classical numerical methods can be applied to any differential equation and are based on well developed mathematical theory and tools. However, their use in high order and/or nonlinear problems, like fluid dynamics or scattering problems, may present unfeasibly high computational space and time requirements. While supervised artificial intelligence techniques can be used to mitigate these computational costs by efficiently learning parts of the solutions, their application necessitates very large datasets for training, which severely limits their usefulness. This project aims to use the computational resources of the Arrhenius cluster to explore the use of physics informed neural networks, an unsupervised learning paradigm in which the loss function is augmented with extra terms that represent the equations that govern the data, for efficiently solving complex problems without the need of any data to learn from. We will implement multiple candidate architectures of physics informed neural networks to test their performance in progressively more complex problems, and perform an exhaustive experimental study of the numerical stability of their training process and its sensitivity to hyperparameters. We aim to find under which conditions a physics informed neural network is preferable to pure classical numerical methods or to hybrid classical methods/AI approaches when studying difficult systems of partial differential equations.