Physics-Informed Neural Networks (PINNs) are an up-and-coming machine learning method to solve partial differential equations. Partial differential equations (PDEs) can be used to describe numerous physical laws. Especially in applications where training data is insufficient to employ purely data-driven approaches, PINNs shine. They combine observational data and prior knowledge about the underlying physical law to a multi-objective loss function. The PDEs constrain the network to make physically plausible predictions, even far outside the training data. Because of their desirable qualities, PINNs quickly gained popularity and were successfully applied to a multitude of problems. However, it became apparent that PINNs can be difficult to train. In particular, PDEs with oscillating solutions pose a challenge and lead to convergence issues.

This thesis aims to analyze two techniques tailored to improve the convergence of PINNs in high-frequency problems. The first technique utilizes sinusoidal activation functions to incorporate an additional prior, while the second introduces trainable weights for more flexibility in balancing the multi-objective loss. We use the following five benchmark problems: the single and double mass-spring-damper model, the wave equation, the viscous Burgers equation, and the Allen-Cahn equation to assess the merits of the methods. A series of experiments allows us to highlight common pitfalls in training PINNs and gives insights into why oscillating problems are so difficult to solve. We demonstrate that the methods have their individual strengths and weaknesses and discuss when they are best applied. Additionally, we show that both techniques can be combined for even better results.