Title: Physics-inspired Machine Learning

Abstract: Combining physics with machine learning is a rapidly growing field of research.Thereby, most work focuses on leveraging machine learning methods to solve problemsin physics. Here, however, we focus on the converse, i.e., physics-inspired machinelearning, which can be described as incorporating structure from physical systems intomachine learning methods to obtain models with better inductive biases. More con-cretely, we propose several physics-inspired deep learning architectures for sequencemodelling based on nonlinear coupled oscillators, Hamiltonian systems and multi-scaledynamical systems. The proposed architectures tackle central problems in the field ofrecurrent sequence modeling, namely the vanishing and exploding gradients problemas well as the issue of insufficient expressive power. Moreover, we discuss physics-inspired learning on graphs, wherein the dynamics of the message-passing propagationare derived from physical systems. We further prove that these methods mitigate theover-smoothing issue, thereby enabling the construction of deep graph neural networks(GNNs). We extensively test all proposed methods on a variety of versatile syntheticand real-world datasets, ranging from image recognition, speech recognition, naturallanguage processing (NLP), medical applications, and scientific computing for sequencemodels, to citation networks, computational chemistry applications, and networks ofarticles and websites for graph learning models.