Networks, or graphs, are a valuable tool for comprehending complex systems - they can represent a wide range of real-world phenomena such as social networks, biological networks, financial systems, transportation and communication networks, and more. Graphs enable modeling various aspects of these systems and help us understand the intricate relationships and interactions between their entities. Apart from being helpful in studying complex systems, machine learning applications to graphs have led to important new applications - from transportation systems and social networks to drug discovery - and have become one of the fastest-growing areas in artificial intelligence. Therefore, graph neural networks (GNNs) are a cornerstone for deep learning applications to data with a non-Euclidean relational structure. Different flavors of GNNs have been shown to be highly efficient for tasks like node classification, representation learning, link prediction, cluster detection, and graph classification. The popularity of GNNs is mainly due to the abundance of data that can be represented as graphs, i.e., as sets of nodes with pairwise connections represented as links.

However, standard graph representations of complex relational data are limited in their representation capabilities as they only capture dyadic relationships among pairs of entities. With the need to model interactions among more than two entities, significant research has focused on higher-order networks and ways to represent, analyze, and learn from them. In recent years, deep learning techniques combined with higher-order network models have gained significant attention as they can effectively capture the multi-relational and multi-dimensional characteristics of complex systems. These models, such as simplicial complexes, manifolds, and hypergraph representations, provide a more faithful representation of the system, enabling a deeper understanding of the intricate relationships within the data. While most higher-order approaches focus on capturing topological patterns and interactions, they are limited in addressing the temporal and spatial dimension of the underlying complex systems, i.e., which nodes can possibly influence each other over space and time. However, to effectively learn and predict such causal dependencies, we are faced with a pressing need. We require scalable software solutions that can leverage higher-order network analytics in combination with deep graph learning techniques for spatio-temporal network data.

Addressing this gap, we are developing pathpyG, an open-source package facilitating GPU-accelerated next-generation network analytics and graph learning for spatio-temporal data on graphs. pathpyG is tailored to analyze time-stamped network data and sequential data that capture multiple short walks or paths observed in a graph or network. Examples of data that can be analyzed with pathpyG include high-resolution time-stamped network data, dynamic social networks, user click streams on the Web, biological pathway data, directed acyclic graphs like citation networks, passenger trajectories in transportation networks, or trajectories of information propagation in social networks. pathpyG utilizes components of pyG and is built upon PyTorch to easily write and train Higher-Order Models for a wide range of applications. Furthermore, pathpyG is fully integrated with Jupiter, providing rich interactive visualizations of (temporal) networks and higher-order models.