Using Neural Architectures to Model Complex Dynamical Systems

Abstract

The natural, physical and social worlds abound with feedback processes that make the challenge of modeling the underlying system an extremely complex one. This paper proposes an end-to-end deep learning approach to modelling such so-called complex systems which addresses two problems: (1) scientific model discovery when we have only incomplete/partial knowledge of system dynamics; (2) integration of graph-structured data into scientific machine learning (SciML) using graph neural networks. It is well known that deep learning (DL) has had remarkable successin leveraging large amounts of unstructured data into downstream tasks such as clustering, classification, and regression. Recently, the development of graph neural networks has extended DL techniques to graph structured data of complex systems. However, DL methods still appear largely disjointed with established scientific knowledge, and the contribution to basic science is not always apparent. This disconnect has spurred the development of physics-informed deep learning, and more generally, the emerging discipline of SciML. Modelling complex systems in the physical, biological, and social sciences within the SciML framework requires further considerations. We argue the need to consider heterogeneous, graph-structured data as well as the effective scale at which we can observe system dynamics. Our proposal would open up a joint approach to the previously distinct fields of graph representation learning and SciML.