105,203 research outputs found
Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A survey
Dynamic networks are used in a wide range of fields, including social network
analysis, recommender systems, and epidemiology. Representing complex networks
as structures changing over time allow network models to leverage not only
structural but also temporal patterns. However, as dynamic network literature
stems from diverse fields and makes use of inconsistent terminology, it is
challenging to navigate. Meanwhile, graph neural networks (GNNs) have gained a
lot of attention in recent years for their ability to perform well on a range
of network science tasks, such as link prediction and node classification.
Despite the popularity of graph neural networks and the proven benefits of
dynamic network models, there has been little focus on graph neural networks
for dynamic networks. To address the challenges resulting from the fact that
this research crosses diverse fields as well as to survey dynamic graph neural
networks, this work is split into two main parts. First, to address the
ambiguity of the dynamic network terminology we establish a foundation of
dynamic networks with consistent, detailed terminology and notation. Second, we
present a comprehensive survey of dynamic graph neural network models using the
proposed terminologyComment: 28 pages, 9 figures, 8 table
Data-driven discovery of coordinates and governing equations
The discovery of governing equations from scientific data has the potential
to transform data-rich fields that lack well-characterized quantitative
descriptions. Advances in sparse regression are currently enabling the
tractable identification of both the structure and parameters of a nonlinear
dynamical system from data. The resulting models have the fewest terms
necessary to describe the dynamics, balancing model complexity with descriptive
ability, and thus promoting interpretability and generalizability. This
provides an algorithmic approach to Occam's razor for model discovery. However,
this approach fundamentally relies on an effective coordinate system in which
the dynamics have a simple representation. In this work, we design a custom
autoencoder to discover a coordinate transformation into a reduced space where
the dynamics may be sparsely represented. Thus, we simultaneously learn the
governing equations and the associated coordinate system. We demonstrate this
approach on several example high-dimensional dynamical systems with
low-dimensional behavior. The resulting modeling framework combines the
strengths of deep neural networks for flexible representation and sparse
identification of nonlinear dynamics (SINDy) for parsimonious models. It is the
first method of its kind to place the discovery of coordinates and models on an
equal footing.Comment: 25 pages, 6 figures; added acknowledgment
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