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Graph Neural Networks (GNNs) have established themselves as a key component in addressing diverse graph-based tasks. Despite their notable successes, GNNs remain susceptible to input perturbations in the form of adversarial attacks. This…
Graph Neural Networks (GNNs) are a form of deep learning that enable a wide range of machine learning applications on graph-structured data. The learning of GNNs, however, is known to pose challenges for memory-constrained devices such as…
A reliable perception has to be robust against challenging environmental conditions. Therefore, recent efforts focused on the use of radar sensors in addition to camera and lidar sensors for perception applications. However, the sparsity of…
We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…
Graph neural networks (GNNs) have achieved remarkable success in a variety of machine learning tasks over graph data. Existing GNNs usually rely on message passing, i.e., computing node representations by gathering information from the…
The regression of multiple inter-connected sequence data is a problem in various disciplines. Formally, we name the regression problem of multiple inter-connected data entities as the "dynamic network regression" in this paper. Within the…
Graph neural networks (GNNs) rely mainly on the message-passing paradigm to propagate node features and build interactions, and different graph learning problems require different ranges of node interactions. In this work, we explore the…
Graph neural networks (GNNs) are commonly described as being permutation equivariant with respect to node relabeling in the graph. This symmetry of GNNs is often compared to the translation equivariance of Euclidean convolution neural…
We present a Graph Neural Network (GNN) that accurately simulates a multidisperse suspension of interacting spherical particles. Our machine learning framework is built upon the recent work of Sanchez-Gonzalez et al. ICML, PMLR, 119,…
In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…
Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved,…
In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for…
In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…
Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our…
This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by…
Graph neural networks (GNNs), which are capable of learning representations from graphical data, are naturally suitable for modeling molecular systems. This review introduces GNNs and their various applications for small organic molecules.…
Graph Neural Networks (GNNs) have paved the way for being a cornerstone in graph-related learning tasks. Yet, the ability of GNNs to capture structural interactions within graphs remains under-explored. In this work, we address this gap by…
Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…
Graph Neural Networks (GNNs) have become the leading paradigm for learning on (static) graph-structured data. However, many real-world systems are dynamic in nature, since the graph and node/edge attributes change over time. In recent…
This work proposes a novel methodology for turbulence modeling in Large Eddy Simulation (LES) based on Graph Neural Networks (GNNs), which embeds the discrete rotational, reflectional and translational symmetries of the Navier-Stokes…