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Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions…

Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive…

Physical systems are commonly represented as a combination of particles, the individual dynamics of which govern the system dynamics. However, traditional approaches require the knowledge of several abstract quantities such as the energy or…

Networks are important structures used to model complex systems where interactions take place. In a basic network model, entities are represented as nodes, and interaction and relations among them are represented as edges. However, in a…

Graph convolutional networks (GCNs) have been very successful in skeleton-based human action recognition where the sequence of skeletons is modeled as a graph. However, most of the GCN-based methods in this area train a deep feed-forward…

Graph neural networks (GNNs) have shown promise in learning the ground-state electronic properties of materials, subverting ab initio density functional theory (DFT) calculations when the underlying lattices can be represented as small…

Graph Convolutional Networks (GCNs) have recently become the primary choice for learning from graph-structured data, superseding hash fingerprints in representing chemical compounds. However, GCNs lack the ability to take into account the…

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,…

We introduce the \emph{Symplectic Generative Network (SGN)}, a deep generative model that leverages Hamiltonian mechanics to construct an invertible, volume-preserving mapping between a latent space and the data space. By endowing the…

Pedestrian trajectory prediction is an important technique of autonomous driving, which has become a research hot-spot in recent years. Previous methods mainly rely on the position relationship of pedestrians to model social interaction,…

Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…

In traditional Graph Neural Networks (GNNs), the assumption of a fixed embedding manifold often limits their adaptability to diverse graph geometries. Recently, Hamiltonian system-inspired GNNs have been proposed to address the dynamic…

The methodology of deriving an adatom lattice-gas Hamiltonian (LGH) from first principles (FP) calculations is revisited. Such LGH cluster expansions compute a large set of lateral pair-, trio-, quarto interactions by solving a set of…

Recently, significant attention has been given to the idea of viewing relational databases as heterogeneous graphs, enabling the application of graph neural network (GNN) technology for predictive tasks. However, existing GNN methods…

The H\"uckel Hamiltonian is an incredibly simple tight-binding model famed for its ability to capture qualitative physics phenomena arising from electron interactions in molecules and materials. Part of its simplicity arises from using only…

Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on predicting separable Hamiltonian systems with their kinematic…

Learning graph convolutional networks (GCNs) is an emerging field which aims at generalizing convolutional operations to arbitrary non-regular domains. In particular, GCNs operating on spatial domains show superior performances compared to…

The construction of spatiotemporal networks using graph convolution networks (GCNs) has become one of the most popular methods for predicting traffic signals. However, when using a GCN for traffic speed prediction, the conventional approach…

The time evolution of physical systems is described by differential equations, which depend on abstract quantities like energy and force. Traditionally, these quantities are derived as functionals based on observables such as positions and…

We consider a general interacting particle system with interactions on a random graph, and study the large population limit of this system. When the sequence of underlying graphs converges to a graphon, we show convergence of the…