Related papers: Graph Neural Stochastic Differential Equations for…

Graph Neural Networks (GNNs) often struggle in preserving high-frequency components of nodal signals when dealing with directed graphs. Such components are crucial for modeling flow dynamics, without which a traditional GNN tends to treat a…

Brownian Dynamics simulations are an important tool for modeling the dynamics of soft matter. However, accurate and rapid computations of the hydrodynamic interactions between suspended, microscopic components in a soft material is a…

Learning representations for graphs plays a critical role in a wide spectrum of downstream applications. In this paper, we summarize the limitations of the prior works in three folds: representation space, modeling dynamics and modeling…

We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…

Graph Neural Networks (GNNs) have made significant advances on several fundamental inference tasks. As a result, there is a surge of interest in using these models for making potentially important decisions in high-regret applications.…

Driven by the outstanding performance of neural networks in the structured Euclidean domain, recent years have seen a surge of interest in developing neural networks for graphs and data supported on graphs. The graph is leveraged at each…

Traffic flow forecasting is a critical spatio-temporal data mining task with wide-ranging applications in intelligent route planning and dynamic traffic management. Recent advancements in deep learning, particularly through Graph Neural…

Transport phenomena in spatially periodic systems far from thermal equilibrium are considered. The main emphasize is put on directed transport in so-called Brownian motors (ratchets), i.e. a dissipative dynamics in the presence of thermal…

While physics conveys knowledge of nature built from an interplay between observations and theory, it has been considered less importantly in deep neural networks. Especially, there are few works leveraging physics behaviors when the…

This work investigates the problem of estimating the weight matrices of a stable time-invariant linear dynamical system from a single sequence of noisy measurements. We show that if the unknown weight matrices describing the system are in…

Observations from dynamical systems often exhibit irregularities, such as censoring, where values are recorded only if they fall within a certain range. Censoring is ubiquitous in practice, due to saturating sensors, limit-of-detection…

Graph convolutional neural networks (GCNNs) have received much attention recently, owing to their capability in handling graph-structured data. Among the existing GCNNs, many methods can be viewed as instances of a neural message passing…

Graph neural networks have been useful in machine learning on graph-structured data, particularly for node classification and some types of graph classification tasks. However, they have had limited use in representing patterning of signals…

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…

Deep learning has been widely used within learning algorithms for robotics. One disadvantage of deep networks is that these networks are black-box representations. Therefore, the learned approximations ignore the existing knowledge of…

Graph neural networks (GNNs) have attracted much attention due to their ability to leverage the intrinsic geometries of the underlying data. Although many different types of GNN models have been developed, with many benchmarking procedures…

Ocean current, fluid mechanics, and many other spatio-temporal physical dynamical systems are essential components of the universe. One key characteristic of such systems is that certain physics laws -- represented as ordinary/partial…

Graph Neural Networks (GNNs) have shown to be powerful tools for graph analytics. The key idea is to recursively propagate and aggregate information along edges of the given graph. Despite their success, however, the existing GNNs are…

Deep neural networks have revolutionized machine learning, yet their training dynamics remain theoretically unclear-we develop a continuous-time, matrix-valued stochastic differential equation (SDE) framework that rigorously connects the…

Neural networks (NN)-based learning algorithms are strongly affected by the choices of initialization and data distribution. Different optimization strategies have been proposed for improving the learning trajectory and finding a better…