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Inspired by the tremendous success of deep Convolutional Neural Networks as generic feature extractors for images, we propose TimeNet: a deep recurrent neural network (RNN) trained on diverse time series in an unsupervised manner using…

Heterogeneous graph learning aims to capture complex relationships and diverse relational semantics among entities in a heterogeneous graph to obtain meaningful representations for nodes and edges. Recent advancements in heterogeneous graph…

We design scalable neural networks adapted to translational symmetries in dynamical systems, capable of inferring untrained high-dimensional dynamics for different system sizes. We train these networks to predict the dynamics of…

Previous work has shown the effectiveness of random walk hitting times as a measure of dissimilarity in a variety of graph-based learning problems such as collaborative filtering, query suggestion or finding paraphrases. However,…

We present a practical algorithm based on symplectic splitting methods to integrate numerically in time the Schr\"odinger equation. When discretized in space, the Schr\"odinger equation can be recast as a classical Hamiltonian system…

There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in…

Hamiltonian dynamics describe a wide range of physical systems. As such, data-driven simulations of Hamiltonian systems are important for many scientific and engineering problems. In this work, we propose kernel-based methods for…

Spatial-temporal graph modeling is an important task to analyze the spatial relations and temporal trends of components in a system. Existing approaches mostly capture the spatial dependency on a fixed graph structure, assuming that the…

Federated learning (FL) algorithms usually sample a fraction of clients in each round (partial participation) when the number of participants is large and the server's communication bandwidth is limited. Recent works on the convergence…

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…

In this note, we propose a symplectic algorithm for the stable manifolds of the Hamilton-Jacobi equations combined with an iterative procedure in [Sakamoto-van~der Schaft, IEEE Transactions on Automatic Control, 2008]. Our algorithm…

In graph signal processing, learning the weighted connections between nodes from a set of sample signals is a fundamental task when the underlying relationships are not known a priori. This task is typically addressed by finding a graph…

We train a small message-passing graph neural network to predict Hamiltonian cycles on Erd\H{o}s-R\'enyi random graphs in a critical regime. It outperforms existing hand-crafted heuristics after about 2.5 hours of training on a single GPU.…

We present a morphological-symmetry-equivariant heterogeneous graph neural network, namely MS-HGNN, for robotic dynamics learning, that integrates robotic kinematic structures and morphological symmetries into a single graph network. These…

In this paper we developed a hierarchical network model, called Hierarchical Prediction Network (HPNet), to understand how spatiotemporal memories might be learned and encoded in the recurrent circuits in the visual cortical hierarchy for…

Numerical methods for developing port-Hamiltonian representations of general linear time-invariant systems are studied. The approach extends previous port-Hamiltonian characterizations to include the general non-minimal case and the case…

Long-term stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the symplectic map representing the…

Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…

Spatio-temporal machine learning is critically needed for a variety of societal applications, such as agricultural monitoring, hydrological forecast, and traffic management. These applications greatly rely on regional features that…

We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach considers the Hamilton-Jacobi form of the equations of…