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Many aspects of graphs have been studied in depth. However, forecasting the structure of a graph at future time steps incorporating unseen, new nodes and edges has not gained much attention. In this paper, we present such an approach. Using…

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…

Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with representative datasets. Recently, an augmented framework has been…

We introduce a class of neural controlled differential equation inspired by quantum mechanics. Neural quantum controlled differential equations (NQDEs) model the dynamics by analogue of the Schr\"{o}dinger equation. Specifically, the hidden…

Current graph neural networks (GNNs) that tackle node classification on graphs tend to only focus on nodewise scores and are solely evaluated by nodewise metrics. This limits uncertainty estimation on graphs since nodewise marginals do not…

This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…

Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…

A data-driven framework is proposed towards the end of predictive modeling of complex spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural networks are used, with the goal of predicting the future state…

The integration and transmission of information in the brain are dependent on the interplay between structural and dynamical properties. Implicit in any pursuit aimed at understanding neural dynamics from appropriate sets of mathematically…

Embodied AI agents that search for objects in large environments such as households often need to make efficient decisions by predicting object locations based on partial information. We pose this as a new type of link prediction problem:…

A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…

This article investigates the effect of explicitly adding auxiliary algebraic trajectory information to neural networks for dynamical systems. We draw inspiration from the field of differential-algebraic equations and differential equations…

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…

Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…

Data-driven surrogate modeling has emerged as a promising approach for reducing computational expenses of multiscale simulations. Recurrent Neural Network (RNN) is a common choice for modeling of path-dependent behavior. However, previous…

Solving large complex partial differential equations (PDEs), such as those that arise in computational fluid dynamics (CFD), is a computationally expensive process. This has motivated the use of deep learning approaches to approximate the…

Graph Neural Networks achieve remarkable results on problems with structured data but come as black-box predictors. Transferring existing explanation techniques, such as occlusion, fails as even removing a single node or edge can lead to…

Graph Neural Networks have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult, especially under distributional shifts. Unlike traditional uncertainty…

Traffic forecasting is important in intelligent transportation systems of webs and beneficial to traffic safety, yet is very challenging because of the complex and dynamic spatio-temporal dependencies in real-world traffic systems. Prior…