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Data assimilation (DA) integrates observational information with model predictions to improve state estimation in complex systems. While filtering provides the basis for online forecasts by using only past and present observations, it can…

Koopman Operator Theory has opened the doors to data-driven learning of globally linear representations of complex nonlinear systems. However, current methodologies for Koopman Operator discovery struggle with uncertainty quantification and…

The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. While recent deep learning approaches have been useful in…

Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems which are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions…

Balancing computational efficiency with robust predictive performance is crucial in supervised learning, especially for critical applications. Standard deep learning models, while accurate and scalable, often lack probabilistic features…

Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is…

This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive…

Convolutional neural networks (CNNs) are deep learning frameworks which are well-known for their notable performance in classification tasks. Hence, many skeleton-based action recognition and segmentation (SBARS) algorithms benefit from…

Graph clustering, a classical task in graph learning, involves partitioning the nodes of a graph into distinct clusters. This task has applications in various real-world scenarios, such as anomaly detection, social network analysis, and…

In this paper we propose a novel Bayesian solution for nonlinear regression in complex fields. Previous solutions for kernels methods usually assume a complexification approach, where the real-valued kernel is replaced by a complex-valued…

We show how to treat systematic uncertainties using Bayesian deep networks for regression. First, we analyze how these networks separately trace statistical and systematic uncertainties on the momenta of boosted top quarks forming fat jets.…

We have developed a new data-driven paradigm for the rapid inference, modeling and simulation of the physics of transport phenomena by deep learning. Using conditional generative adversarial networks (cGAN), we train models for the direct…

Network structures in various backgrounds play important roles in social, technological, and biological systems. However, the observable network structures in real cases are often incomplete or unavailable due to measurement errors or…

In this paper, we generally formulate the dynamics prediction problem of various network systems (e.g., the prediction of mobility, traffic and topology) as the temporal link prediction task. Different from conventional techniques of…

Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…

Data assimilation (DA) plays a pivotal role in diverse applications, ranging from climate predictions and weather forecasts to trajectory planning for autonomous vehicles. A prime example is the widely used ensemble Kalman filter (EnKF),…

Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…

Neural networks in general, from MLPs and CNNs to attention-based Transformers, are constructed from layers of linear combinations followed by nonlinear operations such as ReLU, Sigmoid, or Softmax. Despite their strength, these…

The escalating complexity of network threats and the inherent class imbalance in traffic data present formidable challenges for modern Intrusion Detection Systems (IDS). While Graph Neural Networks (GNNs) excel in modeling topological…

In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…