Related papers: Hierarchical Deep Learning of Multiscale Different…

This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…

Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. Local time-stepping methods overcome that bottleneck by using smaller time-steps…

The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of…

While the depth of modern Convolutional Neural Networks (CNNs) surpasses that of the pioneering networks with a significant margin, the traditional way of appending supervision only over the final classifier and progressively propagating…

Accurate time series prediction is challenging due to the inherent nonlinearity and sensitivity to initial conditions. We propose a novel approach that enhances neural network predictions through differential learning, which involves…

Deep neural networks (DNNs) have recently emerged as effective tools for approximating solution operators of partial differential equations (PDEs) including evolutionary problems. Classical numerical solvers for such PDEs often face…

Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of…

While Hamiltonian mechanics provides a powerful inductive bias for neural networks modeling dynamical systems, Hamiltonian Neural Networks and their variants often fail to capture complex temporal dynamics spanning multiple timescales. This…

The Hierarchical Heavy Hitters problem extends the notion of frequent items to data arranged in a hierarchy. This problem has applications to network traffic monitoring, anomaly detection, and DDoS detection. We present a new streaming…

Time series analysis has gained significant attention due to its critical applications in diverse fields such as healthcare, finance, and sensor networks. The complexity and non-stationarity of time series make it challenging to capture the…

We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution…

Spectral methods of moments provide a powerful tool for learning the parameters of latent variable models. Despite their theoretical appeal, the applicability of these methods to real data is still limited due to a lack of robustness to…

Time-series is ubiquitous across applications, such as transportation, finance and healthcare. Time-series is often influenced by external factors, especially in the form of asynchronous events, making forecasting difficult. However,…

With the rise of deep learning technology in practical applications, Convolutional Neural Networks (CNNs) have been able to assist humans in solving many real-world problems. To enhance the performance of CNNs, numerous network…

Modern deep learning enabled artificial neural networks, such as Deep Neural Network (DNN) and Convolutional Neural Network (CNN), have achieved a series of breaking records on a broad spectrum of recognition applications. However, the…

Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step…

Modeling brain dynamics to better understand and control complex behaviors underlying various cognitive brain functions are of interests to engineers, mathematicians, and physicists from the last several decades. With a motivation of…

We present a hierarchical approach for enhancing the robustness of numerical solvers for modelling radiative MHD flows in multi-dimensions. This approach is based on clustering the entries of the global Jacobian in a hierarchical manner…

Multivariate time series is prevalent in many scientific and industrial domains. Modeling multivariate signals is challenging due to their long-range temporal dependencies and intricate interactions--both direct and indirect. To confront…

Deep neural network-based time series prediction models have recently demonstrated superior capabilities in capturing complex temporal dependencies. However, it is challenging for these models to account for uncertainty associated with…