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Convolutional Neural Networks (CNNs) have achieved significant breakthroughs in various fields. However, these advancements have led to a substantial increase in the complexity and size of these networks. This poses a challenge when…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
In this work we propose a novel approach to utilize convolutional neural networks for time series forecasting. The time direction of the sequential data with spatial dimensions $D=1,2$ is considered democratically as the input of a…
Convergence of a matrix decomposition technique, the multi-field singular value decomposition (MFSVD) which efficiently analyzes nonlinear correlations by simultaneously decomposing multiple fields, is investigated. Toward applications in…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
In health-pollution cohort studies, accurate predictions of pollutant concentrations at new locations are needed, since the locations of fixed monitoring sites and study participants are often spatially misaligned. For multi-pollution data,…
As industrial systems become more complex and monitoring sensors for everything from surveillance to our health become more ubiquitous, multivariate time series prediction is taking an important place in the smooth-running of our society. A…
Recent progress on deep learning relies heavily on the quality and efficiency of training algorithms. In this paper, we develop a fast training method motivated by the nonlinear Conjugate Gradient (CG) framework. We propose the Conjugate…
Complex-valued neural networks (CVNNs) are an emerging field of research in neural networks due to their potential representational properties for audio, image, and physiological signals. It is common in signal processing to transform…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…
This paper aims to accelerate the test-time computation of convolutional neural networks (CNNs), especially very deep CNNs that have substantially impacted the computer vision community. Unlike previous methods that are designed for…
Modeling and simulation of complex fluid flows with dynamics that span multiple spatio-temporal scales is a fundamental challenge in many scientific and engineering domains. Full-scale resolving simulations for systems such as highly…
We present a novel complex number formulation along with tight convex relaxations for the aircraft conflict resolution problem. Our approach combines both speed and heading control and provides global optimality guarantees despite…
Transformer models are increasingly used for solving Partial Differential Equations (PDEs). Several adaptations have been proposed, all of which suffer from the typical problems of Transformers, such as quadratic memory and time complexity.…
Spectroscopic redshift surveys are key tools to trace the large-scale structure (LSS) of the Universe and test the $\Lambda$CDM model. However, using redshifts as distance proxies introduces distortions in the 3D galaxy distribution. If…
Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…
There is an urgent need to build models to tackle Indoor Air Quality issue. Since the model should be accurate and fast, Reduced Order Modelling technique is used to reduce the dimensionality of the problem. The accuracy of the model, that…
In the recent years, field theory on non-commutative (NC) spaces has attracted a lot of attention. Most literature on this subject deals with perturbation theory, although the latter runs into grave problems beyond one loop. Here we present…
Molecular dynamics (MD) simulation is essential for various scientific domains but computationally expensive. Learning-based force fields have made significant progress in accelerating ab-initio MD simulation but are not fast enough for…
The recent development of artificial intelligence (AI) technology, especially the advance of deep neural network (DNN) technology, has revolutionized many fields. While DNN plays a central role in modern AI technology, it has been rarely…