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We propose a multi-step training method for designing generalized linear classifiers. First, an initial multi-class linear classifier is found through regression. Then validation error is minimized by pruning of unnecessary inputs.…
In certain practical engineering applications, there is an urgent need to perform repetitive solving of partial differential equations (PDEs) in a short period. This paper primarily considers three scenarios requiring extensive repetitive…
Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…
This paper proposes a novel deep subspace clustering approach which uses convolutional autoencoders to transform input images into new representations lying on a union of linear subspaces. The first contribution of our work is to insert…
Autoencoders have emerged as a useful framework for unsupervised learning of internal representations, and a wide variety of apparently conceptually disparate regularization techniques have been proposed to generate useful features. Here we…
Learning operators from data is central to scientific machine learning. While DeepONets are widely used for their ability to handle complex domains, they require fixed sensor numbers and locations, lack mechanisms for uncertainty…
We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient(PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on…
Constant envelope (CE) precoding design is of great interest for massive multiuser multi-input multi-output systems because it can significantly reduce hardware cost and power consumption. However, existing CE precoding algorithms are…
We propose a novel \textit{capsule} based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet)…
Recent researches show that machine learning has the potential to learn better heuristics than the one designed by human for solving combinatorial optimization problems. The deep neural network is used to characterize the input instance for…
Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…
Neural Operator Networks (ONets) represent a novel advancement in machine learning algorithms, offering a robust and generalizable alternative for approximating partial differential equations (PDEs) solutions. Unlike traditional Neural…
Deep neural networks perform well on classification tasks where data streams are i.i.d. and labeled data is abundant. Challenges emerge with non-stationary training data streams such as continual learning. One powerful approach that has…
Convolutional neural networks typically encode an input image into a series of intermediate features with decreasing resolutions. While this structure is suited to classification tasks, it does not perform well for tasks requiring…
Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of science and engineering, but their numerical solvers often…
Reconstructing high-fidelity fluid flow fields from sparse sensor measurements is vital for many science and engineering applications but remains challenging because of dimensional disparities between state and observational spaces. Due to…
Monocular depth estimation and defocus estimation are two fundamental tasks in computer vision. Most existing methods treat depth estimation and defocus estimation as two separate tasks, ignoring the strong connection between them. In this…
We introduce a new class of hybrid preconditioners for solving parametric linear systems of equations. The proposed preconditioners are constructed by hybridizing the deep operator network, namely DeepONet, with standard iterative methods.…
Deep neural networks are widely used for classification. These deep models often suffer from a lack of interpretability -- they are particularly difficult to understand because of their non-linear nature. As a result, neural networks are…
The interpretability of neural networks has recently received extensive attention. Previous prototype-based explainable networks involved prototype activation in both reasoning and interpretation processes, requiring specific explainable…