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When neural networks (NNs) are used as a type of nonlinear parametric representation to solve partial differential equations (PDEs), they often display frequency-dependent learning dynamics that can differ from those seen in direct function…

More competent learning models are demanded for data processing due to increasingly greater amounts of data available in applications. Data that we encounter often have certain embedded sparsity structures. That is, if they are represented…

Deep neural networks (DNNs) have achieved great success in the area of computer vision. The disparity estimation problem tends to be addressed by DNNs which achieve much better prediction accuracy in stereo matching than traditional…

Neural operators provide a framework for learning solution operators of partial differential equations (PDEs), enabling efficient surrogate modeling for complex systems. While universal approximation results are now well understood,…

Deep neural networks (DNNs) are state-of-the-art solutions for many machine learning applications, and have been widely used on mobile devices. Running DNNs on resource-constrained mobile devices often requires the help from edge servers…

Deep Neural Networks (DNNs) are computationally and memory intensive, which makes their hardware implementation a challenging task especially for resource constrained devices such as IoT nodes. To address this challenge, this paper…

Popular deep neural networks (DNNs) spend the majority of their execution time computing convolutions. The Winograd family of algorithms can greatly reduce the number of arithmetic operations required and is present in many DNN software…

We propose Impatient Deep Neural Networks (DNNs) which deal with dynamic time budgets during application. They allow for individual budgets given a priori for each test example and for anytime prediction, i.e., a possible interruption at…

Data-driven machine learning approaches are being increasingly used to solve partial differential equations (PDEs). They have shown particularly striking successes when training an operator, which takes as input a PDE in some family, and…

This paper establishes statistical properties of deep neural network (DNN) estimators under dependent data. Two general results for nonparametric sieve estimators directly applicable to DNN estimators are given. The first establishes rates…

Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric…

The prediction accuracy of the deep neural networks (DNNs) after deployment at the edge can suffer with time due to shifts in the distribution of the new data. To improve robustness of DNNs, they must be able to update themselves to enhance…

In time-varying fading channels, channel coefficients are estimated using pilot symbols that are transmitted every coherence interval. For channels with high Doppler spread, the rapid channel variations over time will require considerable…

We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…

Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…

Deep Neural Networks (DNN) achieve human level performance in many image analytics tasks but DNNs are mostly deployed to GPU platforms that consume a considerable amount of power. New hardware platforms using lower precision arithmetic…

Deep neural networks (DNNs) play an important role in machine learning due to its outstanding performance compared to other alternatives. However, DNNs are not suitable for safety-critical applications since DNNs can be easily fooled by…

Neural operators are a type of deep architecture that learns to solve (i.e. learns the nonlinear solution operator of) partial differential equations (PDEs). The current state of the art for these models does not provide explicit…

Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…

Deep learning has been extended to a number of new domains with critical success, though some traditional orienteering problems such as the Travelling Salesman Problem (TSP) and its variants are not commonly solved using such techniques.…