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Convergence rates of training deep neural networks via alternating minimization methods
Training deep neural networks (DNNs) is an important and challenging optimization problem in machine learning due to its non-convexity and...
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Learning Velocity Model for Complex Media with Deep Convolutional Neural Networks
AbstractThe paper considers the problem of velocity model acquisition for a complex media based on boundary measurements. The acoustic model is used...
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Deep limits of residual neural networks
Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are...
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Specialized Pre-Training of Neural Networks on Synthetic Data for Improving Paraphrase Generation
Paraphrase generation is a fundamental problem in natural language processing. Due to the significant success of transfer learning, the “pre-training...
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On the approximation of rough functions with deep neural networks
The essentially non-oscillatory (ENO) procedure and its variant, the ENO-SR procedure, are very efficient algorithms for interpolating...
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Learning spiking neuronal networks with artificial neural networks: neural oscillations
First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and...
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Stochastic perturbation of subgradient algorithm for nonconvex deep neural networks
Choosing a learning rate is a necessary part of any subgradient method optimization. With deeper models such as convolutional neural networks of...
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Limitations of neural network training due to numerical instability of backpropagation
We study the training of deep neural networks by gradient descent where floating-point arithmetic is used to compute the gradients. In this framework...
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Approximation of functions from Korobov spaces by deep convolutional neural networks
The efficiency of deep convolutional neural networks (DCNNs) has been demonstrated empirically in many practical applications. In this paper, we...
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Loss Function Dynamics and Landscape for Deep Neural Networks Trained with Quadratic Loss
AbstractKnowledge of the loss landscape geometry makes it possible to successfully explain the behavior of neural networks, the dynamics of their...
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Discovery of Governing Equations with Recursive Deep Neural Networks
Model discovery based on existing data has been one of the major focuses of mathematical modelers for decades. Despite tremendous achievements in...
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Improved Architectures and Training Algorithms for Deep Operator Networks
Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under...
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Solving Parametric Partial Differential Equations with Deep Rectified Quadratic Unit Neural Networks
Implementing deep neural networks for learning the solution maps of parametric partial differential equations (PDEs) turns out to be more efficient...
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Improved Deep Neural Networks with Domain Decomposition in Solving Partial Differential Equations
An improved neural networks method based on domain decomposition is proposed to solve partial differential equations, which is an extension of the...
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On the regularized risk of distributionally robust learning over deep neural networks
In this paper, we explore the relation between distributionally robust learning and different forms of regularization to enforce robustness of deep...
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Using Deep Neural Networks for Detecting Spurious Oscillations in Discontinuous Galerkin Solutions of Convection-Dominated Convection–Diffusion Equations
Standard discontinuous Galerkin finite element solutions to convection-dominated convection–diffusion equations usually possess sharp layers but also...
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Mesh-Informed Neural Networks for Operator Learning in Finite Element Spaces
Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the...
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Multioutput FOSLS Deep Neural Network for Solving Allen–Cahn Equation
AbstractThis paper utilizes feed-forward neural networks to approximate solutions and their scaled gradients of the Allen–Cahn equation. A...
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How does momentum benefit deep neural networks architecture design? A few case studies
We present and review an algorithmic and theoretical framework for improving neural network architecture design via momentum. As case studies, we...
