We present an approach for solving optimal boundary control problems of nonlinear optics
by using deep learning. For computing high resolution approximations of the solution to the …

In recent years, Deep Convolutional Neural Networks (DCNNs) have been shown to be
effective in low-level vision tasks such as image denoising. DCNN backpropagation is …

These lecture notes provide an overview of Neural Network architectures from a
mathematical point of view. Especially, Machine Learning with Neural Networks is seen as …

Recently, optimal time variable learning in deep neural networks was introduced in Antil et
al. In this manuscript we extend the concept by introducing a regularization term that directly …

The analysis and numerical discretization of a variety of problems related to
electromagnetism, neural network architectures motivated by fractional time derivatives, and …

Motivated by the residual type neural networks (ResNet), this paper studies optimal control
problems constrained by a non-smooth integral equation associated to a fractional …