相关论文: Gradient-enhanced deep neural network approximatio…

Regression with non-Euclidean responses -- e.g., probability distributions, networks, symmetric positive-definite matrices, and compositions -- has become increasingly important in modern applications. In this paper, we propose deep…

Large-scale numerical simulations are used across many scientific disciplines to facilitate experimental development and provide insights into underlying physical processes, but they come with a significant computational cost. Deep neural…

Deep Neural Networks (DNNs) are very popular because of their high performance in various cognitive tasks in Machine Learning (ML). Recent advancements in DNNs have brought beyond human accuracy in many tasks, but at the cost of high…

Deep Neural Networks (DNNs) are a promising tool for Global Navigation Satellite System (GNSS) positioning in the presence of multipath and non-line-of-sight errors, owing to their ability to model complex errors using data. However,…

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem…

In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in…

Uncertainty quantification is an important and challenging problem in deep learning. Previous methods rely on dropout layers which are not present in modern deep architectures or batch normalization which is sensitive to batch sizes. In…

This paper investigates the universal approximation capabilities of Hamiltonian Deep Neural Networks (HDNNs) that arise from the discretization of Hamiltonian Neural Ordinary Differential Equations. Recently, it has been shown that HDNNs…

We propose a novel method to explain trained deep neural networks (DNNs), by distilling them into surrogate models using unsupervised clustering. Our method can be applied flexibly to any subset of layers of a DNN architecture and can…

We apply supervised deep neural networks (DNNs) for pricing and calibration of both vanilla and exotic options under both diffusion and pure jump processes with and without stochastic volatility. We train our neural network models under…

In recent years, deep neural networks (DNNs) have known an important rise in popularity. However, although they are state-of-the-art in many machine learning challenges, they still suffer from several limitations. For example, DNNs require…

This work investigates the impact of data augmentation on confidence calibration and uncertainty estimation in Named Entity Recognition (NER) tasks. For the future advance of NER in safety-critical fields like healthcare and finance, it is…

When employing deep neural networks (DNNs) for semantic segmentation in safety-critical applications like automotive perception or medical imaging, it is important to estimate their performance at runtime, e.g. via uncertainty estimates or…

We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural…

We propose a novel deep neural network (DNN) based approximation architecture to learn estimates of measurements. We detail an algorithm that enables training of the DNN. The DNN estimator only uses measurements, if and when they are…

Deep Neural Networks (DNN) are increasingly used as components of larger software systems that need to process complex data, such as images, written texts, audio/video signals. DNN predictions cannot be assumed to be always correct for…

We propose a simple methodology to approximate functions with given asymptotic behavior by specifically constructed terms and an unconstrained deep neural network (DNN). The methodology we describe extends to various asymptotic behaviors…

K-nearest neighbors (KNN) is one of the earliest and most established algorithms in machine learning. For regression tasks, KNN averages the targets within a neighborhood which poses a number of challenges: the neighborhood definition is…

In this paper, neural network approximation methods are developed for elliptic partial differential equations with multi-frequency solutions. Neural network work approximation methods have advantages over classical approaches in that they…

For Deep Neural Networks (DNNs) to become useful in safety-critical applications, such as self-driving cars and disease diagnosis, they must be stable to perturbations in input and model parameters. Characterizing the sensitivity of a DNN…