Related papers: Transport Analysis of Infinitely Deep Neural Netwo…

The feature map obtained from the denoising autoencoder (DAE) is investigated by determining transportation dynamics of the DAE, which is a cornerstone for deep learning. Despite the rapid development in its application, deep neural…

We present a resilient deep neural network (DNN) framework for decentralized transport and coverage using uncrewed aerial systems (UAS) operating in $\mathbb{R}^n$. The proposed DNN-based mass-transport architecture constructs a layered…

Recent studies revealed the mathematical connection of deep neural network (DNN) and dynamic system. However, the fundamental principle of DNN has not been fully characterized with dynamic system in terms of optimization and generalization.…

We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN…

In the last decade, we have witnessed the introduction of several novel deep neural network (DNN) architectures exhibiting ever-increasing performance across diverse tasks. Explaining the upward trend of their performance, however, remains…

Deep Neural Networks (DNNs) excel at many tasks, often rivaling or surpassing human performance. Yet their internal processes remain elusive, frequently described as "black boxes." While performance can be refined experimentally, achieving…

Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge due to the sparsity of measurements, the heterogeneity of porous media, and the high computational cost of forward…

Among many unsolved puzzles in theories of Deep Neural Networks (DNNs), there are three most fundamental challenges that highly demand solutions, namely, expressibility, optimisability, and generalisability. Although there have been…

The fast and accurate prediction of unsteady flow becomes a serious challenge in fluid dynamics, due to the high-dimensional and nonlinear characteristics. A novel hybrid deep neural network (DNN) architecture was designed to capture the…

This paper presents a comprehensive control-theoretic analysis of water distribution network (WDN) hydraulics. Starting from a general nonlinear differential algebraic equation (DAE) model of WDNs with arbitrary topology and network…

Structural and topological information play a key role in modeling flow and transport through fractured rock in the subsurface. Discrete fracture network (DFN) computational suites such as dfnWorks are designed to simulate flow and…

The generative learning phase of Autoencoder (AE) and its successor Denosing Autoencoder (DAE) enhances the flexibility of data stream method in exploiting unlabelled samples. Nonetheless, the feasibility of DAE for data stream analytic…

Accelerating deep neural networks (DNNs) has been attracting increasing attention as it can benefit a wide range of applications, e.g., enabling mobile systems with limited computing resources to own powerful visual recognition ability. A…

This paper presents a dedicated Deep Neural Network (DNN) architecture that reconstructs space-time traffic speeds on freeways given sparse data. The DNN is constructed in such a way, that it learns heterogeneous congestion patterns using a…

Deep neural networks (DNNs) have recently achieved impressive success across a wide range of real-world vision and language processing tasks, spanning from image classification to many other downstream vision tasks, such as object…

While Graph Neural Networks (GNNs) are powerful models for learning representations on graphs, most state-of-the-art models do not have significant accuracy gain beyond two to three layers. Deep GNNs fundamentally need to address: 1).…

Deep neural networks are being increasingly used for short-term traffic flow prediction, which can be generally categorized as convolutional (CNNs) or graph neural networks (GNNs). CNNs are preferable for region-wise traffic prediction by…

In modern transportation systems, an enormous amount of traffic data is generated every day. This has led to rapid progress in short-term traffic prediction (STTP), in which deep learning methods have recently been applied. In traffic…

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications.…

Neural ordinary differential equations (NODEs) treat computation of intermediate feature vectors as trajectories of ordinary differential equation parameterized by a neural network. In this paper, we propose a novel model, delay…