Related papers: Deep Neural Network-Based High-Precision Identific…

Neural networks are known to be effective function approximators. Recently, deep neural networks have proven to be very effective in pattern recognition, classification tasks and human-level control to model highly nonlinear realworld…

We consider non-spherical rigid body particles in an incompressible fluid in the regime where the particles are too large to assume that they are simply transported with the fluid without back-coupling and where the particles are also too…

Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by…

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

We present an algorithm which is designed to allow the efficient identification and preliminary dynamical analysis of thousands of structures and substructures in large N-body simulations. First we utilise a refined density gradient system…

Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…

The residual neural network (ResNet) is a popular deep network architecture which has the ability to obtain high-accuracy results on several image processing problems. In order to analyze the behavior and structure of ResNet, recent work…

Deep neural networks have shown great achievements in solving complex problems. However, there are fundamental problems that limit their real world applications. Lack of measurable criteria for estimating uncertainty in the network outputs…

While deep learning models and techniques have achieved great empirical success, our understanding of the source of success in many aspects remains very limited. In an attempt to bridge the gap, we investigate the decision boundary of a…

With the increasing application of deep learning in mission-critical systems, there is a growing need to obtain formal guarantees about the behaviors of neural networks. Indeed, many approaches for verifying neural networks have been…

When parameters are weakly identified, bounds on the parameters may provide a valuable source of information. Existing weak identification estimation and inference results are unable to combine weak identification with bounds. Within a…

In this paper, we perform deep neural networks for learning $\psi$-weakly dependent processes. Such weak-dependence property includes a class of weak dependence conditions such as mixing, association,$\cdots$ and the setting considered here…

We consider a deep structured linear network under sparsity constraints. We study sharp conditions guaranteeing the stability of the optimal parameters defining the network. More precisely, we provide sharp conditions on the network…

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…

We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is…

Physics-informed deep learning is a popular trend in the modeling and control of dynamical systems. This paper presents a novel method for rapid online identification of vehicle cornering stiffness coefficient, a crucial parameter in…

MOTIVATION: Proteins fold into complex structures that are crucial for their biological functions. Experimental determination of protein structures is costly and therefore limited to a small fraction of all known proteins. Hence, different…

Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…

A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary…

In the study of high-dimensional data, it is often assumed that the data set possesses an underlying lower-dimensional structure. A practical model for this structure is an embedded compact manifold with boundary. Since the underlying…