Related papers: Physics-Driven Regularization of Deep Neural Netwo…

Despite the efficacy on a variety of computer vision tasks, deep neural networks (DNNs) are vulnerable to adversarial attacks, limiting their applications in security-critical systems. Recent works have shown the possibility of generating…

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…

In various scientific and engineering applications, there is typically an approximate model of the underlying complex system, even though it contains both aleatoric and epistemic uncertainties. In this paper, we present a principled method…

We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in…

Machine learning methods have found novel application areas in various disciplines as they offer low-computational cost solutions to complex problems. Recently, metasurface design has joined among these applications, and neural networks…

The lack of mathematical tractability of Deep Neural Networks (DNNs) has hindered progress towards having a unified convergence analysis of training algorithms, in the general setting. We propose a unified optimization framework for…

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…

Purely data-driven deep neural networks (DNNs) applied to physical engineering systems can infer relations that violate physics laws, thus leading to unexpected consequences. To address this challenge, we propose a physics-model-based DNN…

Data-driven constitutive modeling with neural networks has received increased interest in recent years due to its ability to easily incorporate physical and mechanistic constraints and to overcome the challenging and time-consuming task of…

This survey article is concerned with the application of lattice rules to Deep Neural Networks (DNNs), lattice rules being a family of quasi-Monte Carlo methods. They have demonstrated effectiveness in various contexts for high-dimensional…

The paper discusses regularization properties of artificial data for deep learning. Artificial datasets allow to train neural networks in the case of a real data shortage. It is demonstrated that the artificial data generation process,…

Differential equations are used to model and predict the behaviour of complex systems in a wide range of fields, and the ability to solve them is an important asset for understanding and predicting the behaviour of these systems.…

Recently, deep unfolding methods that guide the design of deep neural networks (DNNs) through iterative algorithms have received increasing attention in the field of inverse problems. Unlike general end-to-end DNNs, unfolding methods have…

The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties…

Learning models for dynamical systems in continuous time is significant for understanding complex phenomena and making accurate predictions. This study presents a novel approach utilizing differential neural networks (DNNs) to model…

Despite their impressive performance, Deep Neural Networks (DNNs) typically underperform Gradient Boosting Trees (GBTs) on many tabular-dataset learning tasks. We propose that applying a different regularization coefficient to each weight…

Deep neural network (DNN)-based adaptive controllers can be used to compensate for unstructured uncertainties in nonlinear dynamic systems. However, DNNs are also very susceptible to overfitting and co-adaptation. Dropout regularization is…

In this paper we consider Deep Neural Networks (DNNs) with a smooth activation function as surrogates for high-dimensional functions that are somewhat smooth but costly to evaluate. We consider the standard (non-periodic) DNNs as well as…

We propose in this work the gradient-enhanced deep neural networks (DNNs) approach for function approximations and uncertainty quantification. More precisely, the proposed approach adopts both the function evaluations and the associated…

Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long time prediction of the evolution of the unknown system. Training a DNN with low…