Related papers: The Newton Scheme for Deep Learning

This paper introduces an innovative physics-informed deep learning framework for metamodeling of nonlinear structural systems with scarce data. The basic concept is to incorporate physics knowledge (e.g., laws of physics, scientific…

In the past decade, deep neural networks (DNNs) came to the fore as the leading machine learning algorithms for a variety of tasks. Their raise was founded on market needs and engineering craftsmanship, the latter based more on trial and…

Deep neural networks, albeit their great success on feature learning in various computer vision tasks, are usually considered as impractical for online visual tracking because they require very long training time and a large number of…

Deep Learning (DL) applications are being used to solve problems in critical domains (e.g., autonomous driving or medical diagnosis systems). Thus, developers need to debug their systems to ensure that the expected behavior is delivered.…

Deep neural networks (DNNs) are machine learning algorithms that have revolutionised computer vision due to their remarkable successes in tasks like object classification and segmentation. The success of DNNs as computer vision algorithms…

Neural machine learning methods, such as deep neural networks (DNN), have achieved remarkable success in a number of complex data processing tasks. These methods have arguably had their strongest impact on tasks such as image and audio…

System identification through learning approaches is emerging as a promising strategy for understanding and simulating dynamical systems, which nevertheless faces considerable difficulty when confronted with power systems modeled by…

Deep convolutional neural network (DCNN) based supervised learning is a widely practiced approach for large-scale image classification. However, retraining these large networks to accommodate new, previously unseen data demands high…

Neural network models can now recognise images, understand text, translate languages, and play many human games at human or superhuman levels. These systems are highly abstracted, but are inspired by biological brains and use only…

Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…

We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second…

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…

We study neural network training (NNT): optimizing a neural network's parameters to minimize the training loss over a given dataset. NNT has been studied extensively under theoretic lenses, mainly on two-layer networks with linear or ReLU…

We propose a tensor neural network ($t$-NN) framework that offers an exciting new paradigm for designing neural networks with multidimensional (tensor) data. Our network architecture is based on the $t$-product (Kilmer and Martin, 2011), an…

Convolutional Neural Network (CNN) has gained state-of-the-art results in many pattern recognition and computer vision tasks. However, most of the CNN structures are manually designed by experienced researchers. Therefore, auto- matically…

In the last decade, special purpose computing systems, such as Neuromorphic computing, have become very popular in the field of computer vision and machine learning for classification tasks. In 2015, IBM's released the TrueNorth…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…

Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal form, which significantly simplifies fast dynamics near slow…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…