Related papers: Neural network-enhanced integrators for simulating…

Recurrent Neural Networks (RNNs) are a class of machine learning algorithms used for applications with time-series and sequential data. Recently, there has been a strong interest in executing RNNs on embedded devices. However, difficulties…

Quantum computers hold great promise for accelerating computationally challenging algorithms on noisy intermediate-scale quantum (NISQ) devices in the upcoming years. Much attention of the current research is directed to algorithmic…

Two neural-network-based numerical schemes are proposed to solve the classical obstacle problems. The schemes are based on the universal approximation property of neural networks, and the cost functions are taken as the energy minimization…

As a method of universal approximation deep neural networks (DNNs) are capable of finding approximate solutions to problems posed with little more constraints than a suitably-posed mathematical system and an objective function.…

Quantum computing has the potential to revolutionize multiple fields by solving complex problems that can not be solved in reasonable time with current classical computers. Nevertheless, the development of quantum computers is still in its…

Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…

Deep learning research over the past years has shown that by increasing the scope or difficulty of the learning problem over time, increasingly complex learning problems can be addressed. We study incremental learning in the context of…

Neural networks have demonstrated significant accuracy across various domains, yet their vulnerability to subtle input alterations remains a persistent challenge. Conventional methods like data augmentation, while effective to some extent,…

Convolution-type integral equations commonly occur in signal processing and image processing. Discretizing these equations yields large and ill-conditioned linear systems. While the classic multigrid method is effective for solving linear…

Isospectral Runge-Kutta methods are well-suited for the numerical solution of isospectral systems such as the rigid body and the Toda lattice. More recently, these integrators have been applied to geophysical fluid models, where their…

The large-scale simulation of dynamical systems is critical in numerous scientific and engineering disciplines. However, traditional numerical solvers are limited by the choice of step sizes when estimating integration, resulting in a…

Although quantum machine learning has shown great promise, the practical application of quantum computers remains constrained in the noisy intermediate-scale quantum era. To take advantage of quantum machine learning, we investigate the…

Simulating the evolution of the gravitational N-body problem becomes extremely computationally expensive as N increases since the problem complexity scales quadratically with the number of bodies. We study the use of Artificial Neural…

While quantum architectures are still under development, when available, they will only be able to process quantum data when machine learning algorithms can only process numerical data. Therefore, in the issues of classification or…

Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…

Neural networks offer a computationally efficient approximation of model predictive control, but they lack guarantees on the resulting controlled system's properties. Formal certification of neural networks is crucial for ensuring safety,…

This paper proposes a quantum-classical algorithm to evaluate and select classical artificial neural networks architectures. The proposed algorithm is based on a probabilistic quantum memory and the possibility to train artificial neural…

Convolutional Neural Networks (CNN) are used mainly to treat problems with many images characteristic of Deep Learning. In this work, we propose a hybrid image classification model to take advantage of quantum and classical computing. The…

Different possible sources are discussed for enhancement of the calculation time when solving ordinary differential equations systems to forecast space objects' motion. This paper presents an approach for building an integrator of ordinary…

We introduce a general and simple structural design called Multiplicative Integration (MI) to improve recurrent neural networks (RNNs). MI changes the way in which information from difference sources flows and is integrated in the…