Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

L Lu, P Jin, G Pang, Z Zhang… - Nature machine …, 2021 - nature.com
It is widely known that neural networks (NNs) are universal approximators of continuous
functions. However, a less known but powerful result is that a NN with a single hidden layer …

Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

L Lu, P Jin, GE Karniadakis - arXiv preprint arXiv:1910.03193, 2019 - arxiv.org
While it is widely known that neural networks are universal approximators of continuous
functions, a less known and perhaps more powerful result is that a neural network with a …

Backpropagation algorithms and reservoir computing in recurrent neural networks for the forecasting of complex spatiotemporal dynamics

PR Vlachas, J Pathak, BR Hunt, TP Sapsis, M Girvan… - Neural Networks, 2020 - Elsevier
We examine the efficiency of Recurrent Neural Networks in forecasting the spatiotemporal
dynamics of high dimensional and reduced order complex systems using Reservoir …

Photonic extreme learning machine by free-space optical propagation

D Pierangeli, G Marcucci, C Conti - Photonics Research, 2021 - opg.optica.org
Photonic brain-inspired platforms are emerging as novel analog computing devices,
enabling fast and energy-efficient operations for machine learning. These artificial neural …

Hamiltonian neural networks for solving equations of motion

M Mattheakis, D Sondak, AS Dogra, P Protopapas - Physical Review E, 2022 - APS
There has been a wave of interest in applying machine learning to study dynamical systems.
We present a Hamiltonian neural network that solves the differential equations that govern …

Physical symmetries embedded in neural networks

M Mattheakis, P Protopapas, D Sondak… - arXiv preprint arXiv …, 2019 - arxiv.org
Neural networks are a central technique in machine learning. Recent years have seen a
wave of interest in applying neural networks to physical systems for which the governing …

Machine learning link inference of noisy delay-coupled networks with optoelectronic experimental tests

A Banerjee, JD Hart, R Roy, E Ott - Physical Review X, 2021 - APS
We devise a machine learning technique to solve the general problem of inferring network
links that have time delays using only time series data of the network nodal states. This task …

Detection of abnormal left ventricular geometry in patients without cardiovascular disease through machine learning: an ECG‐based approach

E Angelaki, ME Marketou, GD Barmparis… - The Journal of …, 2021 - Wiley Online Library
Cardiac remodeling is recognized as an important aspect of cardiovascular disease (CVD)
progression. Machine learning (ML) techniques were applied to basic clinical parameters …

Identification of chimera using machine learning

MA Ganaie, S Ghosh, N Mendola, M Tanveer… - … Journal of Nonlinear …, 2020 - pubs.aip.org
Chimera state refers to the coexistence of coherent and non-coherent phases in identically
coupled dynamical units found in various complex dynamical systems. Identification of …

Unsupervised reservoir computing for solving ordinary differential equations

M Mattheakis, H Joy, P Protopapas - arXiv preprint arXiv:2108.11417, 2021 - arxiv.org
There is a wave of interest in using unsupervised neural networks for solving differential
equations. The existing methods are based on feed-forward networks,{while} recurrent …