Parametric deep energy approach for elasticity accounting for strain gradient effects

An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications

(2020) E. Samaniego et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

The neural particle method – An updated Lagrangian physics informed neural network for computational fluid dynamics

(2020) Henning Wessels et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Adaptive fourth-order phase field analysis using deep energy minimization

(2020) Somdatta Goswami et al.   THEORETICAL AND APPLIED FRACTURE MECHANICS

hp-VPINNs: Variational physics-informed neural networks with domain decomposition

(2020) Ehsan Kharazmi et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain

(2020) Han Gao et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A deep energy method for finite deformation hyperelasticity

(2019) Vien Minh Nguyen-Thanh et al.   EUROPEAN JOURNAL OF MECHANICS A-SOLIDS

Hidden physics models: Machine learning of nonlinear partial differential equations

(2018) Maziar Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

DGM: A deep learning algorithm for solving partial differential equations

(2018) Justin Sirignano et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A unified deep artificial neural network approach to partial differential equations in complex geometries

(2018) Jens Berg et al.   NEUROCOMPUTING

Solving high-dimensional partial differential equations using deep learning

(2018) Jiequn Han et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Deep-learning: investigating deep neural networks hyper-parameters and comparison of performance to shallow methods for modeling bioactivity data

(2017) Alexios Koutsoukas et al.   Journal of Cheminformatics

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

(2016) Steven L. Brunton et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Isogeometric analysis: An overview and computer implementation aspects

(2015) Vinh Phu Nguyen et al.   MATHEMATICS AND COMPUTERS IN SIMULATION

Meshless methods: A review and computer implementation aspects

(2008) Vinh Phu Nguyen et al.   MATHEMATICS AND COMPUTERS IN SIMULATION