Meshless physics-informed deep learning method for three-dimensional solid mechanics
type: Item
instance of: scholarly article
title: Meshless physics-informed deep learning method for three-dimensional solid mechanics
zbMATH Open document ID: 1548.74971
author: Diab W. Abueidda
author: Qiyue Lu
author: S. Koric
published in: International Journal for Numerical Methods in Engineering
publication date: 2024-06-12T00:00:00Z
Mathematics Subject Classification ID: 74S99
zbMATH DE Number: 7863835
zbMATH Keywords: computational mechanics
zbMATH Keywords: machine learning
zbMATH Keywords: meshfree method
zbMATH Keywords: neural networks
zbMATH Keywords: partial differential equations
zbMATH Keywords: physics-informed learning
MaRDI profile type: Publication
cites work: Isogeometric analysis: mathematical and implementational aspects, with applications
cites work: Nonlinear solid mechanics. Theoretical formulations and finite element solution methods
cites work: Q3410728
cites work: On the two-potential constitutive modeling of dielectric elastomers
cites work: Topology optimization of viscoelastic structures using a time-dependent adjoint method
cites work: Topology optimization of nonlinear elastic structures and compliant mechanisms
cites work: Fluid sensing using microcantilevers: from physics-based modeling to deep learning
cites work: Efficient mass and stiffness matrix assembly via weighted Gaussian quadrature rules for B-splines
cites work: Geometric deep learning for computational mechanics. I: Anisotropic hyperelasticity
cites work: Numerical implementation of a neural network based material model in finite element analysis
cites work: Neural algorithm for solving differential equations
cites work: Numerical solution for high order differential equations using a hybrid neural network-optimization method
cites work: Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
cites work: Machine learning in cardiovascular flows modeling: predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
cites work: Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
cites work: Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks
cites work: Solving high-dimensional partial differential equations using deep learning
cites work: Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
cites work: Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
cites work: The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
cites work: DGM: a deep learning algorithm for solving partial differential equations
cites work: An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications
cites work: A deep energy method for finite deformation hyperelasticity
cites work: On the limited memory BFGS method for large scale optimization
cites work: Explicit coupled thermo-mechanical finite element model of steel solidification
cites work: Approximation by superpositions of a sigmoidal function
cites work: Q4830009
cites work: Nonsmooth optimization via quasi-Newton methods
cites work: Parallel mesh partitioning based on space filling curves
DOI: 10.1002/NME.6828
description: scientific article; zbMATH DE number 7863835