Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems
From MaRDI portal
Publication:2679283
DOI10.1016/j.cma.2022.115027OpenAlexW4221152086WikidataQ114196817 ScholiaQ114196817MaRDI QIDQ2679283
Yue Yu, Enrui Zhang, Minglang Yin, George Em. Karniadakis
Publication date: 19 January 2023
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2203.00003
domain decompositionfinite element modelmachine learningconcurrent multiscale couplingneural operator
Artificial neural networks and deep learning (68T07) Finite element methods applied to problems in solid mechanics (74S05)
Related Items (13)
Multiscale modeling of inelastic materials with thermodynamics-based artificial neural networks (TANN) ⋮ Learning deep implicit Fourier neural operators (IFNOs) with applications to heterogeneous material modeling ⋮ Integrated finite element neural network (I-FENN) for non-local continuum damage mechanics ⋮ Phase-field DeepONet: physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionals ⋮ Fully probabilistic deep models for forward and inverse problems in parametric PDEs ⋮ Geometric learning for computational mechanics. III: Physics-constrained response surface of geometrically nonlinear shells ⋮ Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads ⋮ Reliable extrapolation of deep neural operators informed by physics or sparse observations ⋮ Neural integration for constitutive equations using small data ⋮ On the geometry transferability of the hybrid iterative numerical solver for differential equations ⋮ Deep neural operator for learning transient response of interpenetrating phase composites subject to dynamic loading ⋮ MetaNO: how to transfer your knowledge on learning hidden physics ⋮ A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Generalized multiscale finite element methods (GMsFEM)
- A bridging domain method for coupling continua with molecular dynamics
- A spectral element method for fluid dynamics: Laminar flow in a channel expansion
- The heterogeneous multiscale methods
- Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows
- Stability, instability, and error of the force-based quasicontinuum approximation
- A method of homogenization of elastic media
- An introduction to SPH
- An accelerated domain decomposition procedure based on Robin transmission conditions
- Smoothed particle hydrodynamics: Some recent improvements and applications
- Automated tuning for parameter identification and uncertainty quantification in multi-scale coronary simulations
- A machine learning approach for efficient uncertainty quantification using multiscale methods
- An hourglass control algorithm for Lagrangian smooth particle hydrodynamics
- Variational and momentum preservation aspects of smooth particle hydrodynamic formulations
- A partitioned coupling framework for peridynamics and classical theory: analysis and simulations
- Machine learning of multiscale active force generation models for the efficient simulation of cardiac electromechanics
- A robust solution of a statistical inverse problem in multiscale computational mechanics using an artificial neural network
- Non-invasive inference of thrombus material properties with physics-informed neural networks
- A data-driven peridynamic continuum model for upscaling molecular dynamics
- DeepM\&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks
- DeepM\&Mnet for hypersonics: predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators
- Bayesian inference of non-linear multiscale model parameters accelerated by a deep neural network
- A neural network-aided Bayesian identification framework for multiscale modeling of nanocomposites
- The Schwarz alternating method in solid mechanics
- A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis
- Multiscale parareal algorithm for long-time mesoscopic simulations of microvascular blood flow in zebrafish
- A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials
- Fast simulation of Gaussian random fields
- An Iterative Procedure with Interface Relaxation for Domain Decomposition Methods
- Multi-Level Adaptive Solutions to Boundary-Value Problems
- “Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example
- The Theory of Composites
- Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model
- A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow
- A seamless multiscale operator neural network for inferring bubble dynamics
- MultiScale Modeling of Physical Phenomena: Adaptive Control of Models
- Spectral/hp Element Methods for Computational Fluid Dynamics
- The Art of Molecular Dynamics Simulation
- A new constitutive framework for arterial wall mechanics and a comparative study of material models
This page was built for publication: Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems
