N-adaptive Ritz method: a neural network enriched partition of unity for boundary value problems
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Publication:6566038
DOI10.1016/j.cma.2024.117070MaRDI QIDQ6566038
Jonghyuk Baek, Jiun Shyan Chen, Yanran Wang
Publication date: 3 July 2024
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
energy minimizationadaptivityRitz methodpartition of unityneural network enrichmenttransfer-learning
Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
Cites Work
- Unnamed Item
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- Toward a universal h-p adaptive finite element strategy. III: Design of h-p meshes
- Analysis and applications of a generalized finite element method with global-local enrichment functions
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- A fully automatic \(hp\)-adaptivity for elliptic PDEs in three dimensions
- A Lagrangian reproducing kernel particle method for metal forming analysis
- Reproducing kernel particle methods for large deformation analysis of nonlinear structures
- An \(h\)-\(p\) adaptive method using clouds
- The partition of unity finite element method: basic theory and applications
- Filters, reproducing kernel, and adaptive meshfree method
- A manifold learning approach to data-driven computational elasticity and inelasticity
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Model-free data-driven inelasticity
- Exponential convergence of the deep neural network approximation for analytic functions
- DGM: a deep learning algorithm for solving partial differential equations
- Hierarchical deep learning neural network (HiDeNN): an artificial intelligence (AI) framework for computational science and engineering
- SciANN: a Keras/Tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks
- Geometric deep learning for computational mechanics. I: Anisotropic hyperelasticity
- Sobolev training of thermodynamic-informed neural networks for interpretable elasto-plasticity models with level set hardening
- Learning constitutive relations using symmetric positive definite neural networks
- Deep autoencoders for physics-constrained data-driven nonlinear materials modeling
- Parametric deep energy approach for elasticity accounting for strain gradient effects
- A deep energy method for finite deformation hyperelasticity
- Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials
- A physics-constrained data-driven approach based on locally convex reconstruction for noisy database
- An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications
- 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
- Data-driven computational mechanics
- Thermodynamically consistent machine-learned internal state variable approach for data-driven modeling of path-dependent materials
- Distance-preserving manifold denoising for data-driven mechanics
- A stabilized conforming nodal integration for Galerkin mesh-free methods
- Error analysis of collocation method based on reproducing kernel approximation
- Universal approximation bounds for superpositions of a sigmoidal function
- Element‐free Galerkin methods
- Convergence analysis of a hierarchical enrichment of Dirichlet boundary conditions in a mesh-free method
- THE PARTITION OF UNITY METHOD
- A reproducing kernel method with nodal interpolation property
- Reproducing kernel particle methods
- Deep Learning with Python
- A neural network‐enhanced reproducing kernel particle method for modeling strain localization
- A neural kernel method for capturing multiscale high-dimensional micromorphic plasticity of materials with internal structures
- A neural network-based enrichment of reproducing kernel approximation for modeling brittle fracture
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