Neural-integrated meshfree (NIM) method: a differentiable programming-based hybrid solver for computational mechanics
DOI10.1016/J.CMA.2024.117024MaRDI QIDQ6557785
Publication date: 18 June 2024
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
variational formulationsurrogate modelmeshfree methodshybrid approximationdifferentiable programmingphysics-informed learning
Probabilistic models, generic numerical methods in probability and statistics (65C20) Numerical optimization and variational techniques (65K10) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical and other methods in solid mechanics (74S99)
Cites Work
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- A spectral element method for fluid dynamics: Laminar flow in a channel expansion
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
- Solving partial differential equations by collocation using radial basis functions
- The numerical solution of linear ordinary differential equations by feedforward neural networks
- Reproducing kernel particle methods for large deformation analysis of nonlinear structures
- One-dimensional linear advection-diffusion equation: analytical and finite element solutions
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- The discontinuous Petrov-Galerkin method for elliptic problems
- Model-free data-driven inelasticity
- Hierarchical deep learning neural network (HiDeNN): an artificial intelligence (AI) framework for computational science and engineering
- \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
- Discretizationnet: a machine-learning based solver for Navier-Stokes equations using finite volume discretization
- A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
- PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain
- Parallel physics-informed neural networks via domain decomposition
- CAN-PINN: a fast physics-informed neural network based on coupled-automatic-numerical differentiation method
- Scientific machine learning through physics-informed neural networks: where we are and what's next
- Variational physics informed neural networks: the role of quadratures and test functions
- Physics-informed multi-LSTM networks for metamodeling of nonlinear structures
- On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks
- A nonlocal physics-informed deep learning framework using the peridynamic differential operator
- Deep autoencoders for physics-constrained data-driven nonlinear materials modeling
- Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations
- 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
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Data-driven computational mechanics
- Neural algorithm for solving differential equations
- Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems
- Isogeometric neural networks: a new deep learning approach for solving parameterized partial differential equations
- Error analysis of collocation method based on reproducing kernel approximation
- Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
- Element‐free Galerkin methods
- THE PARTITION OF UNITY METHOD
- New concepts in meshless methods
- Data-Driven Science and Engineering
- Reproducing kernel particle methods
- Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
- Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
- JAX-DIPS: neural bootstrapping of finite discretization methods and application to elliptic problems with discontinuities
- A hybrid deep neural operator/finite element method for ice-sheet modeling
- A neural network‐enhanced reproducing kernel particle method for modeling strain localization
- JAX-fluids: a fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows
- JAX-FEM: a differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science
- A neural network-based enrichment of reproducing kernel approximation for modeling brittle fracture
This page was built for publication: Neural-integrated meshfree (NIM) method: a differentiable programming-based hybrid solver for computational mechanics
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6557785)