Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression
From MaRDI portal
Publication:6048987
DOI10.1016/j.camwa.2023.08.016arXiv2302.08216OpenAlexW4386475250MaRDI QIDQ6048987
Mengwu Guo, Andrea Manzoni, Ludovica Cicci, Stefania Fresca, Paolo Zunino
Publication date: 13 October 2023
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2302.08216
parameter estimationsensitivity analysisreduced order modelinguncertainty quantificationGaussian process regressionnonlinear solid mechanics
Artificial neural networks and deep learning (68T07) Learning and adaptive systems in artificial intelligence (68T05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Non intrusive reduced order modeling of parametrized PDEs by kernel POD and neural networks
- A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs
- Biomechanics of soft tissue in cardiovascular systems. Lecture notes for an advanced school on ``Biomechanics of soft tissue, Udine, Italy, September 10--14, 2001
- Making best use of model evaluations to compute sensitivity indices
- Non-intrusive reduced order modeling of nonlinear problems using neural networks
- Projection-based model reduction: formulations for physics-based machine learning
- An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
- Reduced order modelling for unsteady fluid flow using proper orthogonal decomposition and radial basis functions
- Reduced order modeling for nonlinear structural analysis using Gaussian process regression
- Data-driven reduced order modeling for time-dependent problems
- Model order reduction for large-scale structures with local nonlinearities
- POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition
- Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities
- Deep-HyROMnet: a deep learning-based operator approximation for hyper-reduction of nonlinear parametrized PDEs
- B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
- A non-intrusive multifidelity method for the reduced order modeling of nonlinear problems
- Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem
- A nonintrusive reduced order modelling approach using proper orthogonal decomposition and locally adaptive sparse grids
- POD-DEIM model order reduction for strain-softening viscoplasticity
- A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications
- Data-driven operator inference for nonintrusive projection-based model reduction
- A matrix DEIM technique for model reduction of nonlinear parametrized problems in cardiac mechanics
- Efficient model reduction of parametrized systems by matrix discrete empirical interpolation
- Sensitivity analysis for multidimensional and functional outputs
- Multi-fidelity surrogate modeling using long short-term memory networks
- Bayesian operator inference for data-driven reduced-order modeling
- A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
- Nonintrusive reduced-order modeling of parametrized time-dependent partial differential equations
- Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems
- Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation
- Certified Reduced Basis Methods for Parametrized Partial Differential Equations
- Nonlinear model order reduction based on local reduced-order bases
- Data-driven model reduction for the Bayesian solution of inverse problems
- POD-based model reduction with empirical interpolation applied to nonlinear elasticity
- Nonlinear Model Reduction via Discrete Empirical Interpolation
- Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices
- Model Order Reduction in Fluid Dynamics: Challenges and Perspectives
- A deep learning approach to Reduced Order Modelling of parameter dependent partial differential equations
- Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability
- Reduced Basis Methods for Partial Differential Equations
- Reduced basis methods for time-dependent problems
