Label-free learning of elliptic partial differential equation solvers with generalizability across boundary value problems
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Publication:6146999
DOI10.1016/j.cma.2023.116214arXiv2301.13165OpenAlexW4384207518MaRDI QIDQ6146999
Krishna Garikipati, Xiaoxuan Zhang
Publication date: 15 January 2024
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2301.13165
partial differential equationsvariational inferencemulti-task learningtransfer learningBayesian neural networksscientific machine learning
Cites Work
- Unnamed Item
- Weak adversarial networks for high-dimensional partial differential equations
- Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification
- DGM: a deep learning algorithm for solving partial differential equations
- PPINN: parareal physics-informed neural network for time-dependent PDEs
- \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
- Mosaic flows: a transferable deep learning framework for solving PDEs on unseen domains
- B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
- NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations
- Deep learning of free boundary and Stefan problems
- Learning functional priors and posteriors from data and physics
- Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
- Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
- Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
- Adversarial uncertainty quantification in physics-informed neural networks
- ConvPDE-UQ: convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains
- Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
- Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks
- Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations
- 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
- Prediction of aerodynamic flow fields using convolutional neural networks
- A finite element based deep learning solver for parametric PDEs
- Solving high-dimensional partial differential equations using deep learning
- fPINNs: Fractional Physics-Informed Neural Networks
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