A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks
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Publication:2679440
DOI10.1016/j.cma.2022.115671OpenAlexW4307154444MaRDI QIDQ2679440
Publication date: 20 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/2207.10289
partial differential equationsphysics-informed neural networksnon-adaptive uniform samplingresidual point distributionresidual-based adaptive samplinguniform sampling with resampling
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Uses Software
Cites Work
- Unnamed Item
- On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
- Fast generation of 2-D node distributions for mesh-free PDE discretizations
- PPINN: parareal physics-informed neural network for time-dependent PDEs
- A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations
- A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks
- SelectNet: self-paced learning for high-dimensional partial differential equations
- Parallel physics-informed neural networks via domain decomposition
- When and why PINNs fail to train: a neural tangent kernel perspective
- Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
- Meta-learning PINN loss functions
- Residual-based adaptivity for two-phase flow simulation in porous media using physics-informed neural networks
- Physics-informed neural networks for high-speed flows
- Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Adaptive deep neural networks methods for high-dimensional partial differential equations
- Large Sample Properties of Simulations Using Latin Hypercube Sampling
- Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
- Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
- Physics-Informed Neural Networks with Hard Constraints for Inverse Design
- fPINNs: Fractional Physics-Informed Neural Networks
- On the distribution of points in a cube and the approximate evaluation of integrals
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