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Physics-informed neural networks (PINNs) have shown to be an effective tool for solving forward and inverse problems of partial differential equations (PDEs).
On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
John H Halton · 1960
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Monte-Carlo methods, mathuen, 1964
JM Hammersley and DC Handscomb · 1964
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On the distribution of points in a cube and the approximate evaluation of integrals
Il’ya Meerovich Sobol’ · 1967
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Large sample properties of simulations using Latin hypercube sampling
Michael Stein · 1987
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A comparison of three methods for selecting values of input variables in the analysis of output from a computer code
Michael D McKay, Richard J Beckman, and William J Conover · 2000
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Pcg: A family of simple fast space-efficient statistically good algorithms for random number generation
Melissa E O’Neill · 2014
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Fast generation of 2-D node distributions for mesh-free pde discretizations
Bengt Fornberg and Natasha Flyer · 2015
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi, P. Perdikaris, and G.E. Karniadakis · 2019
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fPINNs: Fractional physics-informed neural networks
Guofei Pang, Lu Lu, and George Em Karniadakis · 2019
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Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
Dongkun Zhang, Lu Lu, Ling Guo, and George Em Karniadakis · 2019
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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
Maziar Raissi, Alireza Yazdani, and George Em Karniadakis · 2020
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Physics-informed neural networks for inverse problems in nano-optics and metamaterials
Yuyao Chen, Lu Lu, George Em Karniadakis, and Luca Dal Negro · 2020
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Systems biology informed deep learning for inferring parameters and hidden dynamics
Alireza Yazdani, Lu Lu, Maziar Raissi, and George Em Karniadakis · 2020
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Self-adaptive physics-informed neural networks using a soft attention mechanism
Levi McClenny and Ulisses Braga-Neto · 2020
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PPINN: Parareal physics-informed neural network for time-dependent pdes
Xuhui Meng, Zhen Li, Dongkun Zhang, and George Em Karniadakis · 2020
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Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations
Ameya D. Jagtap and George Em Karniadakis · 2020
Cited alongside, same era.
Solving Allen-Cahn and Cahn-Hilliard equations using the adaptive physics informed neural networks
Colby L Wight and Jia Zhao · 2020
Cited alongside, same era.
Systematic construction of neural forms for solving partial differential equations inside rectangular domains, subject to initial, boundary and interface conditions
Pola Lydia Lagari, Lefteri H Tsoukalas, Salar Safarkhani, and Isaac E Lagaris · 2020
Cited alongside, same era.
Hongwei Guo, Xiaoying Zhuang, Xiaoyu Meng, and Timon Rabczuk · 2020
Cited alongside, same era.
Mitchell Daneker, Zhen Zhang, George Em Kevrekidis, and Lu Lu · 2022
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Meta-learning PINN loss functions
Apostolos F Psaros, Kenji Kawaguchi, and George Em Karniadakis · 2022
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Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
Jeremy Yu, Lu Lu, Xuhui Meng, and George Em Karniadakis · 2022
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When and why PINNs fail to train: A neural tangent kernel perspective
Sifan Wang, Xinling Yu, and Paris Perdikaris · 2022
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Self-adaptive loss balanced physics-informed neural networks
Zixue Xiang, Wei Peng, Xu Liu, and Wen Yao · 2022
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Revisiting PINNs: Generative adversarial physics-informed neural networks and point-weighting method
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Physics-informed neural networks for high-speed flows
Zhiping Mao, Ameya D Jagtap, and George Em Karniadakis · 2020
Cited alongside, same era.
DeepXDE: A deep learning library for solving differential equations
Lu Lu, Xuhui Meng, Zhiping Mao, and George Em Karniadakis · 2021
Cited alongside, same era.
Physics-informed machine learning
George Em Karniadakis, Ioannis G. Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang · 2021
Cited alongside, same era.
Physics-informed neural networks with hard constraints for inverse design
Lu Lu, Raphaël Pestourie, Wenjie Yao, Zhicheng Wang, Francesc Verdugo, and Steven G. Johnson · 2021
Cited alongside, same era.
Understanding and mitigating gradient flow pathologies in physics-informed neural networks
Sifan Wang, Yujun Teng, and Paris Perdikaris · 2021
Cited alongside, same era.
SelectNet: Self-paced learning for high-dimensional partial differential equations
Yiqi Gu, Haizhao Yang, and Chao Zhou · 2021
Cited alongside, same era.
Parallel physics-informed neural networks via domain decomposition
Khemraj Shukla, Ameya D. Jagtap, and George Em Karniadakis · 2021
Cited alongside, same era.
Characterizing possible failure modes in physics-informed neural networks
Aditi Krishnapriyan, Amir Gholami, Shandian Zhe, Robert Kirby, and Michael W Mahoney · 2021
Cited alongside, same era.
Wensheng Li, Chao Zhang, Chuncheng Wang, Hanting Guan, and Dacheng Tao · 2022
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A novel sequential method to train physics informed neural networks for allen cahn and cahn hilliard equations
Revanth Mattey and Susanta Ghosh · 2022
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Improved training of physics-informed neural networks with model ensembles
Katsiaryna Haitsiukevich and Alexander Ilin · 2022
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Respecting causality is all you need for training physics-informed neural networks
Sifan Wang, Shyam Sankaran, and Paris Perdikaris · 2022
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State-of-the-art review of design of experiments for physics-informed deep learning
Sourav Das and Solomon Tesfamariam · 2022
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Investigating molecular transport in the human brain from MRI with physics-informed neural networks
Bastian Zapf, Johannes Haubner, Miroslav Kuchta, Geir Ringstad, Per Kristian Eide, and Kent-Andre Mardal · 2022
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Rethinking the importance of sampling in physics-informed neural networks
Arka Daw, Jie Bu, Sifan Wang, Paris Perdikaris, and Anuj Karpatne · 2022
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RANG: a residual-based adaptive node generation method for physics-informed neural networks
Wei Peng, Weien Zhou, Xiaoya Zhang, Wen Yao, and Zheliang Liu · 2022
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Adaptive deep neural networks methods for high-dimensional partial differential equations
Shaojie Zeng, Zong Zhang, and Qingsong Zou · 2022
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Residual-based adaptivity for two-phase flow simulation in porous media using physics-informed neural networks
John M Hanna, Jose V Aguado, Sebastien Comas-Cardona, Ramzi Askri, and Domenico Borzacchiello · 2022
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