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Physics-informed neural networks (PINNs) incorporate physical knowledge from the problem domain as a soft constraint on the loss function, but recent work has shown that this can lead to optimization difficulties.
Artificial neural networks for solving ordinary and partial differential equations
Isaac E Lagaris, Aristidis Likas, and Dimitrios I Fotiadis · 1998
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Convex optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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Dgm: A deep learning algorithm for solving partial differential equations
Justin Sirignano and Konstantinos Spiliopoulos · 2018
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Maziar Raissi, Paris Perdikaris, and George E Karniadakis · 2019
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Informed machine learning–a taxonomy and survey of integrating knowledge into learning systems
Laura von Rueden, Sebastian Mayer, Katharina Beckh, Bogdan Georgiev, Sven Giesselbach, Raoul Heese, Birgit Kirsch, Julius Pfrommer, Annika Pick, Rajkumar Ramamurthy, et al · 2019
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Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
Yinhao Zhu, Nicholas Zabaras, Phaedon-Stelios Koutsourelakis, and Paris Perdikaris · 2019
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Machine learning for fluid mechanics
Steven L Brunton, Bernd R Noack, and Petros Koumoutsakos · 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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Modeling the dynamics of pde systems with physics-constrained deep auto-regressive networks
Nicholas Geneva and Nicholas Zabaras · 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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Universal differential equations for scientific machine learning
Christopher Rackauckas, Yingbo Ma, Julius Martensen, Collin Warner, Kirill Zubov, Rohit Supekar, Dominic Skinner, Ali Ramadhan, and Alan Edelman · 2020
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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 cardiac activation mapping
Francisco Sahli Costabal, Yibo Yang, Paris Perdikaris, Daniel E Hurtado, and Ellen Kuhl · 2020
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Understanding and mitigating gradient pathologies in physics-informed neural networks
Sifan Wang, Yujun Teng, and Paris Perdikaris · 2020
Cited alongside, same era.
Physics-informed machine learning
George Em Karniadakis, Ioannis G Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang · 2021
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Characterizing possible failure modes in physics-informed neural networks
Aditi Krishnapriyan, Amir Gholami, Shandian Zhe, Robert Kirby, and Michael W Mahoney · 2021
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A dual-dimer method for training physics-constrained neural networks with minimax architecture
Dehao Liu and Yan Wang · 2021
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Deepxde: A deep learning library for solving differential equations
Lu Lu, Xuhui Meng, Zhiping Mao, and George Em Karniadakis · 2021
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Spinn: Sparse, physics-based, and partially interpretable neural networks for pdes
Amuthan A Ramabathiran and Prabhu Ramachandran · 2021
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Das: A deep adaptive sampling method for solving partial differential equations
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Sifan Wang, Hanwen Wang, and Paris Perdikaris · 2020
Cited alongside, same era.
When and why pinns fail to train: A neural tangent kernel perspective
Sifan Wang, Xinling Yu, and Paris Perdikaris · 2020
Cited alongside, same era.
Integrating physics-based modeling with machine learning: A survey
Jared Willard, Xiaowei Jia, Shaoming Xu, Michael Steinbach, and Vipin Kumar · 2020
Cited alongside, same era.
Multi-objective loss balancing for physics-informed deep learning
Rafael Bischof and Michael Kraus · 2021
Cited alongside, same era.
John Hanna, Jose V Aguado, Sebastien Comas-Cardona, Ramzi Askri, and Domenico Borzacchiello · 2021
Cited alongside, same era.
Nsfnets (navier-stokes flow nets): Physics-informed neural networks for the incompressible navier-stokes equations
Xiaowei Jin, Shengze Cai, Hui Li, and George Em Karniadakis · 2021
Cited alongside, same era.
https://github.com/ShashankSubramanian/adaptive-selfsupervision-pinns
Cited in the paper.
Kejun Tang, Xiaoliang Wan, and Chao Yang · 2021
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Zixue Xiang, Wei Peng, Xiaohu Zheng, Xiaoyu Zhao, and Wen Yao · 2021
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Neural networks learn to speed up simulations
C. Edwards · 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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