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This paper empirically studies commonly observed training difficulties of Physics-Informed Neural Networks (PINNs) on dynamical systems.
On the symmetry breaking instability leading to vortex shedding
Shaojie Tang and Nadine Aubry · 1997
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Probabilistic ode solvers with runge-kutta means
Michael Schober, David K Duvenaud, and Philipp Hennig · 2014
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Steven L Brunton, Joshua L Proctor, and J Nathan Kutz · 2016
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Automatic differentiation in machine learning: a survey
Atilim Gunes Baydin, Barak A Pearlmutter, Alexey Andreyevich Radul, and Jeffrey Mark Siskind · 2018
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Visualizing the loss landscape of neural nets
Hao Li, Zheng Xu, Gavin Taylor, Christoph Studer, and Tom Goldstein · 2018
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Deep hidden physics models: Deep learning of nonlinear partial differential equations
Maziar Raissi · 2018
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Numerical gaussian processes for time-dependent and nonlinear partial differential equations
Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 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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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
Maziar Raissi, Alireza Yazdani, and George Em Karniadakis · 2020
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Learning to simulate complex physics with graph networks
Alvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec, and Peter Battaglia · 2020
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Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
Luning Sun, Han Gao, Shaowu Pan, and Jian-Xun Wang · 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.
Numerical simulation data of a two-dimensional flow around a fixed circular cylinder, June 2021
Mouad Boudina · 2021
Cited alongside, same era.
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 E Karniadakis · 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
Inverse Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks
Suryanarayana Maddu, Dominik Sturm, Christian L Müller, and Ivo F Sbalzarini · 2021
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On the Pareto Front of Physics-Informed Neural Networks
Franz M Rohrhofer, Stefan Posch, and Bernhard C Geiger · 2021
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Learning in sinusoidal spaces with physics-informed neural networks
Jian Cheng Wong, Chinchun Ooi, Abhishek Gupta, and Yew-Soon Ong · 2021
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Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustration
Pi-Yueh Chuang and Lorena A Barba · 2022
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Pso-pinn: Physics-informed neural networks trained with particle swarm optimization
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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.
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.
How to avoid trivial solutions in physics-informed neural networks
Raphael Leiteritz and Dirk Pflüger · 2021
Cited alongside, same era.
Physics-informed neural networks with hard constraints for inverse design
Lu Lu, Raphael Pestourie, Wenjie Yao, Zhicheng Wang, Francesc Verdugo, and Steven G Johnson · 2021
Cited alongside, same era.
How pinns cheat: Predicting chaotic motion of a double pendulum
Sophie Steger, Franz M Rohrhofer, and Bernhard C Geiger
Cited in the paper.
Understanding and mitigating gradient flow pathologies in physics-informed neural networks
Sifan Wang, Yujun Teng, and Paris Perdikaris
Cited in the paper.
On the eigenvector bias of fourier feature networks: From regression to solving multi-scale pdes with physics-informed neural networks
Sifan Wang, Hanwen Wang, and Paris Perdikaris
Cited in the paper.
Caio Davi and Ulisses Braga-Neto · 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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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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Modalpinn: an extension of physics-informed neural networks with enforced truncated fourier decomposition for periodic flow reconstruction using a limited number of imperfect sensors
Gaétan Raynaud, Sebastien Houde, and Frederick P Gosselin · 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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