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Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs).
Triangular mesh methods for the neutron transport equation
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Finite volume methods for hyperbolic problems
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Hyperbolic phase transitions in traffic flow
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Hyperbolic conservation laws in continuum physics
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An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
Rafael Borges, Monique Carmona, Bruno Costa, and Wai Sun Don · 2008
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Wave propagation in elastic solids
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Discontinuous Galerkin methods: theory, computation and applications
Bernardo Cockburn, George E Karniadakis, and Chi-Wang Shu · 2012
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A proposal for deployment of wireless sensor network in day-to-day home and industrial appliances for a greener environment
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A first order hyperbolic framework for large strain computational solid dynamics. part i: Total lagrangian isothermal elasticity
Javier Bonet, Antonio J Gil, Chun Hean Lee, Miquel Aguirre, and Rogelio Ortigosa · 2015
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Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2017
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Residual dense network for image super-resolution
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Computational Approximation of Mesoscale Field Dislocation Mechanics at Finite Deformation
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Vikas Dwivedi, Nishant Parashar, and Balaji Srinivasan · 2019
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Limitations of physics informed machine learning for nonlinear two-phase transport in porous media
Olga Fuks and Hamdi A Tchelepi · 2020
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Deepxde: A deep learning library for solving differential equations
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A hybrid physics-informed neural network for nonlinear partial differential equation
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Jingrun Chen, Shi Jin, and Liyao Lyu · 2021
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Neufenet: Neural finite element solutions with theoretical bounds for parametric pdes
Biswajit Khara, Aditya Balu, Ameya Joshi, Soumik Sarkar, Chinmay Hegde, Adarsh Krishnamurthy, and Baskar Ganapathysubramanian · 2021
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Machine learning-accelerated computational solid mechanics: Application to linear elasticity
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Physics-informed neural networks for high-speed flows
Zhiping Mao, Ameya D Jagtap, and George Em Karniadakis · 2020
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Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
Ameya D Jagtap, Ehsan Kharazmi, and George Em Karniadakis · 2020
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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
Ameya D Jagtap, Kenji Kawaguchi, and George Em Karniadakis · 2020
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RoeNets: predicting discontinuity of hyperbolic systems from continuous data
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Understanding and mitigating gradient pathologies in physics-informed neural networks
Sifan Wang, Yujun Teng, and Paris Perdikaris · 2020
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Phygeonet: Physics-informed geometry-adaptive convolutional neural networks for solving parametric pdes on irregular domain
Han Gao, Luning Sun, and Jian-Xun Wang · 2020
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Dislocation pattern formation in finite deformation crystal plasticity
Rajat Arora and Amit Acharya · 2020
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Rajat Arora · 2021
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Physics-informed neural networks for modeling rate-and temperature-dependent plasticity
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Spatio-temporal super-resolution of dynamical systems using physics-informed deep-learning
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Physics-informed neural networks for inverse problems in supersonic flows
Ameya D Jagtap, Zhiping Mao, Nikolaus Adams, and George Em Karniadakis · 2022
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Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for pdes
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Thermodynamically consistent physics-informed neural networks for hyperbolic systems
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Discontinuity computing with physics-informed neural network
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Physics-informed neural networks with adaptive localized artificial viscosity
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Tim De Ryck, Siddhartha Mishra, and Roberto Molinaro · 2022
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Physics-informed attention-based neural network for hyperbolic partial differential equations: application to the buckley–leverett problem
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PhySRNet: Physics informed super-resolution network for application in computational solid mechanics
Rajat Arora · 2022
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Mechanics of micropillar confined thin film plasticity
Abhishek Arora, Rajat Arora, and Amit Acharya · 2022
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