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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, G. Karniadakis
- Computer Science
- J. Comput. Phys.
- 1 February 2019

Abstract We introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear… Expand

Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

- M. Raissi, P. Perdikaris, G. Karniadakis
- Computer Science, Mathematics
- ArXiv
- 28 November 2017

TLDR

Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations

- M. Raissi, P. Perdikaris, G. Karniadakis
- Computer Science, Mathematics
- ArXiv
- 28 November 2017

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial… Expand

Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data

- Yinhao Zhu, N. Zabaras, P. Koutsourelakis, P. Perdikaris
- Physics, Computer Science
- J. Comput. Phys.
- 18 January 2019

TLDR

Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling

- P. Perdikaris, M. Raissi, A. Damianou, N. Lawrence, G. Karniadakis
- Computer Science, Medicine
- Proceedings of the Royal Society A: Mathematical…
- 1 February 2017

TLDR

Machine learning of linear differential equations using Gaussian processes

- M. Raissi, P. Perdikaris, G. Karniadakis
- Mathematics, Computer Science
- J. Comput. Phys.
- 10 January 2017

TLDR

Understanding and mitigating gradient pathologies in physics-informed neural networks

- Sifan Wang, Yujun Teng, P. Perdikaris
- Computer Science, Mathematics
- ArXiv
- 13 January 2020

TLDR

Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems

- M. Raissi, P. Perdikaris, G. Karniadakis
- Mathematics, Physics
- 4 January 2018

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at… Expand

Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations

- M. Raissi, P. Perdikaris, G. Karniadakis
- Mathematics, Computer Science
- SIAM J. Sci. Comput.
- 29 March 2017

TLDR

Adversarial Uncertainty Quantification in Physics-Informed Neural Networks

- Yibo Yang, P. Perdikaris
- Mathematics, Computer Science
- J. Comput. Phys.
- 9 November 2018

TLDR

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