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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 ScienceJ. 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, MathematicsArXiv
- 28 November 2017

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Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations

- M. Raissi
- Mathematics, Computer ScienceJ. Mach. Learn. Res.
- 20 January 2018

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

- M. Raissi, P. Perdikaris, G. Karniadakis
- Computer Science, MathematicsArXiv
- 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

Hidden physics models: Machine learning of nonlinear partial differential equations

- M. Raissi, G. Karniadakis
- Computer Science, MathematicsJ. Comput. Phys.
- 2 August 2017

Abstract While there is currently a lot of enthusiasm about “big data”, useful data is usually “small” and expensive to acquire. In this paper, we present a new paradigm of learning partial… Expand

The Differential Effects of Oil Demand and Supply Shocks on the Global Economy

- P. Cashin, Kamiar Mohaddes, M. Raissi, M. Raissi
- Economics
- 1 October 2012

We employ a set of sign restrictions on the generalized impulse responses of a Global VAR-model, estimated for 38 countries/regions over the period 1979-2011Q2, to discriminate - between… Expand

Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations

- M. Raissi
- Mathematics, Computer ScienceArXiv
- 19 April 2018

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Machine learning of linear differential equations using Gaussian processes

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

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

Deep learning of vortex-induced vibrations

- M. Raissi, Zhicheng Wang, M. Triantafyllou, G. Karniadakis
- Physics, Computer ScienceJournal of Fluid Mechanics
- 26 August 2018

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