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 ScienceJournal of Computational Physics
- 1 February 2019
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
- M. Raissi, P. Perdikaris, G. Karniadakis
- Computer ScienceArXiv
- 28 November 2017
This two part treatise introduces 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 differential equations and demonstrates how these networks can be used to infer solutions topartial differential equations, and obtain physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters.
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
- M. Raissi
- Computer ScienceJournal of machine learning research
- 20 January 2018
This work puts forth a deep learning approach for discovering nonlinear partial differential equations from scattered and potentially noisy observations in space and time by approximate the unknown solution as well as the nonlinear dynamics by two deep neural networks.
Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations
- M. Raissi, P. Perdikaris, G. Karniadakis
- Computer ScienceArXiv
- 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…
Hidden physics models: Machine learning of nonlinear partial differential equations
- M. Raissi, G. Karniadakis
- Computer ScienceJournal of Computational Physics
- 2 August 2017
Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
- M. Raissi, A. Yazdani, G. Karniadakis
- Computer ScienceScience
- 30 January 2020
Hidden fluid mechanics (HFM), a physics-informed deep-learning framework capable of encoding the Navier-Stokes equations into the neural networks while being agnostic to the geometry or the initial and boundary conditions, is developed.
The Differential Effects of Oil Demand and Supply Shocks on the Global Economy
- P. Cashin, Kamiar Mohaddes, M. Raissi, M. Raissi
- EconomicsSSRN Electronic Journal
- 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…
Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems
- M. Raissi, P. Perdikaris, G. Karniadakis
- Computer Science
- 4 January 2018
This work puts forth a machine learning approach for identifying nonlinear dynamical systems from data that combines classical tools from numerical analysis with powerful nonlinear function approximators to distill the mechanisms that govern the evolution of a given data-set.
Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations
- M. Raissi
- Computer Science, MathematicsArXiv
- 19 April 2018
This work approximate the unknown solution by a deep neural network which essentially enables the author to benefit from the merits of automatic differentiation in partial differential equations.
Machine learning of linear differential equations using Gaussian processes
- M. Raissi, P. Perdikaris, G. Karniadakis
- Mathematics, Computer ScienceJournal of Computational Physics
- 10 January 2017
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