• Publications
  • Influence
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
TLDR
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
  • Mathematics, Computer Science
    J. Mach. Learn. Res.
  • 20 January 2018
TLDR
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
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
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
The Differential Effects of Oil Demand and Supply Shocks on the Global Economy
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
Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations
  • M. Raissi
  • Mathematics, Computer Science
    ArXiv
  • 19 April 2018
TLDR
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
TLDR
Gaussian process priors are modified according to the particular form of such operators and are employed to infer parameters of the linear equations from scarce and possibly noisy observations, leading to model discovery from just a handful of noisy measurements.
Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems
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
Deep learning of vortex-induced vibrations
TLDR
A new paradigm of inference in fluid mechanics for coupled multi-physics problems enables velocity and pressure quantification from flow snapshots in small subdomains and can be exploited for flow control applications and also for system identification.
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