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Deep Learning of Turbulent Scalar Mixing
Maziar Raissi, Hessam Babaee, Peyman Givi
Based on recent developments in physics-informed deep learning and deep hidden physics models, we put forth a framework for discovering turbulence models from scattered and potenti…
Deep Learning of Vortex Induced Vibrations
Maziar Raissi, Zhicheng Wang, Michael S. Triantafyllou +1
Vortex induced vibrations of bluff bodies occur when the vortex shedding frequency is close to the natural frequency of the structure. Of interest is the prediction of the lift and…
Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data
Maziar Raissi, Alireza Yazdani, George Em Karniadakis
We present hidden fluid mechanics (HFM), a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navi…
Machine Learning of Space-Fractional Differential Equations
Mamikon Gulian, Maziar Raissi, Paris Perdikaris +1
Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discov…
Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations
Maziar Raissi
Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal g…
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
Maziar Raissi
A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficienc…
Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems
Maziar Raissi, Paris Perdikaris, George Em Karniadakis
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…