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Physics-informed deep generative models
Yibo Yang, Paris Perdikaris
We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference form…
Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
Yibo Yang, Paris Perdikaris
We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Sp…
Learning Parameters and Constitutive Relationships with Physics Informed Deep Neural Networks
Alexandre M. Tartakovsky, Carlos Ortiz Marrero, Paris Perdikaris +2
We present a physics informed deep neural network (DNN) method for estimating parameters and unknown physics (constitutive relationships) in partial differential equation (PDE) mod…
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…
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…