Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

@article{Zhang2019QuantifyingTU,
  title={Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems},
  author={D. Zhang and L. Lu and L. Guo and G. Karniadakis},
  journal={J. Comput. Phys.},
  year={2019},
  volume={397}
}
  • D. Zhang, L. Lu, +1 author G. Karniadakis
  • Published 2019
  • Mathematics, Physics, Computer Science
  • J. Comput. Phys.
  • Abstract Physics-informed neural networks (PINNs) have recently emerged as an alternative way of numerically solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In particular, in addition to the deep neural network (DNN) for the solution, an auxiliary DNN is considered that represents the residual of the PDE. The residual is then combined with the mismatch in the given data of the solution in order to… CONTINUE READING
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    References

    SHOWING 1-10 OF 64 REFERENCES
    Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
    • 209
    • PDF
    Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification
    • 148
    • PDF
    Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations
    • 261
    • PDF
    A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equations
    • 14
    • PDF
    Solving parametric PDE problems with artificial neural networks
    • 97
    • PDF
    Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
    • 55
    • PDF