# 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} }

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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