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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

, , and . Journal of Computational physics, (2019)

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Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems., and . J. Sci. Comput., 22 (1): 385-411 (2005)Karhunen-Loeve Representation of Periodic Second-Order Autoregressive Processes., , and . International Conference on Computational Science, volume 3038 of Lecture Notes in Computer Science, page 827-834. Springer, (2004)Neural-net-induced Gaussian process regression for function approximation and PDE solution., , and . CoRR, (2018)Adaptive ANOVA decomposition of stochastic incompressible and compressible flows., , , and . J. Comput. Phys., 231 (4): 1587-1614 (2012)A new domain decomposition method with overlapping patches for ultrascale simulations: Application to biological flows., and . J. Comput. Phys., 229 (15): 5541-5563 (2010)Hidden physics models: Machine learning of nonlinear partial differential equations., and . J. Comput. Phys., (2018)Multi-fidelity Gaussian process regression for prediction of random fields., , , and . J. Comput. Phys., (2017)A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems., , , and . J. Comput. Phys., (2017)Uncertainty quantification in simulation science., and . J. Comput. Phys., 217 (1): 1-4 (2006)Special Issue on "Fractional PDEs: Theory, Numerics, and Applications"., , and . J. Comput. Phys., (2015)