New semi-analytical solutions of the time-fractional Fokker–Planck equation by the neural network method

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

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Natural Sciences, Computer Science, Physics +16

Approximation by superpositions of a sigmoidal function

George Cybenko · Mathematics of Control Signals and Systems · 1989 · 13.7K citations

Computing, Computer Science, Machine Learning +5

Artificial neural networks for solving ordinary and partial differential equations

IEEE Transactions on Neural Networks · 1998 · 2.2K citations · Full text

Natural Sciences, Computational Engineering, Computer Science +17

Solving high-dimensional partial differential equations using deep learning

Jiequn Han, Arnulf Jentzen, E Weinan · Proceedings of the National Academy of Sciences · 2018 · 1.7K citations · Full text

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Approximate analytical solution for seepage flow with fractional derivatives in porous media

Ji‐Huan He · Computer Methods in Applied Mechanics and Engineering · 1998 · 1.3K citations

Engineering, Petroleum Engineering, Physics +17