Gradient-enhanced physics-informed neural networks based on transfer learning for inverse problems of the variable coefficient differential equations

Artificial neural networks and deep learning (68T07) Numerical optimization and variational techniques (65K10) Inverse problems for PDEs (35R30) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) PDEs with randomness, stochastic partial differential equations (35R60) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41) Rossby waves (76U65)

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