An adaptive Deep Ritz framework with least-squares splitting and adaptive collocation sampling solves fully nonlinear PDEs like the Monge-Ampère equation more flexibly than standard PINNs.
A neural network approach for solving the monge–amp` ere equation with transport boundary condition.Journal of Computational Mathematics and Data Science, 15:100119
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An adaptive Deep Ritz framework for second-order fully nonlinear partial differential equations
An adaptive Deep Ritz framework with least-squares splitting and adaptive collocation sampling solves fully nonlinear PDEs like the Monge-Ampère equation more flexibly than standard PINNs.