PINNs with specialized techniques solve the nonlinear Hamiltonian constraint for generic binary black hole initial data, matching traditional NR accuracy.
(4) is a highly non-linear elliptic partial dif- ferential equation, it is very difficult to learn the solu- tion u directly by PINN
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Solving Hamiltonian Constraint Equation with Physics-Informed Neural Networks
PINNs with specialized techniques solve the nonlinear Hamiltonian constraint for generic binary black hole initial data, matching traditional NR accuracy.