Minimizers of the PINN loss are claimed to converge uniformly to the unique viscosity solution of degenerate elliptic fully nonlinear PDEs, under zero-loss capacity and sample-Hölder assumptions.
SIAM Journal on Mathematics of Data Science 1(4), 780–812 (2019)
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Convergence of Physics-Informed Neural Networks for Fully Nonlinear PDE's
Minimizers of the PINN loss are claimed to converge uniformly to the unique viscosity solution of degenerate elliptic fully nonlinear PDEs, under zero-loss capacity and sample-Hölder assumptions.