Controlled benchmarks on Burgers, Darcy, Allen-Cahn and Navier-Stokes problems show grid unknowns favor discrete adjoint while neural representations favor PINNs, with PINNs cheaper for time-dependent cases and a hybrid strategy recovering adjoint accuracy at lower cost.
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Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems
Controlled benchmarks on Burgers, Darcy, Allen-Cahn and Navier-Stokes problems show grid unknowns favor discrete adjoint while neural representations favor PINNs, with PINNs cheaper for time-dependent cases and a hybrid strategy recovering adjoint accuracy at lower cost.