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The choice between adjoint methods and PINNs hinges on parameter representation, with a hybrid approach offering a cost-effective path to high accuracy in time-dependent inverse problems.
Prediction accuracy alone can mask critical failures in operator fidelity, as our spectral audit uncovers hidden instabilities and inconsistencies in neural operator networks.
Indirect PINNs offer a more accurate and stable approach to PDE-constrained optimal control by explicitly enforcing optimality conditions, outperforming direct PINN methods.
