Audited Surrogate Gradients for Efficient Model-Based Flow Control

Feedback controllers for fluid flows are expensive to design, since each candidate must be evaluated by numerically solving the governing equations with a high-fidelity solver. Differentiable surrogates reduce that cost, but they also introduce a failure mode that prediction error cannot detect. Policy optimization consumes the derivative of the predicted objective with respect to the action, which we call the action gradient. It is the only quantity the optimizer reads from the model, and a surrogate can follow a trajectory closely while misestimating it. This paper addresses this failure mode directly. We build controllers only from action gradients that have been measured. The surrogate action gradient is compared against a central finite-difference estimate from the high-fidelity solver on held-out states, under acceptance thresholds fixed before the comparison, and we call that comparison an audit. A low-dimensional feedback law is then fitted to the audited gradient field. This law initializes a neural policy, and a quadratic penalty holds the policy near it during optimization. The proposed approach is validated on four test cases. The resulting controller outperforms a matched model-free baseline on two test cases and matches it on the other two, and, when the solver cost can be computed completely, it does so using 3 to 250 times fewer high-fidelity solver steps. Three findings explain why each part of the procedure is needed. One surrogate predicts the objective at correlation 0.9996 but its action gradient at only 0.459, so prediction accuracy does not identify a usable surrogate. Another surrogate, whose action gradient correlates at 0.99, makes the objective 0.52 percent worse when it is optimized without the penalty, so an accurate gradient alone does not provide a working controller. And a surrogate that passes the audit at one fixed action fails it around the actions the deployed controller applies, so the pass is local and the gradient must be measured where the controller operates.