Learning While Searching: Inverse Design through Online Refinement and Offline Replay

Predicting a physical system's response from its parameters is a well-established forward problem. Inverse design is harder when the mapping is nonlinear or non-unique and each simulation is expensive. We introduce ORO (Online Refinement, Offline Reuse), a framework that learns while it searches by coupling a forward surrogate with an inverse design network. Online, the inverse network proposes a candidate for a target whose design is unknown; the simulated response corrects the surrogate, and gradients through the corrected surrogate move the inverse network toward the target, with neither simulator derivatives nor an acquisition function. Offline, the accumulated design–response pairs retrain both networks, with achieved responses serving as inverse-training targets whose designs are known, so unsuccessful proposals continue to inform learning at no extra simulation cost. On three synthetic simulators that separate non-uniqueness from ill-conditioning, at a matched budget of 2,000 simulator calls per target including initialization, ORO attains lower mean and median error than genetic search on the true simulator, Bayesian optimization, and genetic search on an offline-trained surrogate, with median errors 5.5, 51.4 and 1.4 times lower than direct genetic search. Removing offline reuse causes learning to stall. Carrying its dataset across twenty targets, ORO matches the accuracy of a 30,000-sample offline surrogate using under 10% of that budget on two of the benchmarks. On a band-pass filter designed with a commercial full-wave solver, it reaches a compliant design in about 1,200 simulations, against 16,300 for a surrogate-based genetic approach.