Multifidelity optimization stops letting cheap runs eat the budget: on DTMB 5415 the hull resistance falls further than the single-fidelity baseline
Synopsis
Multifidelity active learning now folds the choice of fidelity into the choice of where to sample, instead of fixing the location first. MF-CAS scores each candidate by the high-fidelity improvement opportunity per unit cost using decomposed uncertainty intervals; on the constrained 14-dimensional DTMB 5415 hull hydrodynamic optimization with a 100 equivalent-high-fidelity budget, its resistance reduction exceeds that of the single-fidelity LCB baseline, while the multifidelity LCB baseline barely improves on the initial design.
Interpretation
Sampling decisions in multifidelity design optimization become one step: a candidate's location and fidelity level are evaluated together, and low-fidelity runs no longer compete on their own uncertainty-to-cost ratio. Earlier multifidelity lower-confidence-bound strategies first picked a location from the high-fidelity prediction and total uncertainty, then chose the fidelity from each level's uncertainty contribution and cost, so the location was fixed before fidelity value was considered. On the constrained 14-dimensional DTMB 5415 hull resistance minimization problem, MF-CAS reduces resistance by more than the single-fidelity LCB baseline, while the multifidelity LCB baseline shows negligible improvement over the initial design.
The method ranks each candidate by its high-fidelity improvement opportunity divided by the cost of obtaining that high-fidelity response, and treats a low-fidelity run only as an intermediate check on whether a first step is worthwhile. MF-CAS removes the interpolation uncertainty that a low-fidelity observation could resolve, then asks how competitive the candidate remains against other affordable opportunities; a separate low-fidelity evaluation happens only when that effect exceeds the low-fidelity share of the nested cost. Across five independent runs with identical initial designs and a 100 equivalent-high-fidelity budget, MF-CAS averaged 41 low-fidelity and 32 high-fidelity evaluations in the adaptive phase, of which 18 were low-fidelity only and 23 were joint with high fidelity; the multifidelity LCB baseline spent the whole budget on low fidelity, about 80.6 low-fidelity evaluations and no additional high-fidelity evaluations.
Low-fidelity evaluations are confined to an intermediate step toward high-fidelity decisions, so their low cost cannot dominate budget allocation. Multifidelity LCB repeatedly selects low fidelity because its uncertainty-to-cost ratio is large, which can produce extensive low-fidelity exploration before the high-fidelity search advances. MF-CAS brings resistance below a given threshold after about 75 equivalent high-fidelity evaluations, against about 88 for the single-fidelity baseline, and later approaches values neither baseline reaches within the prescribed budget.
Perspective
The demonstrated scope is resistance minimization for the 14-dimensional constrained DTMB 5415 bare hull, with low and high fidelity distinguished by coarse or fine panel distributions on the hull surface, a total budget limited to 100 equivalent high-fidelity evaluations, and five independent runs per method reporting median best high-fidelity resistance with confidence intervals.
The multifidelity LCB baseline shows negligible improvement over the initial design in this setting, a behavior tied to the interaction between the conservative uncertainty estimate and the low-fidelity uncertainty-to-cost ratio; behavior on other design problems, other fidelity levels, or other budgets is not given within the reported scope.