An Active Learning Strategy for Joint Surrogate Models Construction with Compatibility Conditions: Application to VPP

Static Velocity Prediction Programs (VPP) are standard tools in sailing yachts’ design and performance assessment. Predicting the maximal steady velocity of a yacht involves resolving constrained optimization problems. These problems have a prohibitive computational cost when using high-fidelity global modeling of the yacht. This difficulty has motivated the introduction of modular approaches, decomposing the global model into subsystems modeled independently and approximated by surrogate models (response surfaces). The maximum boat speed for prescribed conditions solves an optimization problem for the trimming parameters of the model constrained by compatibility conditions between the subsystems’ surrogate solution (e.g., the yacht equilibrium). The accuracy of the surrogates is then critical for the quality of the resulting VPP. This paper relies on Gaussian Process (GP) models of the subsystems and introduces an original sequential Active Learning Method (ALM) for their joint construction. Our ALM exploits the probabilistic nature of the GP models to decide the enrichment of the training sets using an infilling criterion that combines the predictive uncertainty of the surrogate models and the likelihood of equilibrium at every input point. The resulting strategy enables the concentration of the computational effort around the manifolds where equilibrium is satisfied. The results presented compare ALM with a standard (uninformed) Quasi-Monte Carlo method, which samples the input space of the subsystems uniformly. ALM surrogates have higher accuracy in the equilibrium regions for equal construction cost, with improved mean prediction and reduced prediction uncertainty. We further investigate the effect of the prediction uncertainty on the numerical VPP and in a routing problem.