Inverse design under uncertainty with surrogate models

In the drive towards net zero the aerospace industry is motivated to develop more efficient aerostructures that can accommodate the next generation of propulsion systems that fall outside of the well understood types that are currently in use. The lack of established standards for such designs means that engineers are faced with an increased level of uncertainty in their design choices before any prototypes are built. Machine learning models are becoming a popular tool for expediting the development of novel designs due to their ability to explore and predict the optimal parameters of large design spaces. It is also possible to quantify and introduce uncertainty into particular models so that practitioners can be made aware of the potential variation in their realised designs. In this paper Gaussian Process surrogate models of the performance metrics of the early-stage design of an aircraft wing are created to optimize a subset of design parameters based on some prescribed limits of the intended real system response. This defines the inverse design problem that is solved using Markov Chain Monte Carlo sampling. The approach taken requires novel formulation of a Bayesian machine learning framework. In particular, the work investigates the formation of likelihood functions that are flexible given inputs of different scales, can perform marginalisation of stochastic parameters, account for uncertainty in the surrogate model, and optimise the parameters given more than one constraint. A case study is presented in this paper that highlights both a successful implementation of the framework along with a limitation. It is found that the optimization is sensitive to changes in the variances of the likelihoods such that it can be used as a weight to direct the optimization towards a quantity of interest, therefore adjustment of this parameter is used to balance the optimization.