Sensitivity-Driven Adaptive Surrogate Modeling for Simulation and Optimization of Dynamical Systems

Abstract: This paper develops a surrogate model refinement approach for the simulation of dynamical systems and the solution of optimization problems governed by dynamical systems in which surrogates replace expensive-to-compute state- and control-dependent component functions in the dynamics or objective function. For example, trajectory simulation and optimization tasks for an aircraft depend on aerodynamic coefficient functions whose evaluation requires expensive computational fluid dynamics simulations for every value of the state and control encountered in simulation and optimization algorithms, which would result in prohibitively long run times, often exacerbated further by the lack of derivative information. To overcome this bottleneck, this work employs differentiable surrogates that are computed from values of the true component functions at a few points. The proposed approach updates the current surrogates on an as-needed basis as follows: given a surrogate and corresponding solution of the simulation or optimization problem, the approach combines solution sensitivity information with pointwise error estimates between the true component functions and their surrogates to define an acquisition function that is used to determine new points at which to evaluate the true component function to refine the surrogate. The performance of the proposed approach is demonstrated on a numerical example of a notional hypersonic vehicle with aerodynamic coefficient models that are approximated using kernel interpolation.