We seek to accelerate the selection of an optimal design among many alternatives to meet some functional criteria characterized by an objective function. Traditionally, these functionals are obtained via the solution of a system of partial differential equations (PDEs) that are conditioned on the choice of the design. As a consequence, the state-of-the-art approach for obtaining an optimal design relies on a PDE-constrained optimization using the adjoint method. The adjoint method calculates the gradient of the objective function (with respect to the design criteria) by utilizing the Jacobian (generally with respect to the spatial coordinates) of the forward model. This calculation relies on the solution of an additional PDE system which is generally quite expensive for practical problems. This is a common occurrence for aerodynamic optimization in the presence of turbulence and discontinuities. In this talk, we shall outline preliminary results from the use of machine learning surrogates for optimal design where forward solves are bypassed by surrogate models. We explore different constrained optimization strategies using these surrogates such as the use of gradient-based techniques (useful when the surrogates are differentiable such as neural networks), and gradient-free techniques such as reinforcement learning and Bayesian optimization. Results are shown for transonic airfoil shape optimization, steady-state solver acceleration, turbulence model calibration and chaotic process control.
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