Reduced-order model-based convergence acceleration of reverse mode discrete adjoint solvers

Abstract

This work presents a new technique to reduce the computational cost of sensitivities calculated using a discrete adjoint solver developed via reverse mode automatic differentiation. A fixed-point iterative method is built for the discrete adjoint sensitivity equations by employing the primal time-stepping adjoint approach. The fixed-point sensitivity solution is then accelerated by building a reduced-order model (ROM) that maps the relationship between the sensitivity solution and its corresponding residual. This model is then used to approximate the converged solution, corresponding to a zero residual. While the approximation might not produce the fully converged solution, it typically provides an improved solution that the fixed-point solver can be re-initialized with, which is one of the novel aspects of the present work. After re-initializing the solution, the ROM acceleration technique can be reapplied until the desired convergence criterion is reached. A key feature of the proposed ROM is that it is formed on the fly during a single sensitivity solution. Additionally, its implementation requires only minor modifications to an existing fixed-point iterative solver. The ROM projection technique is evaluated by considering design optimization of horizontal wind turbine blade profiles and cost reductions of 57 to 80% were achieved.