Numerical simulations and optimisation methods, such as mesh adaptation, rely on the accurate and inexpensive use of error estimation methods. Output-error estimation is the most accurate method; however, it relies on the use of approximations in order to be implemented in practice. The proposed method in this thesis relies on the use of super-resolution neural networks to reconstruct the fine adjoint solution from a computed coarse adjoint solution. The proposed method is compared to reference error estimators on an unsteady Burgers’ equation using the method of manufactured solutions, as well as a lid-driven cavity flow. For both of these test cases, it was shown that super-resolution neural networks were able to reconstruct the fine adjoint solution and provide robust and inexpensive output-error estimates at the cost of lower accuracy.
Nonetheless, the accurate estimation of the error indicators gives great confidence in the proposed method’s ability to perform similarly to the adjoint-weighted residual output-error estimate with a mesh adaptation procedure. A cost metric for the computational overhead of the output-error estimate is proposed. This highlights the superior performance of the lower up-scale ratio super-resolution neural networks due to their higher accuracy and lower computational cost than those with higher up-scaling factors. ... Read more