Robust topology optimization with low rank approximation using artificial neural networks

We present a low rank approximation approach for topology optimization of parametrized linear elastic structures. The parametrization is considered on loading and stiffness of the structure. The low rank approximation is achieved by identifying a parametric connection among coarse finite element models of the structure (associated with different design iterates) and is used to inform the high fidelity finite element analysis. We build an Artificial Neural Network (ANN) map between low resolution design iterates and their corresponding interpolative coefficients (obtained from low rank approximations) and use this surrogate to perform high resolution parametric topology optimization. We demonstrate our approach on robust topology optimization with compliance constraints/objective functions and develop error bounds for the the parametric compliance computations. We verify these parametric computations with more challenging quantities of interest such as the p-norm of von Mises stress. To conclude, we use our approach on a 3D robust topology optimization and show significant reduction in computational cost via quantitative measures.

Automated summary

The study introduces a low rank approximation approach for topology optimization of parametrized linear elastic structures. By using an Artificial Neural Network to map low resolution design iterates, the computational cost of high resolution topology optimization is significantly reduced.