A machine learning-aided robust topology optimization method for the design of auxetic metamaterials

We propose a machine learning-aided robust topology optimization (ML-RTO) framework for computational design of lattice auxetic metamaterials under uncertainty. Unlike conventional deterministic topology optimization, which assumes fixed material properties, ML-RTO incorporates statistical variations to define a robust objective function that accounts for randomness in base material properties. To enhance computational efficiency, ML-RTO integrates machine learning algorithms with finite element analysis-based homogenization process. A limited number of finite element simulations are used to generate training data, enabling surrogate models to approximate the relationship between material uncertainty and both the robust objective and its sensitivity. These surrogate models allow for large-scale, high-resolution homogenization with reduced computational cost. By minimizing the robust objective, ML-RTO yields optimised structures with statistically lower performance variation compared to deterministic topology optimization. The flexible framework supports trade-off parameters to guide structural evolution and accommodates diverse uncertainty parameters, statistical models, and distributions. Additionally, ML-RTO inherently favours manufacturable designs by avoiding thin or fine-scale features that are highly sensitive to uncertainty.