A Fourier neural operator-based lightweight machine learning framework for topology optimization

Abstract

The combination of machine learning and topology optimization has preliminarily mitigated the enormous computational costs incurred during optimization processes. Its powerful design capabilities are warmly welcomed by many scholars, but this strategy still faces many problems, such as unclear structural boundaries and high dependence on big data. Here, we propose a new machine learning topology optimization paradigm that learns the mapping relationship between the initial and optimized Level set functions in the infinite-dimensional function space under the Fourier neural operator to truly parameterize the structural model and its mechanical information, thereby achieving purely data-driven topology optimization. A base model trained under the proposed approach could obtain a topological structure with clear and smooth structural boundaries within 0.4 seconds, making it faster than traditional methods by tens of times. In addition, a lightweight retraining strategy under the base model was proposed. Four additional numerical examples were used to demonstrate that this strategy requires only 100 or 200 new samples and 3-6 seconds of retraining time to attain prediction capabilities under different boundary conditions, different meshes (resolution), various initial level set functions, and multiple loads. In addition, we discussed all the experiments and found that most of the mechanical properties of the results were close to the ground truths, while some results were even better than those of the traditional method. Although we only used the maximum structural stiffness as an example, this method can be extended to different objective functions.