Implicit geometry representation via neural operators on Riemannian manifolds for topology optimisation

Abstract

Geometry representation, as a fundamental aspect of topology optimisation, is crucial to meet the growing demand for customised structural designs in Industry 4.0. Implicit neural representation (INR) based on neural network (NN) has emerged as a promising paradigm for geometry representation. To address the limitations of point-wise NN-based INR, this paper proposes a field-wise geometry representation via neural operators on Riemannian manifolds (NORM) for topology optimisation. Verification results demonstrate that the proposed method can not only obtain high-frequency structures with better performance, but also achieve active control of structural frequency and maintain local continuity of the optimised structure.