A Variational-informed Neural Operator for Topology Optimisation
Please login to view abstract download link
This work proposed a novel variational-informed neural operator-based topology optimisation (VINOTO) framework. Unlike existing deep-learning-based topology optimization frameworks , VINOTO employs a variational-informed neural operator (VINO) to replace conventional finite element method (FEM) for computing deformation states [1]. Importantly, this neural operator is trained without labelled displacement data, relying solely on the underlying energy principles. In addition, the proposed framework adopts a pretrained neural operator, leading to substantially improved computational efficiency compared with online solution strategies including conventional numerical methods and physics informed neural network (PINN) [2]. The operator-learning paradigm enables generalisation across varying boundary conditions, source terms, and material properties under the same governing PDE. Furthermore, the VINO framework based on the Fourier neural operator (FNO) [3], which transfer the training from spatial domain to spectral domain, enables resolution-independent behaviour. To assess the feasibility and potential of the proposed VINOTO framework, the performance of VINO in predicting displacement fields for topology-like structures is first evaluated and compared with FEM results. The results demonstrate that VINO can achieve reliable accuracy without requiring any labelled displacement data. Building on these findings, the complete VINOTO framework is then applied to benchmark two-dimensional cantilever beam topology optimisation problems under different loading conditions and resolutions, demonstrating its effectiveness for structural topology optimisation.
