Problem-independent machine learning (PIML)-based topology optimization—A universal approach

Solving topology optimization problem is very computationally demanding especially when high-resolution results are sought for. In the present work, a problem-independent machine learning (PIML) technique is proposed to reduce the computational time associated with finite element analysis (FEA) which constitutes the main bottleneck of the solution process. The key idea is to construct the structural analysis procedure under the extended multi-scale finite element method (EMsFEM) framework, and establish an implicit mapping between the shape functions of EMsFEM and element-wise material densities of a coarse-resolution element through machine learning (ML). Compared with existing works, the proposed mechanistic-based ML technique is truly problem-independent and can be used to solve any kind of topology optimization problems without any modification once the easy-to-implement off-line training is completed. It is demonstrated that the proposed approach can reduce the FEA time significantly. In particular, with the use of the proposed approach, a topology optimization problem with 200 million of design variables can be solved on a personal workstation with an average of only two minutes for FEA per iteration step.