Topology optimization via implicit neural representations

Along with the rapid development of artificial intelligence (AI) technology, scientific research enters a new era of AI. Topology optimization (TO) and AI technology are recently showing a growing trend of cross development, which has received continuous attentions from relative researchers. In this paper, we introduce a concept of Implicit Neural Representations from AI into TO field and establish a novel TO framework which is named as TOINR. In TOINR, the Topology Description Function is the inherent combination factor, which is constructed by a Neural Network (NN) and determines the topology statuses of structural materials in the design domain. We adopt sine as a periodic activation function combined with MLP as the architecture of the NN. The inputs of NN are a predefined set of spatial points’ coordinates, while the outputs are the implicit representations of corresponding topological boundaries. Along with updating NN's parameters (i.e., design variables), the structural topologies iteratively evolve according to the responses analysis results and optimization functions. A boundary-adaptive multi-resolution finite element analysis method is developed to improve the physical response accuracy. At each step of TOINR, we ensure the computational differentiability. Thus, the automatic differentiation is used in sensitivity analysis. The multi-penalty function approach is applied to handle objects with constraints. Besides, we design an adaptive adjustment scheme for learning rates to enhance the stability of the optimization process. Numerical examples illustrate that TOINR can stably obtain optimized structures for different problems with high performance and robustness.