Integration of machine learning (ML) into the topology optimization (TO)
framework is attracting increasing attention, but data acquisition in
data-driven models is prohibitive. Compared with popular ML methods, the
physics-informed neural network (PINN) can avoid generating enormous amounts of
data when solving forward problems and additionally provide better inference.
To this end, a dynamically configured PINN-based topology optimization
(DCPINN-TO) method is proposed. The DCPINN is composed of two subnetworks,
namely the backbone neural network (NN) and the coefficient NN, where the
coefficient NN has fewer trainable parameters. The designed architecture aims
to dynamically configure trainable parameters; that is, an inexpensive NN is
used to replace an expensive one at certain optimization cycles. Furthermore,
an active sampling strategy is proposed to selectively sample collocations
depending on the pseudo-densities at each optimization cycle. In this manner,
the number of collocations will decrease with the optimization process but will
hardly affect it. The Gaussian integral is used to calculate the strain energy
of elements, which yields a byproduct of decoupling the mapping of the material
at the collocations. Several examples with different resolutions validate the
feasibility of the DCPINN-TO method, and multiload and multiconstraint problems
are employed to illustrate its generalization. In addition, compared to finite
element analysis-based TO (FEA-TO), the accuracy of the displacement prediction
and optimization results indicate that the DCPINN-TO method is effective and
efficient.

机器学习与拓扑优化的整合引起了广泛关注，物理信息神经网络（PINN）可以在解决前向问题时避免产生大量数据，并提供更好的推断。因此，提出了一种动态配置的基于 PINN 的拓扑优化方法（DCPINN-TO），该方法通过动态配置可训练参数并使用活跃采样策略，实现对位插值点的选择性采样。经过多个验证例子和多载荷、多约束问题的考察，验证了 DCPINN-TO 方法的可行性，同时与基于有限元分析的拓扑优化方法（FEA-TO）相比，位移预测准确性和优化结果的准确性表明 DCPINN-TO 方法具备高效性和有效性。