Similarity-informed active learning method for efficient multiscale analysis of conformal lattice structures

Conformal lattice structures are increasingly attractive for their geometric adaptability and tunable properties. Fine-scale simulations of these structures remain computationally prohibitive, while multiscale methods can significantly reduce the computational cost. However, the spatially varying microstructures render conventional periodicity-based multiscale methods ineffective. This study proposes a multiscale framework that successfully characterizes the elastic properties of conformal lattice structures composed of arbitrary-shaped unit cells. It is systematically constructed by establishing governing equations at both the macro- and microscales, with a priori error estimates derived for the coupled formulation. The effectiveness of framework requires solving local weak-form problems at each macroscopic quadrature domain. Machine learning can replace these local computations but their accuracy depends on large homogenization datasets, particularly for three-dimensional aperiodic unit cells. To address this, a similarity-informed active learning (SIAL) method is proposed for efficient surrogate modeling of elastic properties. The method uses explicit transformations from the similarity group to identify equivalent geometric states and reduce redundant sampling. These physically defined transformations are incorporated into the preprocessing and postprocessing stages rather than learned implicitly from data, thereby reducing both training and multiscale prediction costs. Numerical examples show that the SIAL significantly reduces the training samples while maintaining high accuracy for stiffness prediction. Compared with conventional active learning, the proposed method captures elasticity variations under geometric transformations with higher accuracy. An integrated multiscale analysis paradigm is established by combining conformal geometry generation, efficient surrogate model construction and macro-microscale coupling computations. This framework provides an efficient and extensible computational scheme for the design and analysis of conformal lattice structures.