Random-Forest-Based Generative Design Framework

Abstract

Metamaterials design for advanced functionality often hinges on the inverse design of nonlinear and condition-dependent responses, which are described by continuous functions. Most existing design methods focus on vector-valued responses (e.g., stiffness and bandgap properties), while inverse design of functional responses remains challenging due to their high-dimensionality, the complexity of accommodating design requirements in inverse-design frameworks, and the potential non-existence or non-uniqueness of feasible solutions. Although generative design approaches have shown promise, they are often data-hungry, rely on heuristic handling of design requirements, and may generate infeasible designs due to the lack of uncertainty quantification. To address these challenges, we introduce a RAndom-forest-based Generative approach (RAG). By leveraging the small-data compatibility of random forests and reformulating the forward mapping, RAG enables data-efficient and discretization-invariant predictions of high-dimensional functional responses. During inverse design, RAG estimates the likelihood of design directly conditioned on the design requirement which can be flexibly specified. The likelihood estimated through the ensemble quantifies the trustworthiness of generated designs while reflecting the relative difficulty across different requirements. The one-to-many mapping is addressed through single-shot design generation by sampling from the likelihood distribution. We demonstrate RAG on: 1) acoustic metamaterials with prescribed partial passbands/stopbands, and 2) mechanical metamaterials with targeted snap-through responses. In the second task, RAG achieves competitive performance using only 40% of the public training dataset required by neural networks. Overall, this lightweight and uncertainty-aware design framework provides a promising pathway for inverse design problems involving high-dimensional property, expensive simulations, and complex design requirements.