# RAG: A Random-Forest-Based Generative Design Framework for Uncertainty-Aware Design of Metamaterials with Complex Functional Response Requirements

arXiv: https://arxiv.org/abs/2601.13233 · HTML: https://mlsanity.com/paper/2601.13233/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 79 references that are in the map.
- First posted on arXiv 19 Jan 2026.

## Builds on (most cited first, 12 of 12)

- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models](https://mlsanity.com/paper/2305.19836/) (2023)
- [Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties](https://mlsanity.com/paper/2302.12881/) (2023)
- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [High-Dimensional Materials and Process Optimization using Data-driven Experimental Design with Well-Calibrated Uncertainty Estimates](https://mlsanity.com/paper/1704.07423/) (2017)
- [GAN-DUF: Hierarchical Deep Generative Models for Design Under Free-Form Geometric Uncertainty](https://mlsanity.com/paper/2202.10558/) (2022)
- [Uncertainty-Aware Mixed-Variable Machine Learning for Materials Design](https://mlsanity.com/paper/2207.04994/) (2022)
- [Generative Inverse Design of Metamaterials with Functional Responses by Interpretable Learning](https://mlsanity.com/paper/2401.00003/) (2023)
- [An Uncertainty-aware Deep Learning Framework-based Robust Design Optimization of Metamaterial Units](https://mlsanity.com/paper/2407.20251/) (2024)
- [GUIDe: Generative and Uncertainty-Informed Inverse Design for On-Demand Nonlinear Functional Responses](https://mlsanity.com/paper/2509.05641/) (2025)
- [Two-scale data-driven design for heat manipulation](https://mlsanity.com/paper/2304.00747/) (2023)

## Abstract (arXiv)

Metamaterials design for advanced functionality often entails the inverse design on nonlinear and condition-dependent responses (e.g., stress-strain relation and dispersion relation), which are described by continuous functions. Most existing design methods focus on vector-valued responses (e.g., Young's modulus and bandgap width), while the inverse design of functional responses remains challenging due to their high-dimensionality, the complexity of accommodating design requirements in inverse-design frameworks, and non-existence or non-uniqueness of feasible solutions. Although generative design approaches have shown promise, they are often data-hungry, handle design requirements heuristically, and may generate infeasible designs without uncertainty quantification. To address these challenges, we introduce a RAndom-forest-based Generative approach (RAG). By leveraging the small-data compatibility of random forests, RAG enables data-efficient predictions of high-dimensional functional responses. During the inverse design, the framework estimates the likelihood through the ensemble which 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 conditional likelihood. We demonstrate RAG on: 1) acoustic metamaterials with prescribed partial passbands/stopbands, and 2) mechanical metamaterials with targeted snap-through responses, using 500 and 1057 samples, respectively. Its data-efficiency is benchmarked against neural networks on a public mechanical metamaterial dataset with nonlinear stress-strain relations. Our framework provides a lightweight, trustworthy pathway to inverse design involving functional responses, expensive simulations, and complex design requirements, beyond metamaterials.