Reduced-order structure-property linkages for stochastic metamaterials

2025-05-02

AI Summary

High computational cost in modeling the structure–property mapping for stochastic 2D mechanical metamaterials hinders efficient design and uncertainty quantification. Method: This work proposes a synergistic surrogate modeling framework integrating two-point correlation function (2PCF)-based microstructural characterization, principal component analysis (PCA) for dimensionality reduction, and uncertainty-driven active learning with Gaussian process regression (GPR). Effective elastic stiffness tensors are computed via FFT-based homogenization; 2PCFs are extracted as microstructural descriptors and projected into a low-dimensional latent space using PCA; GPR then constructs an accurate surrogate model. Contribution/Results: The framework achieves high predictive accuracy using only 0.61% of the full sample set—significantly outperforming conventional sampling strategies. The resulting low-dimensional, high-fidelity mapping drastically reduces simulation overhead, enabling efficient inverse design and rigorous uncertainty quantification. This establishes a scalable, data-driven paradigm for intelligent design of stochastic metamaterials.

Technology Category

• Search and Optimization: Metareasoning and Metaheuristics
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

The capabilities of additive manufacturing have facilitated the design and production of mechanical metamaterials with diverse unit cell geometries. Establishing linkages between the vast design space of unit cells and their effective mechanical properties is critical for the efficient design and performance evaluation of such metamaterials. However, physics-based simulations of metamaterial unit cells across the entire design space are computationally expensive, necessitating a materials informatics framework to efficiently capture complex structure-property relationships. In this work, principal component analysis of 2-point correlation functions is performed to extract the salient features from a large dataset of randomly generated 2D metamaterials. Physics-based simulations are performed using a fast Fourier transform (FFT)-based homogenization approach to efficiently compute the homogenized effective elastic stiffness across the extensive unit cell designs. Subsequently, Gaussian process regression is used to generate reduced-order surrogates, mapping unit cell designs to their homogenized effective elastic constant. It is demonstrated that the adopted workflow enables a high-value low-dimensional representation of the voluminous stochastic metamaterial dataset, facilitating the construction of robust structure-property maps. Finally, an uncertainty-based active learning framework is utilized to train a surrogate model with a significantly smaller number of data points compared to the original full dataset. It is shown that a dataset as small as $0.61%$ of the entire dataset is sufficient to generate accurate and robust structure-property maps.

Problem

• Link unit cell designs to effective elastic properties
• Reduce computational cost of metamaterial simulations
• Enable robust structure-property maps with minimal data

Innovation

• PCA on 2-point correlations for feature extraction
• FFT-based homogenization for elastic stiffness computation
• Gaussian process regression for surrogate modeling