OPERA: A Unified Framework for AI-Assisted Polymer Metamaterial Design Through Operator Learning, Physics Embedding,...

Area of Science:

• Materials Science and Engineering
• Computational Materials Design
• Polymer Metamaterials

Background:

• Additive manufacturing enables polymer metamaterials with geometry-driven mechanical properties.
• Designing these metamaterials requires solving coupled forward (property prediction) and inverse (structure generation) problems.
• Existing inverse design methods face challenges with tensor prediction, training stability, and dataset bias.

Purpose of the Study:

• To present a unified framework, Operator-Physics-Enhanced Reverse Architecture (OPERA), for principled inverse design of polymer metamaterials.
• To address limitations in predicting full elastic tensors, maintaining training manifold consistency, and exploring diverse microstructures.
• To enable the generation of polymer metamaterials with targeted mechanical properties through geometry.

Main Methods:

• Developed a forward surrogate predicting the complete 3x3 plane-stress stiffness tensor (Ceff) with analytical physics constraints.
• Employed a normalizing-flow decoder (Fϕ) jointly trained with the forward surrogate to ensure inverse design stays on the training manifold.
• Augmented a diverse dataset using an active-learning loop and incorporated differentiable regularization for manufacturing constraints (e.g., minimum feature size, connectivity).

Main Results:

• Achieved R2 > 0.99 for directional moduli and density, and R2 > 0.88 for off-diagonal coupling terms and effective Poisson ratio in the forward prediction.
• Reduced the surrogate-PDE re-evaluation gap from over 30% to below 6% for held-out targets using the normalizing-flow decoder.
• Demonstrated high agreement (R2=0.987) between predictions and experimental tensile measurements on FDM-printed specimens across various material designs.

Conclusions:

• The OPERA framework successfully addresses key challenges in the inverse design of polymer metamaterials.
• OPERA enables accurate prediction of full elastic tensors and efficient generation of microstructures with targeted properties.
• The framework shows broad applicability, achieving an average target error of 6.8% across diverse metamaterial designs.