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Abstract Spinodoid architected materials have drawn significant attention due to their unique nature in stochasticity, aperiodicity, and bi-continuity. Compared to classic periodic truss-, beam-, and plate-based lattice architectures, spinodoids are insensitive to manufacturing defects, scalable for high-throughput production, functionally graded by tunable local properties, and material failure resistant due to low-curvature morphology. However, the design of spinodoids is often hindered by the curse of dimensionality with an extremely large design space of spinodoid types, material density, orientation, continuity, and anisotropy. From a design optimization perspective, while genetic algorithms are often beyond the reach of computing capacity, gradient-based topology optimization is challenged by the intricate mathematical derivation of gradient fields with respect to various spinodoid parameters. To address such challenges, we propose a data-driven multiscale topology optimization framework. Our framework reformulates the design variables of spinodoid materials as the parameters of neural networks, enabling automated computation of topological gradients. Additionally, it incorporates a Gaussian Process surrogate for spinodoid constitutive models, eliminating the need for repeated computational homogenization and enhancing the scalability of multiscale topology optimization. Compared to ‘black-box’ deep learning approaches, the proposed framework provides clear physical insights into material distribution. It explicitly reveals why anisotropic spinodoids with tailored orientations are favored in certain regions, while isotropic spinodoids are more suitable elsewhere. This interpretability helps to bridge the gap between data-driven design with mechanistic understanding. To this end, we test our design framework on several numerical experiments. We find our multiscale spinodoid designs with controllable anisotropy achieve better performance than single-scale isotropic counterparts, with clear physics interpretations.
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This content will become publicly available on May 19, 2026
Multiscale Physics‐Informed Neural Networks for the Inverse Design of Hyperuniform Optical Materials
Abstract In this study, multiscale physics‐informed neural networks (MscalePINNs) are employed for the inverse design of finite‐size photonic materials with stealthy hyperuniform (SHU) disordered geometries. Specifically, MscalePINNs are shown to capture the fast spatial variations of complex fields scattered by arrays of dielectric nanocylinders arranged according to isotropic SHU point patterns, thus enabling a systematic methodology to inversely retrieve their effective dielectric profiles. This approach extends the recently developed high‐frequency homogenization theory of hyperuniform media and retrieves more general permittivity profiles for applications‐relevant finite‐size SHU and optical systems, unveiling unique features related to their isotropic nature. In particular, the existence of a transparency region beyond the long‐wavelength approximation is numerically corroborated, enabling the retrieval of effective and isotropic locally homogeneous media even without disorder‐averaging, in contrast to the case of uncorrelated Poisson random patterns. The flexible multiscale network approach introduced here enables the efficient inverse design of more general effective media and finite‐size optical metamaterials with isotropic electromagnetic responses beyond the limitations of traditional homogenization theories.
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- Award ID(s):
- 2207449
- PAR ID:
- 10601121
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Advanced Optical Materials
- Volume:
- 13
- Issue:
- 16
- ISSN:
- 2195-1071
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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