Deep Neural Operator Enabled Concurrent Multitask Design for Multifunctional Metamaterials Under Heterogeneous Fields

Multifunctional metamaterials (MMM) bear promise as next-generation material platforms supporting miniaturization and customization. Despite many proof-of-concept demonstrations and the proliferation of deep learning assisted design, grand challenges of inverse design for MMM, especially those involving heterogeneous fields possibly subject to either mutual meta-atom coupling or long-range interactions, remain largely under-explored. To this end, a data-driven design framework is presented, which streamlines the inverse design of MMMs involving heterogeneous fields. A core enabler is implicit Fourier neural operator (IFNO), which predicts heterogeneous fields distributed across a metamaterial array, thus in general at odds with homogenization assumptions. Additionally, a standard formulation of inverse problem covering a broad class of MMMs is presented, together with gradient-based multitask concurrent optimization identifying a set of Pareto-optimal architecture-stimulus (A-S) pairs. Fourier multiclass blending is proposed to synthesize inter-class meta-atoms anchored on a set of geometric motifs, while enjoying training-free dimension reduction and built-it reconstruction. Interlocking the three pillars, the framework is validated for light-by-light programmable nanoantenna, whose design involves vast space jointly spanned by quasi-freeform supercells, maneuverable incident phase distributions, and conflicting figure-of-merits (FoM) involving on-demand localization patterns. Accommodating all the challenges, the framework can propel future advancements of MMM. A data-driven design framework powered by neural operator for multifunctional metamaterials is proposed. It interlocks a field-to-field surrogate using Fourier neural operators, concurrent multitask optimization for Pareto-optimality, and Fourier multiclass blending for meta-atom synthesis. The framework simultaneously handles the joint architecture-stimulus space, long-range interactions, and trade-offs among functionalities. Its efficacy is demonstrated for concurrent design of spatially addressable metasurfaces. image