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

Doksoo Lee, Lu Zhang, Yue Yu, Wei Chen

Abstract

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, we present a data-driven design framework, 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, in a parameter-/sample-efficient fashion. Additionally, we propose a standard formulation of inverse problem covering a broad class of MMMs, and 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-bylight programmable plasmonic nanoantenna, whose design involves vast space jointly spanned by quasi-freeform supercells, maneuverable incident phase distributions, and conflicting figure-of-merits involving on-demand localization patterns. Accommodating all the challenges without a-priori simplifications, our framework could propel future advancements of MMM.

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

Abstract

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, we present a data-driven design framework, 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, in a parameter-/sample-efficient fashion. Additionally, we propose a standard formulation of inverse problem covering a broad class of MMMs, and 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-bylight programmable plasmonic nanoantenna, whose design involves vast space jointly spanned by quasi-freeform supercells, maneuverable incident phase distributions, and conflicting figure-of-merits involving on-demand localization patterns. Accommodating all the challenges without a-priori simplifications, our framework could propel future advancements of MMM.
Paper Structure (27 sections, 20 equations, 18 figures)

This paper contains 27 sections, 20 equations, 18 figures.

Table of Contents

  1. Introduction
  2. Method
  3. Modeling: Field-to-Field Modeling through Implicit Fourier Neural Operator
  4. Operator Learning
  5. Neural Operator
  6. Implicit Fourier Neural Operator
  7. Optimization: An Inverse Problem Formulation on Multitask Concurrent Optimization of Multifunctional Devices
  8. The Inverse Problem on Programmable Material Systems
  9. A Generic Formalism for Multitask Architecture-Stimulus Concurrent Optimization
  10. Data Generation: Meta-Atom Synthesis through Fourier multiclass blending
  11. Fourier multiclass blending
  12. Case study: Light-by-Light Programmable Plasmonic Metasurfaces
  13. Phase Representation
  14. The Inverse Problem on Digitally Addressable Plasmonic Metasurfaces
  15. Data Acquisition Strategy
  16. ...and 12 more sections

Figures (18)

  • Figure 1: A visual overview of the proposed framework.
  • Figure 2: An overview of the proposed FMB and its instantiation $\mathcal{D}_S$. (a) The six start-up classes chosen from literature. (b) Seventy randomly selected inter-class instances. (c) Two-class linear traversal in the 36D Fourier feature space $\mathcal{Z}$. (d) A 2D shape manifold obtained through Uniform Manifold Approximation and Projection mcinnes2018umap.
  • Figure 3: An illustration of backpropagation in $\mathcal{M_{AS}}$ to obtain the numerical gradients.
  • Figure 4: Prediction results of $\mathcal{M}_{AS}$ for five randomly selected pairs of meta-atoms and input phase fields from the test dataset.
  • Figure 5: A Pareto-optimal solution of the proposed multitask optimization constructed for $\mathcal{T}=\{1, 2, 3\}$. (a) A selected set of target patterns, where a target focusing region is marked with red box. (b) The optimized energy distributions $\{ ||\mathbf{E}||_{1}^2, ||\mathbf{E}||_{2}^2, ||\mathbf{E}||_{3}^2 \}$ that are programmable through the Pareto-optimal meta-atom $\chi^{*}$ paired with the optimized set of task-specific stimuli $\{ \phi^{*} \}=\{\phi_{1}^{*}, \phi_{2}^{*}, \phi_{3}^{*} \}$. (c) The figure-of-merits for each task.
  • ...and 13 more figures