Neural Adjoint Method for Meta-optics: Accelerating Volumetric Inverse Design via Fourier Neural Operators

2026-04-19

AI Summary

This work addresses the computational bottleneck in high-dimensional inverse metasurface design, which traditionally relies on repeated solutions of Maxwell’s equations and is thus prohibitively expensive for industrial-scale applications. The authors propose a neural adjoint method that leverages a staged Fourier Neural Operator (FNO) to efficiently predict three-dimensional adjoint gradient fields directly from permittivity voxel data, bypassing iterative adjoint simulations in conventional finite-difference time-domain (FDTD) solvers. By progressively enhancing high-frequency modeling capacity, the approach accurately preserves peak structures in gradient-sensitive regions, enabling high-fidelity gradient estimation. Demonstrated on spectral demultiplexing, achromatic focusing, and waveguide mode conversion tasks, the method reduces design time from hours to seconds, dramatically accelerating full-wave inverse design.

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• Machine Learning: Optimization
• Multiagent Systems: Adversarial Agents

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Abstract

Meta-optics promises compact, high-performance imaging and color routing. However, designing high-performance structures is a high-dimensional optimization problem: mapping a desired optical output back to a physical 3D structure requires solving computationally expensive Maxwell's equations iteratively. Even with adjoint optimization, broadband design can require thousands of Maxwell solves, making industrial-scale optimization slow and costly. To overcome this challenge, we propose the Neural Adjoint Method, a solver-supervised surrogate that predicts 3D adjoint gradient fields from a voxelized permittivity volume using a Fourier Neural Operator (FNO). By learning the dense, per-voxel sensitivity field that drives gradient-based updates, our method can replace per-iteration adjoint solves with fast predictions, greatly reducing the computational cost of full-wave simulations required during iterative refinement. To better preserve sensitivity peaks, we introduce a stage-wise FNO that progressively refines residual errors with increasing emphasis on higher-frequency components. We curate a meta-optics dataset from paired forward/adjoint FDTD simulations and evaluate it across three tasks: spectral sorting (color routers), achromatic focusing (metalenses), and waveguide mode conversion. Our method reduces design time from hours to seconds. These results suggest a practical route toward fast, large-scale volumetric meta-optical design enabled by AI-accelerated scientific computing.

Problem

• meta-optics
• inverse design
• Maxwell's equations
• computational cost
• adjoint optimization

Innovation

• Neural Adjoint Method
• Fourier Neural Operator
• Meta-optics
• Inverse Design
• Adjoint Optimization