Gradient-Informed Bayesian and Interior Point Optimization for Efficient Inverse Design in Nanophotonics
Authors: Yannik Mahlau, Yannick Augenstein, Tyler W. Hughes, Marius Lindauer, Bodo Rosenhahn
Organizations: Institute of Information Processing, Leibniz University Hannover, Germany · Flexcompute, Watertown, MA, USA · Institute of Artificial Intelligence, Leibniz University Hannover, Germany · L3S Research Center, Hannover, Germany
Inverse design, particularly geometric shape optimization, provides a systematic approach for developing high-performance nanophotonic devices. While numerous optimization algorithms exist, previous global approaches exhibit slow convergence and conversely local search strategies frequently become trapped in local optima. To address the limitations inherent to both local and global approaches, we introduce BONNI: Bayesian optimization through neural network ensemble surrogates with interior point optimization. It augments global optimization with an efficient incorporation of gradient information to determine optimal sampling points. This capability allows BONNI to circumvent the local optima found in many nanophotonic applications, while capitalizing on the efficiency of gradient-based optimization. We demonstrate BONNI's capabilities in the design of a distributed Bragg reflector as well as a dual-layer grating coupler through an exhaustive comparison against other optimization algorithms commonly used in literature. Using BONNI, we were able to design a 10-layer distributed Bragg reflector with only 4.5% mean spectral error, compared to the previously reported results of 7.8% error with 16 layers. Further designs of a broadband waveguide taper and photonic crystal waveguide transition validate the capabilities of BONNI.
Figures & tables
Figure 1: Visualization of the components of BONNI. In the upper plot, the surrogate ensemble is trained on four observations (red dots) and gradients (red arrows), given through evaluations of the true function (dashed black line). The individual neural network predictions in the ensemble are visualized through colored lines, forming a confidence measure of the surrogate model. In the bottom plot, the expected improvement acquisition value is displayed, which is calculated based on mean and standard deviation of the ensemble predictions. The maximum of the acquisition function (green dashed line) is used as the next sampling point for function evaluation (green star). After including the newly sampled point in the dataset of sampled points, this process repeats until convergence or computational budget is exhausted.
Figure 2: Comparison of different optimization algorithms on the Rastrigin function in (a) 10, (b) 50 and (c) 100 dimensions. For all three experiments, function values are rescaled to the interval [−1,0] . The algorithms with dotted lines are local gradient-based algorithms while the solid lines visualize global algorithms. We evaluate the incumbent, which is the best value found given a number of simulations. All optimizations were performed over 100 random initial configurations. The dark lines represent the mean and the shaded regions the standard error over these 100 individual runs.
Figure 3: Optimization results for the DBR. In (a), the optimization results of the different algorithms are visualized. The algorithms with dotted lines are local gradient-based algorithms while the solid lines visualize global algorithms. We evaluate the incumbent, which is the best value found given a number of simulations. All optimizations were performed over 10 random initial configurations. The dark lines represent the mean and the shaded regions the standard error over these 10 individual runs. In (b), the spectrum of the best design found by BONNI is displayed (blue) and compared to the target spectrum, which is a step function around 620 nm (red). In (c), the layer heights for this design of silicon dioxide (blue) and titanium dioxide (red) are visualized.
Figure 4: Comparison of different optimization algorithms on the dual-layer grating coupler. In (a), the setup of the grating coupler is shown. A source (yellow) at the top emits a Gaussian beam onto the two grating layers of silicon Nitride (green) and silicon (pink). Transmission is measured at the output waveguide on the right side. The two grating layers are placed on top of a silicon substrate (brown). In (b), the simulation results are displayed. We evaluate the incumbent, which is the best design found given a number of simulations. All optimizations were performed on 10 random initial configurations and we report mean (solid line) as well as standard error (shaded area). The algorithms with dotted lines are local gradient-based algorithms while the solid lines visualize global algorithms.
Figure 5: Analysis of the best grating coupler design produced by BONNI. In (a), the design configuration with gaps and widths of gratings is shown. In (b), the simulation result of the design is visualized.
Appendix figures & tables3 assets
Supplementary material from the paper’s appendix.
Appendix
Component
Parameter
Value
Ensemble
Ensemble Size ( m )
100
Network Architecture
4-Layer MLP, 256 hidden channels
Activation Function
GeLU [ 26 ]
Group Normalization [ 82 ]
8 Groups
Initialization
He Normal [ 25 ]
Embedding Channels
3
Appendix
Table 1: Hyperparameters for the BONNI Algorithm.
Figure 6: Optimization results for the broadband waveguide taper In (a), the performance of different optimization algorithms for this application is visualized. All optimizations were performed on 5 random initial configurations and we report mean (bold line) as well as standard error (shaded area). The algorithms with dotted lines are local gradient-based algorithms while the solid lines visualize global algorithms. In (b), the best design found by BONNI with its energy distribution is shown.
Figure 7: Optimization results for the photonic crystal waveguide transition. In (a), the simulation results are displayed. All optimizations were performed on 5 random initial configurations and we report mean (solid line) as well as standard error (shaded area). The algorithms with dotted lines are local gradient-based algorithms while the solid lines visualize global algorithms. In (b), the optimal design found by IPOPT is visualized with its Ey -distribution in simulation. The position and radii of the first ten holes in the first three rows (red circles) can be optimized.
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.
Chanik Kang, Hyewon Suk, Haejun Chung
Hanyang University, Department of Artificial Intelligence Semiconductor Engineering Seoul, Korea · Hanyang University, Department of Electronic Engineering Seoul, Korea
The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces. Generative models for inverse design often lack robustness and transferability, whereas evolutionary strategies are robust but struggle in high-dimensional spaces. This paper introduces a Neural Operator-enabled Topology-informed Evolutionary Strategy (NOTES) that integrates dimensionality reduction, representation learning, and evolutionary optimization for efficient and transferable inverse design. NOTES couples a DeepONet-based neural operator with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to perform global optimization in a compact latent space that encodes topology-aware priors while discovering high-performance designs for unseen operating conditions. Applied to nanophotonic beam-deflector inverse design governed by Maxwell's equations, NOTES reduces the design dimensionality from 256 to 25 and consistently achieves over 95 percent efficiency, outperforming CMA-ES, topology optimization, and other baselines. Applied to structural optimization, NOTES discovers designs that achieve compliance down to 246. By decoupling topology learning of a DeepONet from the governing physics in a PDE solver, NOTES provides a flexible and transferable framework for the inverse design of physical systems.
Data-driven inverse design enables efficient generation of nanophotonic structures with prescribed optical responses, but spectrum-to-geometry mapping remains challenging due to non-uniqueness and fine geometric features. This work presents a two-stage deformable-convolutional framework for reconstructing metal--insulator--metal resonator geometries from 80-dimensional absorption spectra. The spectrum is projected to a 150×4×4 latent representation and decoded into a 64×64 resonator mask. Training combines supervised reconstruction with least-squares adversarial refinement initialized from the best supervised checkpoint. A three-run ablation compares deformable convolution with plain convolution, involution, Dynamic Conv, and ODConv under the same architecture. The proposed model achieves 20.79±0.31dB PSNR and 0.8501±0.0082 SSIM, improving over plain convolution by 2.16dB and 0.0831, respectively. It further achieves Dice 0.9623±0.0027, IoU 0.9342±0.0038, and boundary F-score 0.9550±0.0027. Spectral consistency evaluated using a frozen forward surrogate yields RMSE 0.0805±0.0013 and R2=0.7923±0.0065. Learned offsets show stronger adaptive sampling at coarse and intermediate decoder stages. Overall, deformable sampling with supervised initialization and adversarial refinement improves spectrum-conditioned geometry reconstruction.
Waleed Waseer, Muhammad Shahid Jabbar, Muhammad Sohail Ibrahim +1
School of Physics and State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, 610054, China · SDAIA-KFUPM Joint Research Center for Artificial Intelligence, King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia · Interdisciplinary Research Center for Intelligent Secure Systems (IRC-ISS), King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia +1