physics.opticsFeb 20, 2026

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

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Abstract

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][-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

ComponentParameterValue
EnsembleEnsemble Size ( mm )100
 Network Architecture4-Layer MLP, 256 hidden channels
 Activation FunctionGeLU [ 26 ]
 Group Normalization [ 82 ]8 Groups
 InitializationHe Normal [ 25 ]
 Embedding Channels3
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\text{E}_{y} -distribution in simulation. The position and radii of the first ten holes in the first three rows (red circles) can be optimized.

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