BONNI: Gradient-Informed Bayesian and Interior Point Optimization for Efficient Inverse Design in Nanophotonics

TL;DR

BONNI tackles the challenge of high-dimensional, multi-modal nanophotonic inverse design by coupling gradient-enabled Bayesian optimization with neural-network ensembles and an interior-point optimizer. It learns a distribution over $f(x)$ and its gradient $\nabla f(x)$ from data and uses Expected Improvement with an IPOPT inner loop to propose informative samples. The approach demonstrates superior design quality for a five-layer Distributed Bragg Reflector and a 62-parameter dual-layer grating coupler compared with gradient-based locals and gradient-free globals, and shows strong validation on synthetic benchmarks. The work highlights the value of gradient information in shaping the optimization landscape and provides an open-source pipeline for broader adoption, with future work on mixed-variable domains.

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 (8)

• 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.