[Paper Review] Optimizing Photonic Nanostructures via Multi-fidelity Gaussian Processes

Jialin Song, Yury S. Tokpanov+5 more|arXiv (Cornell University)|Nov 15, 2018

Advanced Fluorescence Microscopy TechniquesBiochemistry, Genetics and Molecular Biology16 references3 citations

TL;DR

This paper proposes a multi-fidelity Gaussian process optimization framework to efficiently design plasmonic mirror color filters by leveraging simulations of varying computational cost. It demonstrates that by strategically balancing low-fidelity and high-fidelity simulations, the method achieves superior optimization performance—reaching lower figure of merit values faster—compared to single-fidelity Bayesian optimization and particle swarm optimization.

ABSTRACT

We apply numerical methods in combination with finite-difference-time-domain (FDTD) simulations to optimize transmission properties of plasmonic mirror color filters using a multi-objective figure of merit over a five-dimensional parameter space by utilizing novel multi-fidelity Gaussian processes approach. We compare these results with conventional derivative-free global search algorithms, such as (single-fidelity) Gaussian Processes optimization scheme, and Particle Swarm Optimization---a commonly used method in nanophotonics community, which is implemented in Lumerical commercial photonics software. We demonstrate the performance of various numerical optimization approaches on several pre-collected real-world datasets and show that by properly trading off expensive information sources with cheap simulations, one can more effectively optimize the transmission properties with a fixed budget.

Motivation & Objective

• To address the challenge of optimizing complex photonic nanostructures with high-dimensional, non-convex parameter spaces where analytical models are infeasible.
• To reduce computational cost in nanophotonics design by exploiting multiple fidelity levels of finite-difference time-domain (FDTD) simulations.
• To improve optimization efficiency by integrating low-fidelity simulations (coarse mesh, short simulation time) with high-fidelity simulations (fine mesh, long simulation time).
• To evaluate and compare the performance of multi-fidelity Bayesian optimization against single-fidelity Gaussian processes and particle swarm optimization in real-world nanophotonic design tasks.
• To demonstrate that multi-fidelity methods can achieve better designs within a fixed computational budget by intelligently trading off fidelity and cost.

Proposed method

• The method employs an additive multi-fidelity model where lower-fidelity simulations are modeled as the sum of the target-fidelity function and a fidelity-specific error function.
• Gaussian processes are used to jointly model the target-fidelity function and the error functions of lower-fidelity levels, enabling posterior updates across all fidelity levels using any observation.
• A multi-fidelity expected improvement (MF-MI-Greedy) acquisition function is used to guide the selection of new evaluation points, prioritizing cost-effective exploration in low-fidelity spaces.
• The framework uses square exponential kernels with periodically tuned hyperparameters to adaptively model the correlation between fidelity levels.
• The optimization budget is allocated with 10% used for initial random sampling: low-fidelity for multi-fidelity methods, target-fidelity for single-fidelity baselines.
• The approach is evaluated using real-world FDTD simulations of plasmonic mirror filters at three fidelity levels: 40 fs, 70 fs, and 100 fs simulation times, with corresponding costs of [40, 70, 100].

Experimental results

Research questions

• RQ1 Can multi-fidelity Bayesian optimization outperform single-fidelity Gaussian processes in optimizing photonic nanostructures under a fixed computational budget?
• RQ2 How does the performance of multi-fidelity optimization compare to heuristic methods like particle swarm optimization in nanophotonics design?
• RQ3 To what extent can low-fidelity simulations accelerate convergence to high-quality designs in complex, non-convex optimization landscapes?
• RQ4 What is the impact of different fidelity levels (e.g., mesh resolution and simulation time) on the accuracy and efficiency of the optimization process?
• RQ5 Can the proposed multi-fidelity framework effectively exploit the correlation between simulations of varying fidelity to improve design quality?

Key findings

• The MF-MI-Greedy method achieved a lower final figure of merit (indicating better filter performance) than GP-UCB, MF-GP-UCB, and particle swarm optimization across all tested wavelengths (550 nm, 650 nm, 750 nm).
• Despite a delayed start due to initial low-fidelity exploration, MF-MI-Greedy showed rapid convergence to high-quality solutions once exploitation in the target-fidelity space began.
• The method achieved superior performance with only 100 total evaluations at the target-fidelity cost, demonstrating effective use of the computational budget.
• The multi-fidelity approach consistently outperformed single-fidelity GP-UCB and particle swarm optimization in terms of minimizing the weighted figure of merit across all three wavelengths.
• The results confirm that leveraging low-fidelity simulations can significantly enhance optimization efficiency in nanophotonics design, especially when high-fidelity simulations are expensive.