Determining the optimal learning rate in gradient-based electromagnetic optimization using the Shanks transformation...

Area of Science:

• Photonics
• Computational electromagnetics
• Optimization algorithms

Background:

• Gradient-based optimization is crucial for designing photonic devices.
• Efficient determination of the search direction is established using the adjoint variable method.
• An efficient method for determining the optimal learning rate in line searches is lacking.

Purpose of the Study:

• To introduce an efficient algorithm for determining the optimal learning rate in gradient-based photonic device optimization.
• To enhance the accuracy and performance of photonic device designs.

Main Methods:

• The study employs the Shanks transformation within the Lippmann-Schwinger formalism.
• An iterative line search in a one-dimensional subspace is performed.
• The adjoint variable method is used for determining the search direction.

Main Results:

• The proposed algorithm accurately determines optimal learning rates at each epoch.
• This method achieves this with only a modest increase in computational cost.
• Significant improvements in the figure of merits of the final photonic structures were observed.

Conclusions:

• The developed algorithm efficiently finds optimal learning rates for gradient-based photonic device optimization.
• This approach offers a significant improvement over conventional learning rate estimation methods.
• The method enhances the overall performance of designed photonic devices.