Machine Learning to Predict Quasi TE₀₁₁ Mode Resonances in Double-Stacked Dielectric Cavities

Abstract

We have applied machine learning in a neural network to calculate the quasi TE₀₁₁ mode of a cylindrical microwave cavity with two symmetrically stacked dielectric resonators (DRs) inside, with aspect ratios of the overall cavity being limited to the range of 0.25&#x2013;4. The neural network was trained with 99 970 samples and evaluated using 9564 samples from a holdout dataset. The samples were created using a supercomputer to solve random cavity configurations via finite-element method (FEM) programming. The trained neural network predicts the resonant frequency of the quasi TE₀₁₁ mode and expresses the mode in terms of expansion coefficients of empty cavity TE<inline-formula> <tex-math notation="LaTeX">$_{\mathrm {0\,np}}$ </tex-math></inline-formula> modes, from which plots of the electric and magnetic fields can be made. The predictions are extremely quick, taking &#x007E;0.05&#x2013;0.2 s running on a typical personal computer, and are very accurate when judged against the FEM results: the overall median error in the frequency neural network is 0.2&#x0025;, and the overall median error of the expansion coefficients neural network is 0.003&#x0025;. This should allow designers to much more rapidly determine optimal cavity and DR dimensions and other parameters in order to achieve the frequency and mode they desire, with a speedup of approximately <inline-formula> <tex-math notation="LaTeX">$10\,\,000\times $ </tex-math></inline-formula> compared with FEM calculations alone. A link to the Python implementation of our FEM code and our trained neural network code is provided.