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

We have applied machine learning in a neural network to calculate the quasi TE
₀₁₁
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 0.25–4. 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 TE
₀₁₁
mode and expresses the mode in terms of expansion coefficients of empty cavity TE
$_{\mathrm {0\,np}}$
modes, from which plots of the electric and magnetic fields can be made. The predictions are extremely quick, taking ~0.05–0.2 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%, and the overall median error of the expansion coefficients neural network is 0.003%. 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
$10\,\,000\times $
compared with FEM calculations alone. A link to the Python implementation of our FEM code and our trained neural network code is provided.