Multimode Sensing in a Whispering Gallery Mode Resonator Enabled by Transfer Machine Learning

It is interesting to explore the sensing applications of the numerous of resonance modes in whispering gallery mode (WGM) optical microresonators. Conventional supervised machine learning models have been applied to merge sensing information from a substantial number of WGMs. However, it becomes an important challenge in real-world applications, where only a small amount of online measurement target data are available. In this article, we introduce a transfer machine learning (TML) model, namely, the fuzzy-set-based joint distribution adaptation (FJDA) method, designed for precise temperature prediction using a limited quantity of online measurement target data. This method transforms continuous temperature labels into fuzzy class labels, addressing the issue of traditional joint distribution adaptation (JDA) algorithms being unsuitable for regression tasks. In the experiment, utilizing a temperature sensor based on a WGM resonator, two distinct sets of spectral data are obtained when applying two different input energies to excite the resonator. These two sets of data are, respectively, designated as online target data and offline source data. The proposed FJDA method aims to minimize feature disparities between a limited amount of online target data and a substantial amount of offline source data. It leverages the abundant labeled offline source data to construct an accurate predictor for the unlabeled online target data. The TML method demonstrates a temperature prediction with a mean squared error (MSE) of
$7.86\times 10^{-{4}}$
across the temperature range of 0.5 °C. This demonstrates a 93.5% reduction compared with the result achieved with the conventional supervised regression model, especially in scenarios involving limited online target data.