Predicting the black hole mass and correlations in X-ray reverberating AGN using neural networks

We develop neural network models to predict the black hole mass using 22 reverberating AGN samples in the XMM-Newton archive. The model features include the fractional excess variance ($F_{\rm var}$) in 2-10 keV band, Fe-K lag amplitude, 2-10 keV photon counts and redshift. We find that the prediction accuracy of the neural network model is significantly higher than what is obtained from the traditional linear regression method. Our predicted mass can be confined within $\pm (2$-5) per cent of the true value, suggesting that the neural network technique is a promising and independent way to constrain the black hole mass. We also apply the model to 21 non-reverberating AGN to rule out their possibility to exhibit the lags (some have too small mass and $F_{\rm var}$, while some have too large mass and $F_{\rm var}$ that contradict the $F_{\rm var}$-lag-mass relation in reverberating AGN). We also simulate 3200 reverberating AGN samples using the multi-feature parameter space from the neural network model to investigate the global relations if the number of reverberating AGN increases. We find that the $F_{\rm var}$-mass anti-correlation is likely stronger with increasing number of newly-discovered reverberating AGN. Contrarily, to maintain the lag-mass scaling relation, the tight anti-correlation between the lag and $F_{\rm var}$ must preserve. In an extreme case, the lag-mass correlation coefficient can significantly decrease and, if observed, may suggest the extended corona framework where their observed lags are more driven by the coronal property rather than geometry.