Machine Learning for Nanohertz Gravitational Wave Detection and Parameter Estimation with Pulsar Timing Array

Studies have shown that the use of pulsar timing arrays (PTAs) is among the approaches with the highest potential to detect very low-frequency gravitational waves in the near future. Although the capture of gravitational waves (GWs) by PTAs has not been reported yet, many related theoretical studies and some meaningful detection limits have been reported. In this study, we focused on the nanohertz GWs from individual supermassive binary black holes. Given specific pulsars (PSR J1909$-$3744, PSR J1713$+$0747, PSR J0437$-$4715), the corresponding GW$-$induced timing residuals in PTAs with Gaussian white noise can be simulated. Further, we report the classification of the simulated PTA data and parameter estimation for potential GW sources using machine learning based on neural networks. As a classifier, the convolutional neural network shows high accuracy when the combined signal to noise ratio $\geq$1.33 for our simulated data. Further, we applied a recurrent neural network to estimate the chirp mass ($\mathcal{M}$) of the source and luminosity distance ($\text{D}_{p}$) of the pulsars and Bayesian neural networks (BNNs) to obtain the uncertainties of chirp mass estimation. Knowledge of the uncertainties is crucial to astrophysical observation. In our case, the mean relative error of chirp mass estimation is less than $13.6\%$. Although these results are achieved for simulated PTA data, we believe that they will be important for realizing intelligent processing in PTA data analysis.