Tracing gravitational waves by integrating wavelet, PCA and clustering analysis using pulsar timing array data

Pulsar Timing Arrays (PTAs) are a powerful tool to trace gravitational waves (GWs) signatures in the nanohertz frequency range by precisely monitoring timing residuals of millisecond pulsars. This study explores advancements in PTA methodologies, emphasizing machine learning (ML) techniques, wavelet analysis, and cross-correlation studies to enhance sensitivity to GW signals. Using data from the Indian Pulsar Timing Array (InPTA), we apply Principal Component Analysis (PCA), clustering algorithms, and wavelet-based time-frequency decomposition to improve the detection of the Stochastic Gravitational Wave Background (SGWB).Our analysis reveals a strong correlation (Pearson r = 0.872) between measured pulsar timing residuals and the Hellings-Downs curve, supporting the presence of an SGWB signal. Wavelet decomposition identifies significant low-frequency power, suggesting persistent timing residual structures consistent with GW signatures. PCA indicates that the first component captures ∼84.3% of the variance, highlighting a dominant common signal among pulsars. Clustering analysis reveals distinct pulsar groups, with some showing enhanced correlated noise features, likely linked to GW-induced fluctuations. Additionally, the estimated GW amplitude and spectral index for individual pulsars further reinforce the presence of a stochastic background. These findings demonstrate the effectiveness of dimensionality reduction and clustering techniques in isolating astrophysical signals, enhancing the reliability of GW detection. Our results provide strong support for the existence of an SGWB and showcase the potential of integrating machine learning with traditional pulsar timing analyses to refine GW detection strategies.