Subtracting and Monitoring Tilt-to-length Noise under High Differential Wavefront Sensing Noise Using Convolutional Neural Networks and Time Delay Interferometry

Abstract Gravitational waves (GWs) provide a powerful tool to probe energetic astrophysical events and test fundamental physics, with space-based detectors enabling access to low-frequency signals from massive black hole mergers, extreme mass-ratio inspirals, and other sources. However, the sensitivity of space-based interferometers can be severely compromised by tilt-to-length (TTL) coupling noise, which contaminates phase measurements by converting angular jitter into apparent path length fluctuations. This problem is exacerbated when differential wave front sensing (DWS) systems suffer from high readout noise due to optical misalignments and wave front aberrations. In this work, we introduce a novel framework that integrates convolutional neural networks (CNNs) with time delay interferometry (TDI) to improve the robustness of TTL coupling coefficient estimation under high-noise conditions. The CNN is trained to identify and exclude DWS angular measurements corrupted by noise, while the TDI module adaptively selects optimal combinations that minimize TTL-induced contamination. In addition, an analytical error-based monitoring algorithm is incorporated to track the stability of TTL coefficients. When coefficients remain within their nominal range, the predicted uncertainty band covers the true values, while abrupt excursions beyond the monitoring threshold can be reliably detected. Simulations demonstrate that our method maintains TTL coefficient errors below 0.1 mm rad −1 for the coefficients associated with the selected TDI combination even under degraded DWS readout conditions, while simultaneously providing monitoring bands that capture excursions up to tens of millimeters per radian in agreement with analytical predictions. Our approach ensures that space-based detectors remain effective in resolving weak astrophysical signals despite actual measurement imperfections.