Nonlinear noise regression in gravitational-wave detectors with convolutional neural networks

Currently, the sub-60 Hz sensitivity of gravitational-wave (GW) detectors like Advanced LIGO is limited by the control noises from auxiliary degrees of freedom, which nonlinearly couple to the main GW readout. One particularly promising way to tackle this contamination is to perform nonlinear noise mitigation using machine-learning-based convolutional neural networks (CNNs), which we examine in detail in this study. As in many cases the noise coupling is bilinear and can be viewed as a few fast channels' outputs modulated by some slow channels, we show that we can utilize this knowledge of the physical system and adopt an explicit "slow$\times$fast" structure in the design of the CNN to enhance its performance of noise subtraction. We then examine the requirement in the signal-to-noise ratio (SNR) in both the target channel (i.e., the main GW readout) and in the auxiliary sensors in order to reduce the noise by at least a factor of a few. In the case of limited SNR in the target channel, we further demonstrate that the CNN can still reach a good performance if we adopt curriculum learning techniques, which in reality can be achieved by combining data from quiet times and those from periods with active noise injections.