This award supports research in relativity and relativistic astrophysics, and it addresses the priority areas of NSF's "Windows on the Universe" Big Idea. The LIGO and Virgo instruments have recorded almost 100 gravitational wave signals during the first three observing campaigns of the advanced detector era. This treasure trove of signals is providing unique insights into the astrophysical processes that lead to the formation of black hole and neutron star binaries. When the detectors resume operations in late 2022 or early 2023, new detections are expected be made on an almost daily basis. In addition to increasing the rate at which binary mergers are detected, the increased sensitivity of the instruments will improve the chances of detecting more exotic signals. The enhanced low frequency sensitivity will also mean that signals will be detectable for longer, which increases the chances that noise transients and fluctuations in the noise level will impact the signals. The goals of this project are threefold: significantly improve the processing speed to keep up with the deluge of events; develop new tools to detect and explore exotic signals; and develop new tools to account for noise transients and varying noise levels. The research projects described offer tremendous opportunities for graduate and undergraduate students: the blend of creative activities associated with the development of sophisticated and innovative data analysis techniques, combined with hands on exposure to running existing search pipelines and working with production level computer code will provide excellent training for the next generation of gravitational wave astronomers. These skills are transferable and highly sought after in other fields and in industry.<br/><br/>The most recent LIGO and Virgo observation campaign has emphasized the need for faster signal processing and more robust noise modeling. As the number of detections increases, we are starting to see more extreme systems that push the limits of the signal models used in the analyses. We are also seeing an ever increasing number of signals that were impacted by instrument noise transients (glitches). As the low frequency sensitivity of the detectors improves, the time that the signals are detectable will increase, which further increases the chances that noise transients and drifts in the noise floor will impact the analyses. The proposed research will develop new signal reconstruction techniques that can be used to detect and characterize exotic, un-modeled or poorly understood signals. This technique is especially well suited for detecting deviations from general relativity, and for extracting the post-merger signal from neutron star mergers. The post-merger signal can be used to reveal the interior composition of the merger remnant, and provide important insights into the behavior of matter at super-nuclear densities. Additionally, advanced noise modeling techniques will be deployed that can robustly model non-stationary and non-Gaussian noise. These advances will be combined with fast signal processing techniques that dramatically speed up the analyses, allowing for joint inference of gravitational wave signals, noise transients and non-stationary drifts in the noise floor in minutes, as opposed to the O3 analyses which took days or weeks for each event. Finally, a new algorithm for low latency glitch removal will be implemented that can safely clean the LIGO-Virgo data of noise transients. Real-time glitch removal will be especially important for longer duration signals, such as binary neutron star mergers, as the odds of encountering a glitch grow with the duration of the signal.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.