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Extreme-mass-ratio inspiral (EMRI) signals pose significant challenges in gravitational wave (GW) astronomy owing to their low-frequency nature and highly complex waveforms, which occupy a high-dimensional parameter space with numerous variables. Given their extended inspiral timescales and low signal-to-noise ratios, EMRI signals warrant prolonged observation periods. Parameter estimation becomes particularly challenging due to non-local parameter degeneracies, arising from multiple local maxima, as well as flat regions and ridges inherent in the likelihood function. These factors lead to exceptionally high time complexity for parameter analysis while employing traditional matched filtering and random sampling methods. To address these challenges, the present study applies machine learning to Bayesian posterior estimation of EMRI signals, leveraging the recently developed flow matching technique based on ODE neural networks. Our approach demonstrates computational efficiency several orders of magnitude faster than the traditional Markov Chain Monte Carlo (MCMC) methods, while preserving the unbiasedness of parameter estimation. We show that machine learning technology has the potential to efficiently handle the vast parameter space, involving up to seventeen parameters, associated with EMRI signals. Furthermore, to our knowledge, this is the first instance of applying machine learning, specifically the Continuous Normalizing Flows (CNFs), to EMRI signal analysis. Our findings highlight the promising potential of machine learning in EMRI waveform analysis, offering new perspectives for the advancement of space-based GW detection and GW astronomy.

Detecting the coalescences of massive black hole binaries (MBHBs) is one of the primary targets for space-based gravitational wave observatories such as LISA, Taiji, and Tianqin. The fast and accurate parameter estimation of merging MBHBs is of great significance for the global fitting of all resolvable sources, as well as the astrophysical interpretation of gravitational wave signals. However, such analyses usually entail significant computational costs. To address these challenges, inspired by the latest progress in generative models, we explore the application of continuous normalizing flows (CNFs) on the parameter estimation of MBHBs. Specifically, we employ linear interpolation and trig interpolation methods to construct transport paths for training CNFs. Additionally, we creatively introduce a parameter transformation method based on the symmetry in the detector's response function. This transformation is integrated within CNFs, allowing us to train the model using a simplified dataset, and then perform parameter estimation on more general data, hence also acting as a crucial factor in improving the training speed. In conclusion, for the first time, within a comprehensive and reasonable parameter range, we have achieved a complete and unbiased 11-dimensional rapid inference for MBHBs in the presence of astrophysical confusion noise using CNFs. In the experiments based on simulated data, our model produces posterior distributions comparable to those obtained by nested sampling.

Time Delay Interferometry (TDI) is an indispensable step in the whole data processing procedure of space-based gravitational wave detection, as it mitigates the overwhelming laser frequency noise, which would otherwise completely bury the gravitational wave signals. Knowledge on the inter-spacecraft optical paths (i.e. delays) is one of the key elements of TDI. Conventional method for inter-spacecraft ranging mainly relies on the pseudo-random noise (PRN) code signal modulated onto the lasers. To ensure the reliability and robustness of this ranging information, it would be highly beneficial to develop other methods which could serve as cross-validations or backups. This paper explores the practical implementation of an alternative data-driven approach - time delay interferometry ranging (TDIR) - as a ranging technique independent of the PRN signal. Distinguished from previous research, our TDIR algorithm significantly relaxes the stringent requirement for clock synchronization imposed by traditional TDI procedure. By framing TDIR as a Bayesian parameter estimation problem and employing a general polynomial parametrization, we demonstrate our algorithm with simulated data based on the numerical orbit of Taiji. In the presence of laser frequency noise and secondary noises, the estimated median values of delays are only 5.28 ns away from the ground truths, capable of suppressing laser frequency noise to the desired level. Additionally, we have also analysed the requirements of mitigating optical bench noise and clock noise on TDIR, and presented an illustrative example for the impact of laser locking.

Gravitational wave (GW) astronomy is witnessing a transformative shift from terrestrial to space-based detection, with missions like Taiji at the forefront. While the transition brings unprecedented opportunities for exploring massive black hole binaries (MBHBs), it also imposes complex challenges in data analysis, particularly in parameter estimation amidst confusion noise. Addressing this gap, we utilize scalable normalizing flow models to achieve rapid and accurate inference within the Taiji environment. Innovatively, our approach simplifies the data's complexity, employs a transformation mapping to overcome the year-period time-dependent response function, and unveils additional multimodality in the arrival time parameter. Our method estimates MBHBs several orders of magnitude faster than conventional techniques, maintaining high accuracy even in complex backgrounds. These findings significantly enhance the efficiency of GW data analysis, paving the way for rapid detection and alerting systems and enriching our ability to explore the universe through space-based GW observation., Comment: 14 pages, 7 figures. Published version

Onboard electrostatic suspension inertial sensors are important applications for gravity satellites and space gravitational wave detection missions, and it is important to suppress noise in the measurement signal. Due to the complex coupling between the working space environment and the satellite platform, the process of noise generation is extremely complex, and traditional noise modeling and subtraction methods have certain limitations. With the development of deep learning, applying it to high-precision inertial sensors to improve the signal-to-noise ratio is a practically meaningful task. Since there is a single noise sample and unknown true value in the measured data in orbit, odd-even sub-samplers and periodic sub-samplers are designed to process general signals and periodic signals, and adds reconstruction layers consisting of fully connected layers to the model. Experimental analysis and comparison are conducted based on simulation data, GRACE-FO acceleration data and Taiji-1 acceleration data. The results show that the deep learning method is superior to traditional data smoothing processing sol, Comment: 16 pages, 17 figures

Coalescing supermassive black hole binaries (SMBHBs) are the primary source candidates for low frequency gravitational wave (GW) detections, which could bring us deep insights into galaxy evolutions over cosmic time and violent processes of spacetime dynamics. Promising candidates had been found based on optical and X-ray observations, which claims for new and ready-to-use GW detection approaches before the operations of space-borne antennas. We show that, satellite laser ranging (SLR) missions could serve as probes of coalescing SMBHBs through the GW-induced resonant effects. Lasting and characteristic imprints caused by such resonances in the residual distances or accelerations from SLR measurements are studied, and the detection SNR is analyzed with both the current and future improved ranging precisions. Within redshift $z \sim 1$, the threshold SNR=5 requires 1-2 years of accumulated data for the current precision and months of data for improved precision, which are workable for the data processing of SLR missions. Meanwhile, joint detections with multiple SLR missions could further improve the total SNR and the confidence level. Such a detection scheme could fulfill the requirement of a tentative SMBHB probe during the preparing stage of LISA and Taiji, and it requires no further investment to any new and advanced facilities. It is also worthwhile to look back and re-process the archived data from the past decades, in where resonant signals from SMBHBs might be hidden., Comment: 12 pages, 10 figures

Taiji-1 is the first technology demonstration satellite of the Taiji program of China's space-borne gravitational wave antenna. After the demonstration of the key individual technologies, Taiji-1 continues collecting the data of the precision orbit determinations, satellite attitudes, and non-conservative forces exerted on the S/C. Therefore, during its free-fall, Taiji-1 can be viewed as operating in the high-low satellite-to-satellite tracking mode of a gravity recovery mission. In this work, we have selected and analyzed the one month data from Taiji-1's observations, and developed the techniques to resolve the long term interruptions and disturbances in the data due to the scheduled technology demonstration experiments. The first global gravity model \texttt{TJGM-r1911}, that independently derived from China's own satellite mission, is successfully built from Taiji-1's observations. Compared with gravity models from CHAMP and other satellite gravity missions, the accuracy discrepancies exist, which is mainly caused by the data discontinuity problem. As the extended free-falling phase been approved, Taiji-1 could serve as a gravity recovery mission for China since 2022 and it will provide us the independent measurement of both the static and the monthly time-variable global gravity field., Comment: 17 pages, 15 figures

The space-borne gravitational wave (GW) detectors, LISA and TAIJI, are planned to be launched in the 2030s. The dual detectors with comparable sensitivities will form a network observing GW with significant advantages. In this work, we investigate the three possible LISA-TAIJI networks for the different location and orientation compositions of LISA orbit ($+60^\circ$ inclination and trailing the Earth by $20^\circ$) and alternative TAIJI orbit configurations including TAIJIp ($+60^\circ$ inclination and leading the Earth by $20^\circ$), TAIJIc ($+60^\circ$ inclination and co-located with LISA), TAIJIm ($-60^\circ$ inclination and leading the Earth by $20^\circ$). In the three LISA-TAIJI configurations, the LISA-TAIJIm network shows the best performance on the sky localization and polarization determination for the massive binary system due to their better complementary antenna pattern, and LISA-TAIJIc could achieve the best cross-correlation and observe the stochastic GW background with an optimal sensitivity., Comment: 12 pages, 6 figures

In the centenary year of Einstein's General Theory of Relativity, this paper reviews the current status of gravitational wave astronomy across a spectrum which stretches from attohertz to kilohertz frequencies. Sect. 1 of this paper reviews the historical development of gravitational wave astronomy from Einstein's first prediction to our current understanding the spectrum. It is shown that detection of signals in the audio frequency spectrum can be expected very soon, and that a north-south pair of next generation detectors would provide large scientific benefits. Sect. 2 reviews the theory of gravitational waves and the principles of detection using laser interferometry. The state of the art Advanced LIGO detectors are then described. These detectors have a high chance of detecting the first events in the near future. Sect. 3 reviews the KAGRA detector currently under development in Japan, which will be the first laser interferometer detector to use cryogenic test masses. Sect. 4 of this paper reviews gravitational wave detection in the nanohertz frequency band using the technique of pulsar timing. Sect. 5 reviews the status of gravitational wave detection in the attohertz frequency band, detectable in the polarisation of the cosmic microwave background, and discusses the prospects for detection of primordial waves from the big bang. The techniques described in sects. 1-5 have already placed significant limits on the strength of gravitational wave sources. Sects. 6 and 7 review ambitious plans for future space based gravitational wave detectors in the millihertz frequency band. Sect. 6 presents a roadmap for development of space based gravitational wave detectors by China while sect. 7 discusses a key enabling technology for space interferometry known as time delay interferometry., Comment: published (2015)

The present work reports on a feasibility study commissioned by the Chinese Academy of Sciences of China to explore various possible mission options to detect gravitational waves in space alternative to that of the eLISA/LISA mission concept. Based on the relative merits assigned to science and technological viability, a few representative mission options descoped from the ALIA mission are considered. A semi-analytic Monte Carlo simulation is carried out to understand the cosmic black hole merger histories starting from intermediate mass black holes at high redshift as well as the possible scientific merits of the mission options considered in probing the light seed black holes and their coevolution with galaxies in early Universe. The study indicates that, by choosing the armlength of the interferometer to be three million kilometers and shifting the sensitivity floor to around one-hundredth Hz, together with a very moderate improvement on the position noise budget, there are certain mission options capable of exploring light seed, intermediate mass black hole binaries at high redshift that are not readily accessible to eLISA/LISA, and yet the technological requirements seem to within reach in the next few decades for China.