arXiv subjects

Anand S. Sengupta

Publications and source records attributed to Anand S. Sengupta.

At least 19 recordsLinked to original sources

arXiv2026

Fast Bayesian Inference for Long-Duration Gravitational-Wave Signals in 3G detectors

Third-generation (3G) gravitational-wave detectors will observe binary-neutron-star inspirals for nearly a day, so Earth's rotation becomes part of the signal rather than a negligible correction. This destroys the usual separation between intrinsic and extrinsic parameters and creates a major computational bottleneck for Bayesian inference. We show that the exact five-harmonic Jaranowski-Krolak-Schutz (JKS) decomposition restores the separation of the rotating antenna amplitude response from the computationally expensive intrinsic waveform calculations. By sampling the intrinsic waveform on a frequency grid set by its phase curvature and then applying error-controlled relative binning, likelihood evaluations for a 21.3-h signal are accelerated by O(10^4), making day-long 3G signal inference practical.

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arXiv2026

Stochastic template banks for GW searches using low-discrepancy sequences

Matched filtering remains the most sensitive method for detecting gravitational waves from compact binary coalescences. The efficiency of such searches depends on how well a discrete template bank covers the underlying parameter space. Conventional geometric, stochastic, and hybrid placement methods can lead to uneven coverage and redundant templates in higher dimensions. Hybrid methods are generally the most efficient among these, while stochastic methods are simpler to implement, particularly when the parameter-space metric is difficult to compute. In practice, both approaches rely on uniform random sampling, which often requires a large number of proposal points to achieve adequate coverage. We find that stochastic template banks constructed using low-discrepancy sequences achieve comparable recovery fractions while requiring 27.5\% fewer proposal points in two dimensions and 12\% fewer in three dimensions. The final template count changes only marginally ($\sim 1\%$), consistent with the metric-volume constraints of the covering problem. The primary benefit of low-discrepancy sampling is therefore a reduction in the size of the initial proposal set, leading to lower memory usage and reduced bookkeeping during bank generation. Since the final template count is governed mainly by the metric volume of the target parameter space, the wall-clock speed-up is more modest than the reduction in proposal count. Nevertheless, low-discrepancy sampling provides a simple and scalable improvement to stochastic template-bank generation for current and future gravitational-wave searches.

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arXiv2026

Probing missing physics from inspiralling compact binaries via time-frequency tracks

The orbital evolution of binary black hole (BBH) systems is determined by the component masses and spins of the black holes and the governing gravity theory. Gravitational wave (GW) signals from the evolution of BBH orbits offer an unparalleled opportunity for examining the predictions of General Relativity (GR) and for searching for missing physics in the current waveform models. We present a method of stacking up the time-frequency pixel energies through the orbital frequency evolution with the flexibility of gradually shifting the orbital frequency curve along the frequency axis. We observe a distinct energy peak corresponding to the GW signal's quadrupole mode. If an alternative theory of gravity is considered and the analysis of the BBH orbital evolution is executed following GR, the energy distribution on the time-frequency plane will be significantly different. We propose a new consistency test to check whether our theoretical waveform explains the BBH orbital evolution. Through the numerical simulation of beyond-GR theory of gravity and utilizing the framework of second-generation interferometers, we demonstrate the efficiency of this new method in detecting any possible departure from GR. Finally, when applied to an eccentric BBH system and GW190814, which shows the signatures of higher-order multipoles, our method provides an exquisite probe of missing physics in the GR waveform models.

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arXiv2026

IndIGO-D: Probing Compact Binary Coalescences in the Decihertz GW Band

We study IndIGO-D, a decihertz gravitational-wave mission concept, focusing on a specific configuration in which three spacecraft fly in formation to form an L-shaped interferometer in a heliocentric orbit. The two orthogonal arms share a common vertex, providing a space-based analogue of terrestrial Michelson detectors, while operating in an optimised configuration that yields ppm-level arm-length stability. Assuming 1000 km arm length, we analyse the orbital motion and antenna response, and assess sensitivity across the [0.1 - 10] Hz band bridging LISA and next-generation ground-based interferometers. Using fiducial sensitivity curves provided by the IndIGO-D collaboration, we compute horizon distances for different source classes. Intermediate-mass black-hole binaries with masses $10^{2}$ - $10^{3} \, M_\odot$ are detectable to redshifts $z \sim 10^{3}$, complementing the reach of LISA and terrestrial detectors. Binary neutron star systems are observable to a horizon distance of $z \lesssim 0.3$, allowing continuous multi-band coverage with Voyager-class interferometers from the decihertz regime to merger. A Bayesian parameter-estimation study of a GW170817-like binary shows that the sky localization area improves from $\sim 21 \,\mathrm{deg}^2$ at one month to $0.3 \,\mathrm{deg}^2$ at six hours pre-merger! These sky areas are readily tiled by wide-field time-domain telescopes such as the Rubin Observatory, whose $9.6 \,\mathrm{deg}^2$ field of view and r-band depth enable high-cadence, repeated coverage of GW170817-like kilonovae at this distance and beyond. IndIGO-D exploits the rapid evolution of binaries in the decihertz band to bridge the gap between millihertz and terrestrial observations, enabling early warnings on timescales from months to hours and enhancing the prospects for multi-band and multi-messenger discoveries.

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arXiv2025

Rapid parameter estimation with the full symphony of compact binary mergers using meshfree approximation

We present a fast Bayesian inference framework to address the growing computational cost of gravitational-wave parameter estimation. The increased cost is driven by improved broadband detector sensitivity, particularly at low frequencies due to advances in detector commissioning, resulting in longer in-band signals and a higher detection rate. Waveform models now incorporate features like higher-order modes, further increasing the complexity of standard inference methods. Our framework employs meshfree likelihood interpolation with radial basis functions to accelerate Bayesian inference using the IMRPhenomXHM waveform model that incorporates higher modes of the gravitational-wave signal. In the initial start-up stage, interpolation nodes are placed within a constant-match metric ellipsoid in the intrinsic parameter space. During sampling, likelihood is evaluated directly using the precomputed interpolants, bypassing the costly steps of on-the-fly waveform generation and overlap-integral computation. We improve efficiency by sampling in a rotated parameter space aligned with the eigenbasis of the metric ellipsoid, where parameters are uncorrelated by construction. This speeds up sampler convergence. This method yields unbiased parameter recovery when applied to 100 simulated neutron-star-black-hole signals (NSBH) in LIGO-Virgo data, while reducing computational cost by up to an order of magnitude for the longest-duration signal. The meshfree framework equally applies to symmetric compact binary systems dominated by the quadrupole mode, supporting parameter estimation across a broad range of sources. Applied to a simulated NSBH signal in Einstein Telescope data, where the effects of Earth's rotation are neglected for simplicity, our method achieves an O(10^4) speed-up, demonstrating its potential use in the third-generation (3G) era.

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arXiv2025

Probing dark matter halo profiles with multi-band observations of gravitational waves

In this paper, we evaluate the potential of multiband gravitational wave observations from a deci-Hz space-based detector and third-generation ground-based gravitational wave detectors to constrain the properties of dark matter spikes around intermediate-mass ratio inspirals. The presence of dark matter influences the orbital evolution of the secondary compact object through dynamic friction, which leads to a phase shift in the gravitational waveform compared to the vacuum case. Our analysis shows that the proposed Indian space-based detector GWSat, operating in the deciHz frequency band, provides the most stringent constraints on the dark matter spike parameters, as IMRIs spend a significant portion of their inspiral phase within its sensitivity range. While third-generation ground-based detectors such as the Einstein Telescope and Cosmic Explorer offer additional constraints, their contribution is somewhat limited, particularly for higher-mass systems where the signal duration in their frequency bands is shorter. However, for systems with detector-frame total masses $M_z < 400 \rm M_{\odot}$, Cosmic Explorer and Einstein Telescope could improve the estimation of the chirp mass, symmetric mass ratio, luminosity distance, and dark matter spike power-law index by more than $15\%$. Nonetheless, their impact on the constraint of spike density is minimal. These results highlight the crucial role of deciHz space-based detectors in probing dark matter interactions with gravitational wave sources.

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arXiv2025

Accelerated parameter estimation of supermassive black hole binaries in LISA using a meshfree approximation

The Laser Interferometer Space Antenna (LISA) will be capable of detecting gravitational waves (GWs) in the milli-Hertz band. Among various sources, LISA will detect the coalescence of supermassive black hole binaries (SMBHBs). Accurate and rapid inference of parameters for such sources will be important for potential electromagnetic follow-up efforts. Rapid Bayesian inference with LISA includes additional complexities as compared to current generation terrestrial detectors in terms of time and frequency dependent antenna response functions. In this work, we extend a recently developed, computationally efficient technique that uses meshfree interpolation methods to accelerate Bayesian reconstruction of compact binaries. Originally developed for second-generation terrestrial detectors, this technique is now adapted for LISA parameter estimation. Using the full inspiral, merger, and ringdown waveform (PhenomD) and assuming rigid adiabatic antenna response function, we show faithful inference of SMBHB parameters from GW signals embedded in stationary, Gaussian instrumental noise. We discuss the computational cost and performance of the meshfree approximation method in estimating the GW source parameters.

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arXiv2024

Fast and faithful interpolation of numerical relativity surrogate waveforms using meshfree approximation

Several theoretical waveform models have been developed over the years to capture the gravitational wave emission from the dynamical evolution of compact binary systems of neutron stars and black holes. As ground-based detectors improve their sensitivity at low frequencies, the real-time computation of these waveforms can become computationally expensive, exacerbating the steep cost of rapidly reconstructing source parameters using Bayesian methods. This paper describes an efficient numerical algorithm for generating high-fidelity interpolated compact binary waveforms at an arbitrary point in the signal manifold by leveraging computational linear algebra techniques such as singular value decomposition and meshfree approximation. The results are presented for the time-domain \texttt{NRHybSur3dq8} inspiral-merger-ringdown (IMR) waveform model that is fine tuned to numerical relativity simulations and parameterized by the two component-masses and two aligned spins. For demonstration, we target a specific region of the intrinsic parameter space inspired by the previously inferred parameters of the \texttt{GW200311\_115853} event -- a binary black hole system whose merger was recorded by the network of advanced-LIGO and Virgo detectors during the third observation run. We show that the meshfree interpolated waveforms can be evaluated in $\sim 2.3$ ms, which is about $\times 38$ faster than its brute-force (frequency-domain tapered) implementation in the \textsc{PyCBC} software package at a median accuracy of $\sim \mathcal{O}(10^{-5})$. The algorithm is computationally efficient and scales favourably with an increasing number of dimensions of the parameter space. This technique may find use in rapid parameter estimation and source reconstruction studies.

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arXiv2024

Template bank to search for exotic gravitational wave signals from astrophysical compact binaries

Modeled searches of gravitational wave signals from compact binary mergers rely on template waveforms determined by the theory of general relativity (GR). Once a signal is detected, one generally performs the model agnostic test of GR, either looking for consistency between the GR waveform and data or introducing phenomenological deviations to detect the departure from GR. The non-trivial presence of beyond-GR physics can alter the waveform and could be missed by the GR template-based searches. A recent study [Phys. Rev. D 107, 024017 (2023)] targeted the binary black hole merger, assuming the parametrized deviation in lower post-Newtonian terms and demonstrated a mild effect on the search sensitivity. Surprisingly, for the search space of binary neutron star (BNS) systems where component masses range from 1 to $2.4\:\rm{M}_\odot$ and parametrized deviations span $1σ$ width of the deviation parameters measured from the GW170817 event, the GR template bank is highly ineffectual for detecting the non-GR signals. Here, we present a new hybrid method to construct a non-GR template bank for the BNS search space. The hybrid method uses the geometric approach of three-dimensional lattice placement to cover most of the parameter space volume, followed by the random method to cover the boundary regions of parameter space. We find that the non-GR bank size is $\sim$15 times larger than the conventional GR bank and is effectual towards detecting non-GR signals in the target search space.

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arXiv2024

Pinpointing coalescing binary neutron star sources with the IGWN, including LIGO-Aundha

LIGO-Aundha (A1), the Indian gravitational wave detector, is expected to join the IGWN and begin operations in the early 2030s. We study the impact of A1 on the accuracy of determining the direction of incoming transient signals from coalescing BNS sources with moderately high SNRs. It is conceivable that A1's sensitivity, effective bandwidth, and duty cycle will improve incrementally through multiple detector commissioning rounds to achieve the desired `LIGO-A+' design sensitivity. For this purpose, we examine A1 under two distinct noise PSDs. One mirrors the conditions during the O4 run of the LIGO Hanford and Livingston detectors, simulating an early commissioning stage, while the other represents the A+ design sensitivity. We consider various duty cycles of A1 at the sensitivities mentioned above for a comprehensive analysis. We show that even at the O4 sensitivity with a modest $20\%$ duty cycle, A1's addition to the IGWN leads to a $15\%$ reduction in median sky-localization errors ($ΔΩ_{90\%}$) to $5.6$~sq.~deg. At its design sensitivity and $80\%$ duty cycle, this error shrinks further to $2.4$~sq.~deg, with 84\% sources localized within a nominal error box of $10$~sq.~deg! Even in the worst-case scenario, where signals are sub-threshold in A1, we demonstrate its critical role in reducing the localization uncertainties of the BNS source. Our results are obtained from a large Bayesian PE study using simulated signals injected in a heterogeneous network of detectors using the recently developed meshfree approximation aided rapid Bayesian inference pipeline. We consider a seismic cut-off frequency of 10 Hz for all the detectors. We also present hypothetical improvements in sky localization for a few GWTC-like events injected in real data and demonstrate A1's role in resolving the degeneracy between the luminosity distance and inclination angle parameters.

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arXiv2024

Prompt sky localization of compact binary sources using a meshfree approximation

The number of gravitational wave signals from the merger of compact binary systems detected in the network of advanced LIGO and Virgo detectors is expected to increase considerably in the upcoming science runs. Once a confident detection is made, it is crucial to reconstruct the source's properties rapidly, particularly the sky position and chirp mass, to follow up on these transient sources with telescopes operating at different electromagnetic bands for multi-messenger astronomy. In this context, we present a rapid parameter estimation (PE) method aided by mesh-free approximations to accurately reconstruct properties of compact binary sources from data gathered by a network of gravitational wave detectors. This approach builds upon our previous algorithm [L. Pathak et al., Fast likelihood evaluation using meshfree approximations for reconstructing compact binary sources, https://journals.aps.org/prd/abstract/10.1103/PhysRevD.108.064055, Phys. Rev. D 108, 064055 (2023)] to expedite the evaluation of the likelihood function and extend it to enable coherent network PE in a ten-dimensional parameter space, including sky position and polarization angle. Additionally, we propose an optimized interpolation node placement strategy during the start-up stage to enhance the accuracy of the marginalized posterior distributions. With this updated method, we can estimate the properties of binary neutron star (BNS) sources in approximately 2.4~(2.7) min for the \TaylorF~(\texttt{IMRPhenomD}) signal model by utilizing 64 CPU cores on a shared memory architecture. Furthermore, our approach can be integrated into existing parameter estimation pipelines, providing a valuable tool for the broader scientific community. We also highlight some areas for improvements to this algorithm in the future, which includes overcoming the limitations due to narrow prior bounds.

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arXiv2023

Does the speed of gravitational waves depend on the source velocity?

The second postulate of special relativity states that the speed of light in vacuum is independent of the emitter's motion. The test of this postulate so far remains unexplored for gravitational radiation. We analyze data from the LIGO-Virgo detectors to test this postulate within the ambit of a model where the speed of the emitted GWs ($c'$) from a binary depends on a characteristic velocity $\tilde{v}$ proportional to that of the reduced one-body system as $c' = c + k\, \tilde{v}$, where $k$ is a constant. We have estimated the upper bound on the 90\% credible interval over $k$ to be ${k \leq 8.3 \times {10}^{-18}}$, which is several orders of magnitude more stringent compared to previous bounds obtained from electromagnetic observations. The Bayes' factor supports the second postulate with a strong evidence that the data is consistent with the null hypothesis $k = 0$, upholding the principle of relativity for gravitational interactions.

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arXiv2023

Fast likelihood evaluation using meshfree approximations for reconstructing compact binary sources

Several rapid parameter estimation methods have recently been advanced to deal with the computational challenges of the problem of Bayesian inference of the properties of compact binary sources detected in the upcoming science runs of the terrestrial network of gravitational wave detectors. Some of these methods are well-optimized to reconstruct gravitational wave signals in nearly real-time necessary for multi-messenger astronomy. In this context, this work presents a new, computationally efficient algorithm for fast evaluation of the likelihood function using a combination of numerical linear algebra and mesh-free interpolation methods. The proposed method can rapidly evaluate the likelihood function at any arbitrary point of the sample space at a negligible loss of accuracy and is an alternative to the grid-based parameter estimation schemes. We obtain posterior samples over model parameters for a canonical binary neutron star system by interfacing our fast likelihood evaluation method with the nested sampling algorithm. The marginalized posterior distributions obtained from these samples are statistically identical to those obtained by brute force calculations. We find that such Bayesian posteriors can be determined within a few minutes of detecting such transient compact binary sources, thereby improving the chances of their prompt follow-up observations with telescopes at different wavelengths. It may be possible to apply the blueprint of the meshfree technique presented in this study to Bayesian inference problems in other domains.

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arXiv2022

Beyond general relativity: designing a template-based search for exotic gravitational wave signals

Accurate waveform models describing the complete evolution of compact binaries are crucial for the maximum likelihood detection framework, testing the predictions of General Relativity (GR) and investigating the possibility of an alternative theory of gravity. Deviations from GR could manifest in subtle variations of the numerical value of the GW signal's post-Newtonian (PN) phasing coefficients. Once the search pipelines confirm an unambiguous signal detection, deviations of the signal phasing coefficients at various PN orders are routinely measured and reported. As the search templates themselves do not incorporate any deviations from GR, they may miss astrophysical signals carrying a significant departure from general relativity. We present a parametrized template-based search for exotic gravitational-wave signals beyond General Relativity by incorporating deviations to the signal's phasing coefficients at different post-Newtonian orders in the search templates. We present critical aspects of the new search, such as improvements in search volume and its effect on various parts of the parameter space. In particular, we demonstrate a factor x2 increase in search sensitivity (at a fixed false-alarm rate) to beyond-GR exotic signals by using search templates that admit a range of departures from general relativity. We also present the results from a re-analysis of the 10-days long duration of LIGO's O1 data, including the epoch of the GW150914 event, highlighting the differences from a standard search. We indicate several directions for future research, including ways of making the proposed new search computationally more efficient.

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arXiv2021

Random projections in gravitational-wave searches from compact binaries II: efficient reconstruction of the detection statistic

Low-latency gravitational wave search pipelines such as GstLAL take advantage of low-rank factorization of the template matrix via singular value decomposition (SVD). With unprecedented improvements in detector bandwidth and sensitivity in advanced-LIGO and Virgo detectors, one expects several orders of magnitude increase in the size of template banks. This poses a formidable computational challenge in factorizing huge template matrices. Previously, [in Kulkarni et al. [6]], we introduced the idea of random projection (RP)-based matrix factorization as a computationally viable alternative to SVD, applicable for large template banks. This follow-up paper demonstrates the application of a block-wise randomized matrix factorization (RMF) algorithm for computing low-rank factorizations at a preset average fractional loss of SNR. This new scheme is shown to be more efficient in the context of the LLOID framework of the GstLAL search pipeline. Further, it is well-known that for huge template banks, the total computational cost of the search is dominated by reconstructing the detection statistic compared to that of filtering the data. However, optimizing the reconstruction cost has not been addressed satisfactorily so far in the available literature. We show that it is possible to approximately reconstruct the time-series of the matched-filter detection statistic at a fraction of the total cost using the matching pursuit algorithm. Combining the two algorithms presented in this paper can handle online searches involving large template banks more efficiently. We have analyzed the total computational cost in detail and offer various tips for optimally applying the RMF scheme in different parts of the parameter space. The algorithms presented in this paper are designed in a suitable manner that can be efficiently implemented over a distributed computing architecture.

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arXiv2021

The SPIIR online coherent pipeline to search for gravitational waves from compact binary coalescences

This paper presents the SPIIR pipeline used for public alerts during the third advanced LIGO and Virgo observation run (O3 run). The SPIIR pipeline uses infinite impulse response (IIR) filters to perform extremely low-latency matched filtering and this process is further accelerated with graphics processing units (GPUs). It is the first online pipeline to select candidates from multiple detectors using a coherent statistic based on the maximum network likelihood ratio statistic principle. Here we simplify the derivation of this statistic using the singular-value-decomposition (SVD) technique and show that single-detector signal-to-noise ratios from matched filtering can be directly used to construct the statistic for each sky direction. Coherent searches are in general more computationally challenging than coincidence searches due to extra search over sky direction parameters. The search over sky directions follows an embarrassing parallelization paradigm and has been accelerated using GPUs. The detection performance is reported using a segment of public data from LIGO-Virgo's second observation run. We demonstrate that the median latency of the SPIIR pipeline is less than 9 seconds, and present an achievable roadmap to reduce the latency to less than 5 seconds. During the O3 online run, SPIIR registered triggers associated with 38 of the 56 non-retracted public alerts. The extreme low-latency nature makes it a competitive choice for joint time-domain observations, and offers the tantalizing possibility of making public alerts prior to the merger phase of binary coalescence systems involving at least one neutron star.

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arXiv2021

Unveiling the spectrum of inspiralling binary black holes

The higher-multipoles of gravitational wave signals from coalescing compact binaries play a vital role in the accurate reconstruction of source properties, bringing about a deeper and nuanced understanding of fundamental physics and astrophysics. Their effect is most pronounced in systems with asymmetric masses having an orbital geometry that is not face-on. The detection of higher-multipoles of GW signals from any single, isolated merger event is challenging, as there is much less power in comparison to the dominant quadrupole mode. In this paper, we present a new method for their detection by combining multiple events observed in interferometric gravitational wave detectors. Sub-dominant modes present in (the inspiral part of) the signal from separate events are stacked using time-frequency spectrogram of the data. We demonstrate that this procedure enhances the signal-to-noise ratio of the higher-multipole components and thereby leads to increased chances of their detection. From Monte-Carlo simulations, we estimate that a combination of $\sim 100$ events observed in two-detector coincidence can lead to the detection of the higher-multipole components with a $\geq$ 95\% detection probability. The advanced-LIGO detectors are expected to record these many binary black hole merger events within a month of operation at design sensitivity. We also present results from the analysis of data from O1 and O2 science runs containing previously detected events using our new method.

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arXiv2019

Random projections in gravitational wave searches of compact binaries

Random projection (RP) is a powerful dimension reduction technique widely used in the analysis of high dimensional data. We demonstrate how this technique can be used to improve the computational efficiency of gravitational wave searches from compact binaries of neutron stars or black holes. Improvements in low-frequency response and bandwidth due to detector hardware upgrades pose a data analysis challenge in the advanced LIGO era as they result in increased redundancy in template databases and longer templates due to the higher number of signal cycles in-band. The RP-based methods presented here address both these issues within the same broad framework. We first use RP for an efficient, singular value decomposition inspired template matrix factorization and develop a geometric intuition for why this approach works. We then use RP to calculate approximate time-domain match correlations in a lower dimensional vector space. For searches over parameters corresponding to non-spinning binaries with a neutron star and a black hole, a combination of the two methods can reduce the total on-line computational cost by an order of magnitude over a nominal baseline. This can, in turn, help free-up computational resources needed to go beyond current spin-aligned searches to more complex ones involving generically spinning waveforms.

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