arXiv subjects

Tonghua Liu

Publications and source records attributed to Tonghua Liu.

At least 19 recordsLinked to original sources

arXiv2026

Probing Dark Matter Substructure with Wave-Optics Distortions of Strongly Lensed LISA Gravitational Waves

Strong lensing changes the phase of a gravitational-wave signal as well as its amplitude and arrival time. We study whether this phase information can distinguish between three dark-matter structures in the lens: a Navarro--Frenk--White halo (NFW), a self-interacting dark matter (SIDM) halo, and a fuzzy-dark-matter field (FDM). We generate waveforms for the detectable lensed massive-black-hole-binary population of a four-year LISA mission and fit every signal with the same smooth singular-isothermal-ellipsoid lens with external shear. In 132 lens systems, 311 images are resolved as separate signals in time. NFW and SIDM produce real waveform changes, but their slowly varying part is largely degenerate with the constant, gradient, and Hessian of the smooth Fermat potential at the image. The coherent density fluctuations of FDM leave a larger frequency-dependent residual after this fit. The NFW--FDM and SIDM--FDM populations become distinguishable with about 60 and 110 resolved image waveforms, respectively. These results show that repeated lensed LISA signals can probe the spatial form of dark matter in lens galaxies, rather than only the total lensing mass.

astro-ph.CO↗

arXiv2026

Late-time cosmological constraints on three holographic dark energy models with DESI DR2 BAO and Type Ia supernovae

We constrain three holographic-inspired dark energy models, namely holographic dark energy (HDE), agegraphic dark energy (ADE), and Ricci dark energy (RDE), using late-time observations from cosmic chronometers, Type Ia supernovae (SNe Ia), DESI DR2 baryon acoustic oscillations (BAO), and {redshift-space distortion (RSD) growth measurements}. Five data combinations are considered: $H(z)+$Pantheon+, $H(z)+$DESI DR2+Pantheon+, $H(z)+$DESI DR2+DES-Dovekie, $H(z)+$DESI DR2+DESY5, and {$H(z)+$DESI DR2+DES-Dovekie+RSD}. We perform Bayesian Markov chain Monte Carlo parameter estimation and compare the models with AIC and BIC. In the BAO-included combinations, HDE gives $H_0\simeq67.3$--$68.0~\mathrm{~km~s^{-1}~Mpc^{-1}}$, $\Omega_{m0}\simeq0.270$--$0.272$, and $c\simeq1$, indicating an expansion history close to the de Sitter boundary rather than a robust phantom regime. ADE yields a stable agegraphic parameter $n\simeq2.78$--$2.81$, while RDE gives $\gamma\simeq0.53$--$0.55$ and persistently favors a low matter density, $\Omega_{m0}\simeq0.215$--$0.219$. {Treating $r_d$ as a free parameter reveals a strong negative correlation between $H_0$ and $r_d$, and the RSD-included combination provides a growth-level consistency check through $f\sigma_8(z)$ without constituting a full perturbative stability analysis.} None of the three models significantly alleviates the Hubble tension. Overall, HDE shows the most balanced phenomenological behavior among the three models, although current late-time data do not decisively prefer it over $\Lambda\text{CDM}$.

physics.gen-ph↗

arXiv2026

Extragalactic test of General Relativity with time-delay gravitational lenses

Strong gravitational lensing, a key prediction of General Relativity (GR), offers a unique environment for examining alternative modified gravity theories. In this Letter, we employ a model-independent approach to estimate the parameterized post-Newtonian parameter $\gamma_{\rm PPN}$ using the time-delay measurements from H0LiCOW strong lensing systems. To minimize potential biases from cosmological models in testing GR, we use Gaussian Process regression (GPR) to reconstruct angular diameter distances ($D_{\rm A}$) from the newest baryon acoustic oscillation (BAO) measurements, provided by the Dark Energy Spectroscopic Instrument (DESI) DR2 data. Based on the reconstructed angular diameter distances and four H0LiCOW lenses, we directly estimate the post-Newtonian parameter $\gamma_{\rm PPN}=0.93^{+0.16}_{-0.17}$ and the sound horizon scale $r_{\rm d}=136.36^{+5.14}_{-3.20}~{\rm Mpc}$. This is the first simultaneous measurement of $\gamma_{\rm PPN}$ and $r_{\rm d}$ without any assumptions about the contents of the universe or the theory of gravity. In the new framework of distance ratio $D_{\Delta t}/D_{\rm l}$ which avoids the bias introduced by $r_{\rm d}$, the $\gamma_{\rm PPN}$ constraint can be further improved to $\gamma_{\rm PPN}=0.89^{+0.19}_{-0.15}$. Our results provide a direct test of GR at the extragalactic scale, which is well consistent with the prediction of GR within $1\sigma$.

astro-ph.CO↗

arXiv2026

Finite-Core Signatures in LISA-Band Wave-Optics Lensing by Low-Mass Dark Matter Halos

LISA-band gravitational waves from massive binary black holes can be diffractively lensed by low-mass dark matter halos and subhalos, so their frequency-dependent amplification can probe the inner density profile. We isolate the generic finite-core part of this signal by comparing fixed-mass Navarro-Frenk-White (NFW) and cored-NFW lenses and propagating both profiles to the complex wave-optics amplification factor. A finite core smooths the time-delay response and reshapes the diffraction peak; an NFW template with a lower concentration can mimic part of the effect, but structured complex residuals remain after time and phase alignment. The residual peaks for intermediate cores, $r_c/r_s\simeq0.25$--$0.3$. An SIDM-inspired isothermal-core profile gives the same qualitative response, showing that the signal is not an artifact of one cored parameterization. For a fiducial LISA source, an appreciable mismatch requires favorable near alignment and $M_{\rm vir}\gtrsim 10^7M_\odot$. The result is a finite-core baseline for isolated line-of-sight halos and for subhalos perturbing strongly lensed macro-images.

astro-ph.CO↗

arXiv2026

Identification of Lensed Gravitational-Wave Beat Patterns by LISA

Strong lensing of massive black hole binaries can produce multiple gravitational-wave images with different magnifications and arrival times. LISA signals remain in band for months to years, allowing multiple lensed images to overlap during the inspiral stage and generate beat patterns. A singular isothermal sphere lens model is adopted to describe the lensing configuration, and two-image beat waveforms are constructed from massive black hole binary signals. To isolate the beat pattern itself, waveform mismatch is evaluated only during the overlapping inspiral stage before the coalescence of the first image, excluding contributions from the delayed merger peak of the second image. Using the HS-nod-SN (B+20) strong-lensing population, the occurrence rate of identifiable beat events is estimated, and Bayesian parameter estimation is performed with a beat template. Beat patterns are most readily identified when the lensing time delay is short and the delayed image has a relatively large magnification. Among 196 detectable two-image lensed events, 92 satisfy the temporal-overlap condition and 14 satisfy the beat-identification criterion, corresponding to an identifiable beat fraction of about 7\%. Posterior inference shows that the beat template can recover the lensing time delay and magnification parameters for a representative beat event. These results indicate that lensed beat patterns constitute a distinguishable subset of strongly lensed LISA events and provide a unique observational signature of strong lensing in the LISA band.

astro-ph.CO↗

arXiv2026

Mock Catalogs of Strongly Lensed Gravitational Waves via a Halo Model Approach with Space-borne Detectors

Future space-borne gravitational-wave (GW) detectors, such as LISA and DECIGO, are expected to detect a large number of GW events, a fraction of which may be strongly lensed by intervening galaxies or galaxy clusters. In this work, we develop a comprehensive framework to simulate strongly lensed GWs in the context of space-borne detectors. Based on realistic astrophysical models for both the source population and the lens distribution, we construct mock catalogs of lensed GW events, referred to as \textbf{GW-LMC-Space}. Our results show that, for a four-year LISA observation, the expected number of lensed events ranges from $0$ to $131$, depending on the adopted formation model of massive black hole binaries (MBHBs). The corresponding lensing probability for MBHBs can reach up to $\sim 0.3\%$. For DECIGO, we find that the number of lensed events in a one-year observation is expected to lie in the range of $0$--$44$, with a lensing probability of $\sim 0.15\%$ for stellar-mass binary black holes (BBHs), binary neutron stars (BNSs), and neutron star--black hole binaries (NSBHs). We further show that the overlap of lensed signals is a common feature in space-borne detectors, which can significantly affect both the signal-to-noise ratio (SNR) estimation and event identification. These results highlight the importance of accounting for signal overlap in the analysis of strongly lensed GW events in future space-borne GW observations.

astro-ph.CO↗

arXiv2026

Metastability in Emergent Dark Energy: A New Framework Confronting Cosmological Observations

We propose the Metastable Emergent Dark Energy (MEDE) model, a novel phenomenological extension of the Phenomenological (PEDE) and Generalized (GEDE) Emergent Dark Energy frameworks, in which dark energy exhibits a transitionary behavior, appearing at late times and vanishing toward the future. This model naturally enables a smooth crossing of the phantom divide line in the dark energy equation of state, as hinted at by recent observations. The MEDE model is defined by a hyperbolic tangent dark energy equation of state $w(z)=-1-\Delta\tanh[\log_{10}((1+z)/(1+z_t))]$, introducing only two free parameters, the transition redshift $z_t$ and the variation amplitude $\Delta$, allowing both the emergent and transitionary behavior of dark energy. We constrain the MEDE model using a combined dataset of Planck CMB, DESI DR2 BAO, and different compilations of Type Ia supernovae, obtaining $z_t=0.425^{+0.084}_{-0.120}$ and $\Delta =0.87^{+0.29}_{-0.35}$ (for CMB+DESI+PantheonPlus), indicating a statistically significant deviation from the cosmological constant. Statistical comparisons show that the MEDE model is preferred over $\Lambda$CDM by the combined dataset, with $\Delta \rm DIC_{ MEDE-\Lambda CDM}= -9.29$. The MEDE model performs comparably to the CPL dynamical dark energy parametrization ($\Delta \rm DIC_{MEDE-CPL} = 0.74$), with no strong statistical distinction from CPL using current data. Notably, MEDE preserves the success of $\Lambda$CDM in describing early-universe physics and naturally accommodates the phantom-crossing signature indicated by the latest low-redshift observations. The MEDE scenario provides a compelling dark energy phenomenology that may guide us toward interesting theoretical implications.

astro-ph.CO↗

arXiv2026

A Non-Iterative Algorithm for Clearing Two-Layer Energy-Sharing Markets with Voltage Constraints

Real-time hierarchical energy-sharing markets are promising to coordinate large numbers of prosumers. Still, most existing clearing methods rely on linearized or DC power-flow models and do not explicitly handle reactive power or voltage-security constraints. With AC network constraints, the problem becomes a large-scale bilevel Mathematical Program with Equilibrium Constraints (MPEC) that is difficult to solve in real time. This paper develops a non-iterative clearing algorithm for two-layer energy-sharing markets with voltage constraints. We first derive an efficient best-response function for each lower-layer energy-sharing market and reduce the equilibrium search to one dimension by exploiting the pricing-coupling structure. We then embed this function into the upper-layer network-constrained problem and reformulate the bilevel MPEC as a single-level mixed-integer second-order cone program (MISOCP), which is computationally tractable. Case studies on the IEEE 123-bus system with 12,300 prosumers show that the proposed method preserves nodal voltages within prescribed limits and delivers solutions with maximum errors below 0.01\% in 0.829 s.

math.OC↗

arXiv2026

Polarization Birefringence and Waveform Systematics in GW231123

GW231123 is a short, massive binary-black-hole event whose source properties show strong waveform dependence. We use this event to test gravitational-wave polarization birefringence, modeled as a frequency-dependent rotation of the tensor-polarization basis. Instead of sampling a distance-normalized coefficient directly, we sample the band-differential rotation $\delta_{\rm br}=\Delta(448\,\mathrm{Hz})-\Delta(20\,\mathrm{Hz})$ with prior $[-\pi,\pi]$, and report the derived coefficient $\beta_{\rm br}^{\rm derived}$ for comparison with standard propagation parametrizations. We analyze three waveform families: IMRPhenomXPHM (XPHM), IMRPhenomXO4a (XO4a), and NRSur7dq4. The derived posteriors are consistent with the general relativity value, giving $90\%$ upper limits $|\beta_{\rm br}^{\rm derived}|_{90}=0.378,\,0.097,\,0.273$ for XPHM, XO4a, and NRSur7dq4, respectively. The directly sampled $\delta_{\rm br}$ posterior remains broad, with $|\delta_{\rm br}|_{90}\simeq2.8\,\mathrm{rad}$, so the accumulated rotation across the analysis band is weakly constrained. The Bayes factors are waveform dependent: $\ln\mathcal{B}_{\rm br/GR}=-1.26\pm0.30$, $+3.64\pm0.28$, and $-0.86\pm0.29$, respectively. We therefore find no waveform-robust evidence for parity-violating propagation. The positive XO4a result is better interpreted as a waveform-dependent birefringence-like response associated with the mass-ratio--distance--spin degeneracy of this short high-mass event.

astro-ph.HE↗

arXiv2026

Model-Independent Reconstruction of Quintessence Potential and Kinetic Energy from DESI DR2 and Pantheon+ Supernovae

We present a model-independent reconstruction of the quintessence scalar field's dynamics-both its potential and kinetic energy-directly from the latest cosmological observations. Our analysis combines DESI DR2 baryon acoustic oscillation measurements with the Pantheon plus Type Ia supernova compilation, employing Gaussian process with four distinct covariance kernels to avoid theoretical priors on the potential's functional form. Key findings reveal a monotonically decreasing potential with redshift, consistent with thawing quintessence, and a kinetic energy that crosses zero near $z\sim 1$, marking the dark energy-matter equality epoch. Notably, while apparent negative kinetic energy values emerge at intermediate redshifts (0.5<z<1.0), these are statistical artifacts within uncertainties, arising from error amplification in derivative reconstruction rather than new physics. Our results demonstrate the power of non-parametric methods to constrain dynamical dark energy and show minimal dependence on the choice of cosmological priors, whether from local (SH0ES) or early-universe (Planck) measurements.

astro-ph.CO↗

arXiv2026

Testing General Relativity on Galactic Scales via DESI-BAO and Strong Lensing: Circumventing Assumptions on the Hubble Constant, Sound Horizon, and Dark Energy

We present a cosmological model-independent framework for testing general relativity (GR) on galactic scales by combining baryon acoustic oscillation (BAO) angular scale measurements with 120 galaxy-scale strong gravitational lensing systems. Using artificial neural networks (ANNs) and cubic spline reconstruction, we reconstruct the BAO angular scale from SDSS, BOSS, eBOSS, and DESI Data Release 2 (DR2), and infer the angular diameter distances to lenses and sources. Crucially, All the quantities used in the GR test are derived from observations and are independent of cosmological parameters such as the Hubble constant, the sound horizon, or the dark energy equation of state, minimizing potential biases from model-dependent distance priors. These distances are then incorporated into the strong lensing likelihood to constrain the parameterized post-Newtonian (PPN) parameter $\gamma_{\rm PPN}$ under two lens mass models: a constant-density-slope model ($P_1$) and a redshift-evolving model ($P_2$). For the $P_1$ model, the ANN reconstruction yields $\gamma_{\rm PPN} = 1.102^{+0.148}_{-0.125}$, consistent with GR at $1\sigma$ confidence level, while the cubic spline gives $\gamma_{\rm PPN} = 1.150^{+0.139}_{-0.118}$, consistent with GR at $2\sigma$ confidence level. For the $P_2$ model, the ANN reconstruction gives $\gamma_{\rm PPN} = 1.315^{+0.181}_{-0.155}$, compatible with GR at $2\sigma$, while the spline gives $\gamma_{\rm PPN} = 1.485^{+0.193}_{-0.168}$, showing mild tension at $\sim2.5\sigma$. The constraints exhibit a clear dependence on the adopted lens mass model, underscoring the critical role of lens modeling. No significant correlation is observed between $\gamma_{\rm PPN}$ and the Einstein radius. Overall, current galaxy-scale observations are consistent with GR, providing no evidence for deviations from Einstein's theory on kiloparsec scales.

astro-ph.CO↗

arXiv2026

Mock Catalogs of Strongly Lensed Gravitational Waves via A Halo Model Approach with Ground-based Detectors

As plans for the construction of third-generation gravitational wave (GW) detectors advance, research into strongly lensed GWs has become increasingly critical. It is anticipated that hundreds of multi-image lensed GWs will be detected annually. We present a comprehensive suite of lensed GW mock catalog derived from a composite lens mass model incorporating dark matter halos, galaxies, and subhalos. We analyze three source populations with four detector network configurations considering the earth rotation. Our simulations encompass not only conventional doublets and quadruplets but also subhalo-lensed events, highly magnified systems, and complete three or five image systems with a detectable central image, a feature distinct from optical lensing. For the joint ET+CE network, we forecast an annual detection rate of approximately 400 doublets and 36 quadruplets. Notably, this population includes roughly 107 events lensed by subhalos and 20 complete systems with detectable central images. Furthermore, we analyze high-magnification events ($\mu > 3$), predicting approximately 360 such cases. Under a more relaxed selection criterion that requires only at least one lensed signal to exceed the detection threshold, we estimate a total of approximately 617 lensed events. We also investigate the impact of variations in lens mass models and stellar evolution models on event rates, as well as the distributions of SNR pairs and time delays. These results establish a more physically grounded statistical prior for the future identification and authentication of lensed GW signals. The Gravitational Waves-Lensing Mock Catalog (GW-LMC) have been made publicly available.

astro-ph.CO↗

arXiv2026

Evidence for deviation in gravitational light deflection from general relativity at cosmological scales with KiDS-Legacy and CMB lensing

General relativity (GR) faces challenges from cosmic acceleration and observational tensions, necessitating stringent tests at cosmological scales. In this work, we probe GR deviations via a $\mu$--$\Sigma$ modified gravity parameterization, integrating KiDS-Legacy weak lensing (WL) data (1347 deg$^2$, $z\leq 2.0$), joint cosmic microwave background (CMB) data from Planck, ACT, and SPT, DESI DR2 baryon acoustic oscillation, and DES-Dovekie supernova data. KiDS-Legacy significantly improves constraint precision: $\mu_0$ (matter clustering) by $\sim 60\%$ and $\Sigma_0$ (gravitational light deflection) by $\sim 43\%$ relative to CMB alone. In the $\Lambda$CDM background, $\mu_0 = 0.21\pm 0.21$ is consistent with GR, while $\Sigma_0 = 0.149\pm 0.051$ deviates from GR at the 3.0$\sigma$ level. Furthermore, within the observationally preferred $w_0w_a$CDM background, this deviation in gravitational light deflection persists at the 2.2$\sigma$ level. This deviation is likely driven by the higher amplitudes in the large-scale CMB lensing measurements. This precise separation of GR-consistent matter clustering and deviant light deflection provides key observational clues for new physics or data systematics. Our work underscores the critical role of synergizing high-precision CMB and WL data in advancing GR tests.

astro-ph.CO↗

arXiv2025

Improved Identification of Strongly Lensed Gravitational Waves with Host Galaxy Locations

We present a Bayesian framework that enhances the identification of strongly lensed gravitational waves (GWs) by incorporating informative positional priors from the Euclid galaxy lens catalog. The core of our method introduces a two-step reweighting scheme: first, gravitational wave parameter estimation is performed under a uniform sky prior; the resulting posterior is then used to reweight galaxy positions within the Euclid catalog, constructing an astrophysically informed positional prior. Comparing this Euclid-informed prior against a uniform prior within our framework reveals distinct behaviors. While the posterior estimates of the intrinsic waveform parameters show little sensitivity to the prior change, the Bayes factor for lensing identification exhibits significant prior dependence. Crucially, for truly lensed event pairs, the Bayes factor systematically increases, whereas for unlensed pairs it decreases. This dual effect is vital for robust discrimination. Our analysis demonstrates that this multi-messenger approach significantly improves the confidence of lensing searches. For lensed pairs, the method boosts the Bayes factor by an average factor of $\sim 10$, while effectively suppressing false positives for unlensed coincidences. This underscores the critical importance of prior specification and showcases the substantial gains achievable by synergizing gravitational-wave data with electromagnetic survey information.

astro-ph.CO↗

arXiv2025

CSST Strong Lensing Preparation: Cosmological Constraints Forecast from CSST Galaxy-Scale Strong Lensing

Strong gravitational lensing by galaxies is a powerful tool for studying cosmology and galaxy structure. The China Space Station Telescope (CSST) will revolutionize this field by discovering up to $\sim$100,000 galaxy-scale strong lenses, a huge increase over current samples. To harness the statistical power of this vast dataset, we forecast its cosmological constraining power using the gravitational-dynamical mass combination method. We create a realistic simulated lens sample and test how uncertainties in redshift and velocity dispersion measurements affect results under ideal, optimistic, and pessimistic scenarios. We find that increasing the sample size from 100 to 10,000 systems dramatically improves precision: in the $\Lambda$CDM model, the uncertainty on the matter density parameter, $\Omega_m$, drops from 0.2 to 0.01; in the $w$CDM model, the uncertainty on the dark energy equation of state, $w$, decreases from 0.3 to 0.04. With 10,000 lenses, our constraints on dark energy are twice as tight as those from the latest DESI BAO measurements. We also compare two parameter estimation techniques -- MultiNest sampling and Bayesian Hierarchical Modeling (BHM). While both achieve similar precision, BHM provides more robust estimates of intrinsic lens parameters, whereas MultiNest is about twice as fast. This work establishes an efficient and scalable framework for cosmological analysis with next-generation strong lensing surveys.

astro-ph.CO↗

arXiv2025

Probing potential redshift-dependent systematics in the Hubble tension: Model-independent $H_0$ constraints from DESI R2

We present a determination of the Hubble constant ($H_0$) using the latest observational data from multiple cosmological probes, providing an independent geometric calibration of the SN Ia distance scale. By combining baryon acoustic oscillation (BAO) measurements from the second data release of the Dark Energy Spectroscopic Instrument (DESI DR2), cosmic chronometer $H(z)$ data, and the Pantheon Plus Type Ia supernova (SN Ia) sample, we reconstruct the cosmic expansion history through Gaussian process regression without assuming a specific cosmological model. Our analysis fully incorporates the complete covariance structure and yields $H_0$ constraints at five distinct redshifts: $65.72 \pm 1.99$ (z=0.51), $67.78 \pm 1.75$ (z=0.706), $70.74 \pm 1.39$ (z=0.934), $71.04 \pm 1.93$ (z=1.321), and $68.37 \pm 3.95~\mathrm{km~s^{-1}~Mpc^{-1}}$ (z=1.484). The Bayesian combination of these measurements gives $\hat{H}_0 = 69.29 \pm 0.81~\mathrm{km~s^{-1}~Mpc^{-1}}$ with 1.2\% precision, which occupies an intermediate position between the Planck CMB result and the SH0ES local measurement. While we observe a non-monotonic pattern in $H_0$ values across redshifts, statistical tests show this apparent evolution is not significant (p = 0.208). Our approach delivers independent constraints at multiple redshifts, enabling investigation of potential redshift-dependent systematic effects in the Hubble tension. The results demonstrate that an independent geometric method yields an $H_0$ value consistent with the intermediate range of current measurements, providing a crucial cross-check of distance ladder determinations.

astro-ph.CO↗

arXiv2025

Identifying Microlensing by Compact Dark Matter through Diffraction Patterns in Gravitational Waves with Machine Learning

Gravitational wave lensing, particularly microlensing by compact dark matter (DM), offers a unique avenue to probe the nature of dark matter. However, conventional detection methods are often computationally expensive, inefficient, and sensitive to waveform systematics. In this work, we introduce the Wavelet Convolution Detector (WCD), a deep learning framework specifically designed to identify wave-optics diffraction patterns imprinted in gravitationally lensed signals. The WCD integrates multi-scale wavelet analysis within residual convolutional blocks to efficiently extract time-frequency interference structures, and is trained on a realistically generated dataset incorporating compact DM mass functions and astrophysical lensing probabilities. This work is the first machine learning-based approach capable of identifying such wave-optics signatures in lensed gravitational waves. Tested on simulated binary black hole events, the model achieves 92.2\% accuracy (AUC=0.965), with performance rising to AUC$\sim$0.99 at high SNR. Crucially, it maintains high discriminative power across a wide range of lens masses without retraining, demonstrating particular strength in the low-impact-parameter and high-lens-mass regimes where wave-optics effects are most pronounced. Compared to Bayesian inference, the WCD provides orders-of-magnitude faster inference, making it a scalable and efficient tool for discovering compact DM through lensed gravitational waves in the era of third-generation detectors.

astro-ph.IM↗

arXiv2025

Identification of Strongly Lensed Gravitational Wave Events Using Squeeze-and-Excitation Multilayer Perceptron Data-efficient Image Transformer

With the advancement of third-generation gravitational wave detectors, the identification of strongly lensed gravitational wave (GW) events is expected to play an increasingly vital role in cosmology and fundamental physics. However, traditional Bayesian inference methods suffer from combinatorial computational overhead as the number of events grows, making real-time analysis infeasible. To address this, we propose a deep learning model named Squeeze-and-Excitation Multilayer Perceptron Data-efficient Image Transformer (SEMD), based on Vision Transformers, which classifies strongly lensed GW events by modeling morphological similarity between time-frequency spectrogram pairs. By integrating Squeeze-and-Excitation attention mechanisms and multilayer perceptrons , SEMD achieves strong feature extraction and discrimination. Trained and evaluated on simulated datasets using Advanced LIGO and Einstein Telescope noise, the model demonstrates robustness and generalization across different detector sensitivities and physical conditions, highlighting the promise of deep learning for rapid identification of strongly lensed GW signals.

astro-ph.IM↗