arXiv subjects

Xu Xiao

Publications and source records attributed to Xu Xiao.

At least 19 recordsLinked to original sources

arXiv2026

Improved Cosmological Constraints from Morphology-Based Marked Correlation Functions

The cosmic web contains morphology-dependent information that is not fully captured by standard two-point statistics. We construct morphology-based marked correlation functions (MCFs) by assigning marks to halos according to the cosmic-web morphology identified with the \textsc{Nexus} algorithm. Using the \textsc{Kun} simulation suite, which spans 129 $w_0w_a$CDM cosmologies, we build Gaussian-process emulators for the MCFs as functions of cosmological parameters and tracer bias. We then apply the emulators to mock halo catalogues from the independent \textsc{Jiutian} simulation and perform a joint likelihood analysis to quantify the resulting cosmological constraints. We consider two marker choices: a discrete morphology marker and a continuous morphology strength marker. The continuous marker improves the Figure of Merit (FoM) by a factor of $\sim 8.6$ relative to the standard 2PCF and reduces the $1\sigma$ uncertainty on $\sigma_8$ by a factor of $\sim 5$. The discrete marker gives a more modest FoM improvement of $\sim 17\%$. We further test the impact of tracer selection by varying the halo mass threshold by a factor of $\sim 4.5$. Even for the lowest mass threshold, the continuous marker remains unbiased and achieves a FoM about $\sim 3.4$ times higher than that of the 2PCF alone. These results show that morphology-based MCFs, combined with simulation-based emulation, provide a useful framework for extracting additional cosmological information from large-scale structure surveys.

astro-ph.CO↗

arXiv2026

Cosmological Constraints from Bias-Robust Wavelet Scattering Statistics for Stage-IV Galaxy Surveys

A central challenge in precision cosmology with galaxy surveys is to extract non-Gaussian information from large-scale structure while controlling systematic uncertainties such as tracer bias. Conventional clustering statistics, such as the two-point correlation function (2PCF), capture limited nonlinear information and typically require explicit bias modeling, which can introduce systematic errors if the adopted bias prescription is inaccurate. To address this problem, we introduce $R^{\rm wst}$, a bias-robust statistic constructed from $m$-mode ratios of the wavelet scattering transform (WST). Using simulation-based inference, we train a Gaussian-process-regression emulator on the \texttt{Kun} simulation suite and use \texttt{JiuTian} simulations for covariance estimation and validation. The emulator achieves percent-level accuracy, sufficient for the expected observational uncertainties. We show that $R^{\rm wst}$ yields unbiased constraints on $\Omega_m$, $\sigma_8$, $n_s$, and $w_0$, and improves the breaking of the $\Omega_m$--$\sigma_8$ degeneracy by about a factor of two compared with 2PCF. Its constraining power remains stable across a broad range of tracer-bias scenarios, demonstrating that $R^{\rm wst}$ can mitigate bias-induced systematics without explicit bias modeling. These results establish $R^{\rm wst}$ as a powerful and robust statistic for precision cosmology with Stage-IV surveys.

astro-ph.CO↗

arXiv2026

Cosmological constraints from neighbor-density-weighted marked correlation functions

We investigate whether neighbor-density-weighted marked correlation functions (MCFs) can extract cosmological information beyond the standard redshift-space two-point correlation function (2PCF). Using the Kun suite of 129 $w_0w_a$CDM$+\sum m_\nu$ simulations in $1~h^{-1}{\rm Gpc}$ boxes, we construct Gaussian-process emulators for the normalized scale statistic $\widehat{W}^{\alpha}(s)$ and the angular statistic $\widehat{W}^{\alpha}_{\Delta s}(\mu)$. We perform joint analyses combining multiple mark parameters $\alpha$ and quantify the information gain using the FoM in the $\Omega_m$--$\sigma_8$ plane. Relative to the 2PCF case, three-mark combinations improve the FoM by factors of $1.7$--$2.5$, while five-mark combinations increase the gain to $1.9$--$2.4$, depending on the statistic and mark definition. We further compare density and normalized-gradient marks, finding that they are nearly redundant for isotropic statistics but complementary for angular statistics, where their combination improves the FoM by up to $43\%$. Tests of scale range and halo selection show that the marked statistics remain robust under changes in analysis choices, with the angular statistic retaining additional cosmological information that is less sensitive to tracer selection. Our results demonstrate that MCFs substantially enhance cosmological constraints beyond the standard 2PCF and provide a robust probe for next-generation galaxy surveys.

astro-ph.CO↗

arXiv2026

Resolving the Gibbs Phenomenon in Fractional Fourier Series via Inverse Polynomial Reconstruction

The fractional Fourier series generalizes the classical Fourier series by introducing a rotation angle $\alpha$ in the time-frequency plane, but inherits the Gibbs phenomenon for piecewise smooth functions. Unlike the classical setting, the chirp modulation factor renders the fractional partial sum complex-valued, corrupting both real and imaginary components simultaneously and making direct adaptation of classical remedies insufficient. The Inverse Polynomial Reconstruction Method (IPRM) resolves the Gibbs phenomenon by enforcing that the Fourier coefficients of a Gegenbauer polynomial expansion match the given spectral data, rather than projecting the corrupted partial sum onto a polynomial basis. This paper extends the IPRM to fractional Fourier series for the first time. The fractional transformation matrix is derived and its conditioning is shown to be governed by an $\alpha$-independent Gram matrix, which reveals the dependence on the Gegenbauer parameter $\lambda$ and the polynomial degree $m$, while being entirely insensitive to the transform angle. An $L^{\infty}$ error estimate is established, guaranteeing exponential convergence for analytic functions. Numerical experiments on piecewise analytic test functions demonstrate complete elimination of the Gibbs phenomenon and confirm the theoretical predictions.

math.NA↗

arXiv2026

Closing the Observational Gap in Cosmic Dynamics: AI-Enabled Reconstruction of the Universe's Vorticity and Rotational Flow Morphology

The cosmic vorticity field, an essential tracer of nonlinear structure formation, has remained observationally inaccessible because transverse galaxy motions are difficult to measure and analytic models struggle to capture shell-crossing. Here we report an empirical reconstruction of this field by applying an artificial intelligence framework trained on simulations of the concordance LambdaCDM model to Sloan Digital Sky Survey galaxies. The recovered three-dimensional velocity and vorticity fields reveal coherent vortical structures, including spiral flows in clusters, filaments, and voids, and the cosmic web inferred from vorticity closely matches that derived from density segmentation. The power spectra of the reconstructed velocity and vorticity fields agree statistically with LambdaCDM predictions, and the inferred velocity field effectively removes redshift-space distortions, yielding an almost isotropic clustering signal. These converging lines of evidence, obtained from an independent perspective, reinforce the concordance cosmological model. By closing a long-standing observational gap, our results highlight the potential of AI-driven reconstruction to access otherwise unobservable quantities and to address fundamental questions in cosmology and galaxy formation.

astro-ph.CO↗

arXiv2025

Finite difference method for nonlinear damped viscoelastic Euler-Bernoulli beam model

We propose and analyze the numerical approximation for a viscoelastic Euler-Bernoulli beam model containing a nonlinear strong damping coefficient. The finite difference method is used for spatial discretization, while the backward Euler method and the averaged PI rule are applied for temporal discretization. The long-time stability and the finite-time error estimate of the numerical solutions are derived for both the semi-discrete-in-space scheme and the fully-discrete scheme. Furthermore, the Leray-Schauder theorem is used to derive the existence and uniqueness of the fully-discrete numerical solutions. Finally, the numerical results verify the theoretical analysis.

math.NA↗

arXiv2025

AI-Driven Reconstruction of Large-Scale Structure from Combined Photometric and Spectroscopic Surveys

Galaxy surveys are crucial for studying large-scale structure (LSS) and cosmology, yet they face limitations--imaging surveys provide extensive sky coverage but suffer from photo-$z$ uncertainties, while spectroscopic surveys yield precise redshifts but are sample-limited. To take advantage of both photo-$z$ and spec-$z$ data while eliminating photo-$z$ errors, we propose a deep learning framework based on a dual UNet architecture that integrates these two datasets at the field level to reconstruct the 3D photo-$z$ density field. We train the network on mock samples representative of stage-IV spectroscopic surveys, utilizing CosmicGrowth simulations with a $z=0.59$ snapshot containing $2048^3$ particles in a $(1200~h^{-1}\rm Mpc)^3$ volume. Several metrics, including correlation coefficient, MAE, MSE, PSNR, and SSIM, validate the model's accuracy. Moreover, the reconstructed power spectrum closely matches the ground truth at small scales ($k \gtrsim 0.06~h/\rm Mpc$) within the $1\sigma$ confidence level, while the UNet model significantly improves the estimation of photo-$z$ power spectrum multipoles. This study demonstrates the potential of deep learning to enhance LSS reconstruction by using both spectroscopic and photometric data.

astro-ph.IM↗

arXiv2024

Robust PCA Based on Adaptive Weighted Least Squares and Low-Rank Matrix Factorization

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA methods commonly use $\ell_1$ norm regularization to enforce sparsity, but this approach can introduce bias and result in suboptimal estimates, particularly in the presence of significant noise or outliers. Non-convex regularization methods have been proposed to mitigate these challenges, but they tend to be complex to optimize and sensitive to initial conditions, leading to potential instability in solutions. To overcome these challenges, in this paper, we propose a novel RPCA model that integrates adaptive weighted least squares (AWLS) and low-rank matrix factorization (LRMF). The model employs a {self-attention-inspired} mechanism in its weight update process, allowing the weight matrix to dynamically adjust and emphasize significant components during each iteration. By employing a weighted F-norm for the sparse component, our method effectively reduces bias while simplifying the computational process compared to traditional $\ell_1$-norm-based methods. We use an alternating minimization algorithm, where each subproblem has an explicit solution, thereby improving computational efficiency. Despite its simplicity, numerical experiments demonstrate that our method outperforms existing non-convex regularization approaches, offering superior performance and stability, as well as enhanced accuracy and robustness in practical applications.

cs.LG↗

arXiv2024

AI-Powered Reconstruction of Dark Matter Velocity Fields from Redshift-Space Halo Distribution

We propose a UNet-based deep learning model to reconstruct the real-space dark matter (DM) velocity field from the redshift-space distribution of sparse DM halos. Using various statistical measures, we show that the reconstructed velocity components--including velocity magnitude, momentum, and divergence--closely match the ground truth, achieving better than 10% relative error and a correlation coefficient of 0.88. In the power spectrum comparison over $k \in [0.05, 0.3] h/{\rm Mpc}$, the UNet reconstruction outperforms linear theory and agrees with the true field within $2\sigma$. The model also effectively corrects redshift-space distortions (RSD), yielding unbiased power spectrum multipoles of DM fields within $2\sigma$. Notably, the UNet remains robust even with incomplete halo mass information. These results highlight the model's broad applicability to cosmological analyses, including RSD, cosmic web studies, the kinetic Sunyaev-Zel'dovich effect, and BAO reconstruction.

astro-ph.CO↗

arXiv2024

Deep learning for cosmological parameter inference from a dark matter halo density field

We propose a lightweight deep convolutional neural network (lCNN) to estimate cosmological parameters from simulated three-dimensional dark matter (DM) halo distributions and associated statistics. The training dataset comprises 2000 realizations of a cubic box with a side length of 1000 $h^{-1}{\rm Mpc}$, and interpolated over a cubic grid of $300^3$ voxels, with each simulation produced using $512^3$ DM particles and $512^3$ neutrinos. Under the flat $Λ$CDM model, simulations vary standard six cosmological parameters including $Ω_m$, $Ω_b$, $h$, $n_s$, $σ_8$, $w$, along with the neutrino mass sum, $M_ν$. We find that: 1) within the framework of lCNN, extracting large-scale structure information is more efficient from the halo density field compared to relying on the statistical quantities including the power spectrum, the two-point correlation function, and the coefficients from wavelet scattering transform; 2) combining the halo density field with its Fourier transformed counterpart enhances predictions, while augmenting the training dataset with measured statistics further improves performance; 3) achieving high accuracy in inferring $Ω_m$, $h$, and $σ_8$ by the neural network model, while being inefficient in predicting $Ω_b$, { $n_s$}, $M_ν$ and $w$; 4) { compared to the simple fully connected network trained with three statistical quantities, our CNN yields statistically reduced errors, showing improvements of approximately 23\% for $Ω_m$, 11\% for $h$, 8\% for $n_s$, and 21\% for $σ_8$. Additionally, in comparison with the likelihood-based analysis on $P(k)$ data, our CNN provides much tighter constraints on parameters, especially on $Ω_m$ and $σ_8$.} Our study emphasizes this lCNN-based novel approach in extracting large-scale structure information and estimating cosmological parameters.

astro-ph.CO↗

arXiv2024

Effective versus Floquet theory for the Kerr parametric oscillator

Parametric gates and processes engineered from the perspective of the static effective Hamiltonian of a driven system are central to quantum technology. However, the perturbative expansions used to derive static effective models may not be able to efficiently capture all the relevant physics of the original system. In this work, we investigate the conditions for the validity of the usual low-order static effective Hamiltonian used to describe a Kerr oscillator under a squeezing drive. This system is of fundamental and technological interest. In particular, it has been used to stabilize Schrödinger cat states, which have applications for quantum computing. We compare the states and energies of the effective static Hamiltonian with the exact Floquet states and quasi-energies of the driven system and determine the parameter regime where the two descriptions agree. Our work brings to light the physics that is left out by ordinary static effective treatments and that can be explored by state-of-the-art experiments.

quant-ph↗

arXiv2023

A driven quantum superconducting circuit with multiple tunable degeneracies

We present the experimental discovery of multiple simultaneous degeneracies in the spectrum of a Kerr oscillator subjected to a squeezing drive. This squeezing, in combination with the Kerr interaction creates an effective static two-well potential in the frame rotating at half the frequency of the sinusoidal driving force. Remarkably, these degeneracies can be turned on-and-off on demand, and their number is tunable. We find that when the detuning $Δ$ between the frequency of the oscillator and characteristic frequency of the drive equals an even multiple of the Kerr coefficient $K$, $Δ/K = 2m$, the oscillator displays $m + 1$ exact, parity-protected, spectral degeneracies, insensitive to the drive amplitude. The degeneracies stem from the unusual destructive interference of tunnel paths in the classically forbidden region of the double well static effective potential that models our experiment. Exploiting this interference, we measure a peaked enhancement of the incoherent well-switching lifetime creating a super-protected cat qubit in the ground state manifold of our oscillator. {Our results demonstrate the relationship between degeneracies and noise protection in quantum systems.

quant-ph↗

arXiv2023

A diagrammatic method to compute the effective Hamiltonian of driven nonlinear oscillators

In this work, we present a new diagrammatic method for computing the effective Hamiltonian of driven nonlinear oscillators. At the heart of our method is a self-consistent perturbation expansion developed in phase space, which establishes a direct correspondence between the diagram and algebra. Each diagram corresponds to a Hamiltonian term, the prefactor of which, like those in Feynman diagrams, involves a simple counting of topologically equivalent diagrams. Leveraging the algorithmic simplicity of our diagrammatic method, we provide a readily available computer program that generates the effective Hamiltonian to arbitrary order. We show the consistency of our schemes with existing perturbation methods such as the Schrieffer-Wolff method. Furthermore, we recover the classical harmonic balance scheme from our result in the limit of $\hbar\rightarrow0$. Our method contributes to the understanding of dynamic control within quantum systems and achieves precision essential for advancing future quantum information processors. To demonstrate its value and versatility, we analyze five examples from the field of superconducting circuits. These include an experimental proposal for the Hamiltonian stabilization of a three-legged Schr\"odinger cat, modeling of energy renormalization phenomena in superconducting circuits experiments, a comprehensive characterization of multiphoton resonances in a driven transmon, a proposal for an inductively shunted transmon circuit, and a characterization of classical ultra-subharmonic bifurcation in driven oscillators. Lastly, we benchmark the performance of our method by comparing it with experimental data and exact Floquet numerical diagonalization.

quant-ph↗

arXiv2023

AI-assisted reconstruction of cosmic velocity field from redshift-space spatial distribution of halos

The peculiar velocities of dark matter halos are crucial to study many issues in cosmology and galaxy evolution. In this study, by using the state-of-the-art deep learning technique, a UNet-based neural network, we propose to reconstruct the peculiar velocity field from the redshift-space distribution of dark matter halos. Through a point-to-point comparison and examination of various statistical properties, we demonstrate that, the reconstructed velocity field is in good agreement with the ground truth. The power spectra of various velocity field components, including velocity magnitude, divergence and vorticity, can be successfully recovered when $k\lesssim 1.1$ $h/\rm Mpc$ (the Nyquist frequency of the simulations) at about 80% accuracy. This approach is very promising and presents an alternative method to correct the redshift-space distortions using the measured 3D spatial information of halos. Additionally, for the reconstruction of the momentum field of halos, UNet achieves similar good results. Hence the applications in various aspects of cosmology are very broad, such as correcting redshift errors and improving measurements in the structure of the cosmic web, the kinetic Sunyaev-Zel'dovich effect, BAO reconstruction, etc.

astro-ph.CO↗

arXiv2023

Numerical approximation based on deep convolutional neural network for high-dimensional fully nonlinear merged PDEs and 2BSDEs

This paper proposes two efficient approximation methods to solve high-dimensional fully nonlinear partial differential equations (NPDEs) and second-order backward stochastic differential equations (2BSDEs), where such high-dimensional fully NPDEs are extremely difficult to solve because the computational cost of standard approximation methods grows exponentially with the number of dimensions. Therefore, we consider the following methods to overcome this difficulty. For the merged fully NPDEs and 2BSDEs system, combined with the time forward discretization and ReLU function, we use multi-scale deep learning fusion and convolutional neural network (CNN) techniques to obtain two numerical approximation schemes, respectively. Finally, three practical high-dimensional test problems involving Allen-Cahn, Black-Scholes-Barentblatt, and Hamiltonian-Jacobi-Bellman equations are given so that the first proposed method exhibits higher efficiency and accuracy than the existing method, while the second proposed method can extend the dimensionality of the completely NPDEs-2BSDEs system over $400$ dimensions, from which the numerical results highlight the effectiveness of proposed methods.

math.NA↗

arXiv2022

On the static effective Lindbladian of the squeezed Kerr oscillator

We derive the static effective Lindbladian beyond the rotating wave approximation (RWA) for a driven nonlinear oscillator coupled to a bath of harmonic oscillators. The associated dissipative effects may explain orders of magnitude differences between the predictions of the ordinary RWA model and results from recent superconducting circuits experiments on the Kerr-cat qubit. The higher-order dissipators found in our calculations have important consequences for quantum error-correction protocols and parametric processses.

quant-ph↗

arXiv2022

The squeezed Kerr oscillator: spectral kissing and phase-flip robustness

By applying a microwave drive to a specially designed Josephson circuit, we have realized an elementary quantum optics model, the squeezed Kerr oscillator. This model displays, as the squeezing amplitude is increased, a cross-over from a single ground state regime to a doubly-degenerate ground state regime. In the latter case, the ground state manifold is spanned by Schrödinger-cat states, i.e. quantum superpositions of coherent states with opposite phases. For the first time, having resolved up to the tenth excited state in a spectroscopic experiment, we confirm that the proposed emergent static effective Hamiltonian correctly describes the system, despite its driven character. We also find that the lifetime of the coherent state components of the cat states increases in steps as a function of the squeezing amplitude. We interpret the staircase pattern as resulting from pairwise level kissing in the excited state spectrum. Considering the Kerr-cat qubit encoded in this ground state manifold, we achieve for the first time quantum nondemolition readout fidelities greater than 99%, and enhancement of the phase-flip lifetime by more than two orders of magnitude, while retaining universal quantum control. Our experiment illustrates the crucial role of parametric drive Hamiltonian engineering for hardware-efficient quantum computation.

quant-ph↗

arXiv2022

Second-order accurate numerical scheme with graded meshes for the nonlinear partial integrodifferential equation arising from viscoelasticity

This paper establishes and analyzes a second-order accurate numerical scheme for the nonlinear partial integrodifferential equation with a weakly singular kernel. In the time direction, we apply the Crank-Nicolson method for the time derivative, and the product-integration (PI) rule is employed to deal with Riemann-Liouville fractional integral. From which, the non-uniform meshes are utilized to compensate for the singular behavior of the exact solution at $t=0$ so that our method can reach second-order convergence for time. In order to formulate a fully discrete implicit difference scheme, we employ a standard centered difference formula for the second-order spatial derivative, and the Galerkin method based on piecewise linear test functions is used to approximate the nonlinear convection term. Then we derive the existence and uniqueness of numerical solutions for the proposed implicit difference scheme. Meanwhile, stability and convergence are proved by means of the discrete energy method. Furthermore, to demonstrate the effectiveness of the proposed method, we utilize a fixed point iterative algorithm to calculate the discrete scheme. Finally, numerical experiments illustrate the feasibility and efficiency of the proposed scheme, in which numerical results are consistent with our theoretical analysis.

math.NA↗