arXiv subjects

Yingxiang Xu

Publications and source records attributed to Yingxiang Xu.

9 recordsLinked to original sources

arXiv2026

AquaFlow: A Monocular Gaussian Splatting SLAM for Underwater Streaming Reconstruction

Recent monocular 3D Gaussian Splatting (3DGS) streaming reconstruction methods have achieved impressive performance by balancing reconstruction quality and efficiency. However, extending these frameworks to underwater scenes remains challenging due to severe visual degradation, such as light attenuation and scattering, which degrades camera pose tracking and distorts scene geometry. To address these challenges, we propose AquaFlow, a monocular Gaussian Splatting streaming reconstruction framework for efficient and high-fidelity underwater reconstruction. Specifically, AquaFlow fine-tunes a 3D vision foundation model on large-scale underwater data for robust pose and pointmap estimation, and introduces a medium-guided incremental Gaussian initialization strategy for streaming mapping. Furthermore, we develop a streaming-compatible hybrid scene representation that integrates structured, distance-conditioned neural Gaussians with a physics-inspired optical model to compensate for underwater image formation effects, enabling accurate scene reconstruction. We evaluate AquaFlow on a comprehensive dataset of 62 diverse underwater trajectories, collected from both public benchmarks and in-the-wild web videos across various scales. Extensive experiments demonstrate that AquaFlow achieves state-of-the-art tracking and rendering performance, reducing average localization error by 13.2% and improving PSNR by 4.74 dB compared to WaterSplat-SLAM.

cs.CV↗

arXiv2026

M^3: Dense Matching Meets Multi-View Foundation Models for Monocular Gaussian Splatting SLAM

Streaming reconstruction from uncalibrated monocular video remains challenging, as it requires both high-precision pose estimation and computationally efficient online refinement in dynamic environments. While coupling 3D foundation models with SLAM frameworks is a promising paradigm, a critical bottleneck persists: most multi-view foundation models estimate poses in a feed-forward manner, yielding pixel-level correspondences that lack the requisite precision for rigorous geometric optimization. To address this, we present M^3, which augments the Multi-view foundation model with a dedicated Matching head to facilitate fine-grained dense correspondences and integrates it into a robust Monocular Gaussian Splatting SLAM. M^3 further enhances tracking stability by incorporating dynamic area suppression and cross-inference intrinsic alignment. Extensive experiments on diverse indoor and outdoor benchmarks demonstrate state-of-the-art accuracy in both pose estimation and scene reconstruction. Notably, M^3 reduces ATE RMSE by 64.3% compared to VGGT-SLAM 2.0 and outperforms ARTDECO by 2.11 dB in PSNR on the ScanNet++ dataset.

cs.CV↗

arXiv2026

Novel Product Manifold Modeling and Orthogonality-Constrained Neural Network Solver for Parameterized Generalized Inverse Eigenvalue Problems

A parameterized orthogonality-constrained neural network is proposed for the first time to solve the parameterized generalized inverse eigenvalue problem (PGIEP) on product manifolds, offering a new perspective to address PGIEP. The key contributions are twofold. First, we construct a novel model for the PGIEP, where the optimization variables are located on the product of a Stiefel manifold and a Euclidean manifold. This model enables the application of optimization algorithms on the Stiefel manifold, a capability that is not achievable with existing models. Additionally, the gradient Lipschitz continuity of the objective function is proved. Second, a parameterized Stiefel multilayer perceptron (P-SMLP) that incorporates orthogonality constraints is proposed. Through hard constraints, P-SMLP enables end-to-end training without the need of alternating training between the two manifolds, providing a robust computational framework for generic PGIEPs. Numerical experiments demonstrate the effectiveness of the proposed method.

math.NA↗

arXiv2025

Heterogeneous optimized Schwarz Methods for heat conduction in composites with thermal contact resistance

Heat transfer in composites is critical in engineering, where imperfect layer contact causes thermal contact resistance (TCR), leading to interfacial temperature discontinuity. We propose solving this numerically using the optimized Schwarz method (OSM), which decouples the heterogeneous problem into homogeneous subproblems. This avoids ill-conditioned systems from monolithic solving due to high contrast and interface jumps. Both energy estimate and Fourier analysis are used to prove the convergence of this algorithm when the standard Robin condition is applied to transmit information between subdomains. To achieve fast convergence, instead of the standard Robin, the scaled Robin transmission condition is proposed, and the involved free parameter is rigorously optimized. The results reveal several new findings due to the presence of TCR: first, the larger the TCR, the faster the OSM converges; second, mesh-independent convergence is achieved in the asymptotic sense, in contrast to the mesh-dependent results without TCR; and last, the heterogeneity contrast benefits the convergence, with a larger contrast leading to faster convergence. Interestingly, different from the case without TCR, the thermal conductivity also benefits the convergence, similar to the effect of heterogeneity. Numerical experiments confirm the theoretical findings and demonstrate the method's potential for nonlinear problems on irregular domains.

math.NA↗

arXiv2025

Lie Symmetry Net: Preserving Conservation Laws in Modelling Financial Market Dynamics via Differential Equations

This paper employs a novel Lie symmetries-based framework to model the intrinsic symmetries within financial market. Specifically, we introduce Lie symmetry net (LSN), which characterises the Lie symmetries of the differential equations (DE) estimating financial market dynamics, such as the Black-Scholes equation. To simulate these differential equations in a symmetry-aware manner, LSN incorporates a Lie symmetry risk derived from the conservation laws associated with the Lie symmetry operators of the target differential equations. This risk measures how well the Lie symmetries are realised and guides the training of LSN under the structural risk minimisation framework. Extensive numerical experiments demonstrate that LSN effectively realises the Lie symmetries and achieves an error reduction of more than one order of magnitude compared to state-of-the-art methods. The code is available at https://github.com/Jxl163/LSN_code.

math.AP↗

arXiv2024

Orthogonal Constrained Neural Networks for Solving Structured Inverse Eigenvalue Problems

This paper introduces a novel neural network for efficiently solving Structured Inverse Eigenvalue Problems (SIEPs). The main contributions lie in two aspects: firstly, a unified framework is proposed that can handle various SIEPs instances. Particularly, an innovative method for handling nonnegativity constraints is devised using the ReLU function. Secondly, a novel neural network based on multilayer perceptrons, utilizing the Stiefel layer, is designed to efficiently solve SIEP. By incorporating the Stiefel layer through matrix orthogonal decomposition, the orthogonality of similarity transformations is ensured, leading to accurate solutions for SIEPs. Hence, we name this new network Stiefel Multilayer Perceptron (SMLP). Furthermore, SMLP is an unsupervised learning approach with a lightweight structure that is easy to train. Several numerical tests from literature and engineering domains demonstrate the efficiency of SMLP.

math.NA↗

arXiv2020

Deep Domain Decomposition Method: Elliptic Problems

This paper proposes a deep-learning-based domain decomposition method (DeepDDM), which leverages deep neural networks (DNN) to discretize the subproblems divided by domain decomposition methods (DDM) for solving partial differential equations (PDE). Using DNN to solve PDE is a physics-informed learning problem with the objective involving two terms, domain term and boundary term, which respectively make the desired solution satisfy the PDE and corresponding boundary conditions. DeepDDM will exchange the subproblem information across the interface in DDM by adjusting the boundary term for solving each subproblem by DNN. Benefiting from the simple implementation and mesh-free strategy of using DNN for PDE, DeepDDM will simplify the implementation of DDM and make DDM more flexible for complex PDE, e.g., those with complex interfaces in the computational domain. This paper will firstly investigate the performance of using DeepDDM for elliptic problems, including a model problem and an interface problem. The numerical examples demonstrate that DeepDDM exhibits behaviors consistent with conventional DDM: the number of iterations by DeepDDM is independent of network architecture and decreases with increasing overlapping size. The performance of DeepDDM on elliptic problems will encourage us to further investigate its performance for other kinds of PDE and may provide new insights for improving the PDE solver by deep learning.

math.NA↗

arXiv2012

Numerical Computation of Takens-Bogdanov Points for Delay Differential Equations

The paper presents a numerical technique for computing directly the Takens-Bogdanov points in the nonlinear system of differential equations with one constant delay and two parameters. By representing the delay differential equations as abstract ordinary differential equations in their phase spaces, the quadratic Takens-Bogdanov point is defined and a defining system for it is produced. Based on the descriptions for the eigenspace associated with the double zero eigenvalue, we reduce the defining system to a finite dimensional algebraic equation. The quadratic Takens-Bogdanov point, together with the corresponding values of parameters, is proved to be the regular solution of the reduced defining system and then can be approximated by the standard Newton iteration directly.

math.NA↗

arXiv2012

Preservation of Takens-Bogdanov bifurcations for delay differential equations by Euler discretization

A new technique for calculating the normal forms associated with the map restricted to the center manifold of a class of parameterized maps near the fixed point is given first. Then we show the Takens-Bogdanov point of delay differential equations is inherited by the forward Euler method without any shift and turns into a 1:1 resonance point. The normal form near the 1:1 resonance point for the numerical discretization is calculated next by applying the new technique to the map defined by the forward Euler method. The local dynamical behaviors are analyzed in detail through the normal form. It shows the Hopf point branch and the homoclinic branch emanating from the Takens-Bogdanov point are $O(\varepsilon)$ shifted by the forward Euler method, where $\varepsilon$ is step size. At last, a numerical experiment is carried to show the results.

math.NA↗