生成时间: 2026年06月18日 07:21:49

重点关注论文数量: 0

了解领域论文数量: 3

不相关论文数量: 14

了解领域论文（摘要翻译）

1. 基于广义核插值的参数依赖哈密顿动力系统保辛预测

Symplecticity-preserving prediction of parameter-dependent Hamiltonian dynamics by Generalized Kernel Interpolation

作者: Robin Herkert, Tobias Ehring, Bernard Haasdonk

类别: math.NA

发布日期: 2026-06-17

arXiv ID: 2606.18937v1

链接: http://arxiv.org/abs/2606.18937v1

摘要翻译

中文标题: 基于广义核插值的参数依赖哈密顿动力系统保辛预测

摘要翻译: 我们将文献[1]中基于核的辛预测器扩展到参数增强的情境，其中学习到的流映射代理不仅依赖于状态，还依赖于附加变量，如物理参数和宏时间步长。该方法在参数和宏步增强的域上使用乘积核分析，并通过隐式辛欧拉型更新构造预测。因此，对于每个固定的可容许参数和时间步长实例，所得到的大步长预测器本身是辛的。训练问题被表述为再生核希尔伯特空间中的梯度埃尔米特-伯克霍夫插值。通过贪婪中心选择获得高效的代理。我们证明，非增强情境的收敛分析适用于乘积核框架，并推导相应的预测误差界。针对变摆长和变时间步长的单摆以及参数依赖的离散化波动方程的数值实验，说明了所提方法的精确性和结构保持行为。

2. 梯度流的具有拉回校正的标量追踪 SAV 格式

Scalar-Tracking SAV Schemes with Pullback Corrections for Gradient Flows

作者: Shiheng Zhang, Jie Shen

类别: math.NA

发布日期: 2026-06-17

arXiv ID: 2606.18551v1

链接: http://arxiv.org/abs/2606.18551v1

摘要翻译

中文标题: 梯度流的具有拉回校正的标量追踪 SAV 格式

摘要翻译: 标量辅助变量 (SAV) 方法构造了梯度流的线性、无条件能量稳定的时间离散。在一阶 SAV 步中，消去辅助变量表明状态方程是一个半隐式更新，并附加了一个来自前一非线性力的秩一正半定校正。多 SAV (MSAV) 方法按分量产生此校正，得到一个秩最多为能量分量数的校正。这分离了 MSAV 中通常耦合的两个机制：追踪非线性能量的标量变量个数和施加于状态方程的校正的秩。我们引入一族拉回校正的 SAV (PB-SAV) 方法，它保留单个标量辅助变量，但用一个由容许分量分解诱导的拉回校正代替秩一 SAV 校正。该校正保持正半定，秩最多为分量个数，且可以逐步变化而不改变标量能量追踪变量。我们证明了固定分解和步依赖分解的修正能量耗散律，推导了一个细化恒等式，其增益为显式的加权方差，并给出了对标准半隐式求解的低秩扰动的 Sherman-Morrison-Woodbury 实现。我们还在有限维情形下证明了拉回校正正是非线性能量的最小二乘表示的 Gauss-Newton 矩阵。在有限维梯度流、Allen-Cahn 动力学和非局部 Cahn-Hilliard 模型上的数值实验展示了 PB-SAV 主要改变一阶误差常数的情形以及显著提高轨迹精度的情形。

3. 具有重叠光滑子和谱粗网格的代数多重网格的两层收敛性

Two-level convergence of Algebraic Multigrid with Overlapping Smoothers and Spectral Coarse Grids

作者: O. A. Krzysik, B. S. Southworth, H. Al Daas

类别: math.NA

发布日期: 2026-06-16

arXiv ID: 2606.18404v1

链接: http://arxiv.org/abs/2606.18404v1

摘要翻译

中文标题: 具有重叠光滑子和谱粗网格的代数多重网格的两层收敛性

摘要翻译: 我们最近开发了最小二乘代数多重网格区域分解（LS-AMG-DD）求解器，作为一种代数多层方法，适用于具有Gram表示(A=G^{\top}G)的稀疏对称正定矩阵 \cite{southworth2026lsamgdd}。许多问题类均具有此种结构，包括许多协调有限元离散。该求解器利用非重叠代数聚集上的局部特征值问题构造粗空间，并在诱导的重叠子域上使用Schwarz型光滑子。本文为该求解器建立了一个新的两层收敛性理论。我们的理论证明，该求解器的粗空间在按聚集分块的块Jacobi光滑子诱导的范数下满足一个弱逼近性质，并且相应的逼近常数由一个用户可控的局部谱截断阈值界住。我们将这一逼近性质与乘法型两层循环的标准精细理论相结合。所得的两层界被简洁地分解为截断阈值与光滑子范数比较常数的乘积；我们对块Jacobi和重叠加性Schwarz光滑子导出了这些常数的显式界。我们还针对加性Schwarz方法建立了新的收敛性界，该界由一个平凡可计算的常数表出，且该常数以着色常数为上界。在标量(H^1)、向量(H(\operatorname{div}))和向量(H(\operatorname{curl}))有限元问题上的数值实验为理论提供了支持性证据，包括该求解器对网格细化和多项式次数不敏感的证据。

不相关论文（基本信息）

1. EnKF算法的共轭梯度表述

A Conjugate Gradient Formulation of the EnKF Algorithm

作者: Sanghyun Lee, Zhengqi Liu, Jonathan Valyou, Ludmil Zikatanov

类别: math.NA

发布日期: 2026-06-17

arXiv ID: 2606.19224v1

链接: http://arxiv.org/abs/2606.19224v1

摘要: Ensemble Kalman Filter (EnKF) based data assimilation algorithms synthesize predictive numerical forecast models with accumulated data as time evolves and account for model uncertainty and noisy measurements. The computational cost of these algorithms can be expensive, in particular for highly dimensional dynamical systems. Often, EnKF based algorithms have traded accuracy for reduced computational cost. In this paper, we present a novel parallelizable Conjugate Gradient-based Ensemble Kalman Filter (CGD-EnKF) algorithm that maintains comparable computational cost to efficient algorithms while realizing better state estimation accuracy in select cases. Here, we established the new approach by reformulating a matrix inverse calculation with a classical Conjugate Gradient (CGD) method. In addition, we discuss the upper error bound under CGD, error convergence to the classical EnKF result, and the computational complexity of the algorithm. We also showcase the CGD-EnKF-Reduced algorithm that is shown to be further computationally efficient for highly dimensional dynamical systems under small ensemble formulation. Numerical examples demonstrate the performance of our proposed algorithms and analytical properties, highlighting their comparability and advantages with respect to some benchmark EnKF algorithms.

2. 评估 Rust 在科学计算中的稀疏矩阵核

Evaluating Rust for Sparse Matrix Kernels in Scientific Computing

作者: Luca Lombardo, Fabio Durastante

类别: cs.MS, math.NA

发布日期: 2026-06-17

arXiv ID: 2606.19213v1

链接: http://arxiv.org/abs/2606.19213v1

摘要: Sparse matrix kernels form the computational backbone of scientific computing, traditionally relying on C/C++ and Fortran implementations that prioritize performance over memory safety. This work evaluates Rust as a systems-level alternative for sparse linear algebra by implementing and benchmarking three core workloads: sparse matrix-vector multiplication (SpMV), Lanczos-based Krylov methods, and matrix-exponential evaluation. We compare native Rust code against established baselines (Intel oneMKL, Eigen, PETSc, and PSBLAS) across a suite of representative matrices. Our results show that Rust’s sparse kernels achieve performance comparable to Eigen and PSBLAS, tracking the state-of-the-art for CSC formats, while trailing PETSc’s advanced blocked CSR optimizations. By analyzing compile-time monomorphization, SIMD vectorization, and FFI boundaries, we assess the practical impact of Rust’s safety model and ecosystem readiness. The study provides concrete, evidence-based guidance for modernizing high-performance numerical software stacks.

3. 一种用于斯托克斯流的性能可移植快速Ewald求和

A performance portable fast Ewald summation for Stokes flow

作者: Gabriel Kosmacher, Ziyu Du, Joar Bagge, George Biros

类别: math.NA, cs.DC, physics.comp-ph

发布日期: 2026-06-17

arXiv ID: 2606.19059v1

链接: http://arxiv.org/abs/2606.19059v1

摘要: We present GPU algorithms for Ewald summation methods for accelerating N-body Stokes flow problems in periodic domains. Like most N-body codes, Ewald sums use a near-field/far-field decomposition. The near field involves particle-to-particle (P2P) interactions. The far field primarily involves particle-to-grid (P2G) and grid-to-particle (G2P) interactions, as well as Fast Fourier Transforms. For each interaction, we investigate several algorithmic variants. Our implementation uses PyKokkos, a Python interface for the Kokkos C++ parallel programming framework, which supports portability to AMD/NVIDIA GPU and ARM/x86 CPU architectures. Double and single-precision numerical results, alongside analytical performance models, confirm the efficiency of our algorithms on AMD and NVIDIA GPU and on ARM and AMD CPU architectures. The P2P interaction achieves around 73% compute efficiency on NVIDIA H200, 84% on NVIDIA A100, 60% on AMD MI300, 52% on Grace CPU, and 68% on AMD Epyc CPU. A straightforward implementation of the P2G kernel can become a computational bottleneck. We introduce a novel P2G algorithm that achieves up to 16$\times$ speedup compared to a baseline GPU implementation. The overall Ewald sum code processes approximately 8 million particles per second on a H200 GPU, and about a half-million particles per second on a Grace CPU, for nine digits of accuracy. We also perform a multi-GPU weak scaling test on up to 256 million particles (64 GPUs) that shows bounded communication cost for all stages except the all-to-all particle sorting, which can be reduced to neighbor communication in the relevant time-stepping regime.

4. 具有混合Mittag-Leffler-Caputo-Fabrizio算子的分数阶SVIR传染病模型的保结构格式

Structure-Preserving Schemes for a Fractional SVIR Epidemic Model with a Hybrid Mittag-Leffler-Caputo-Fabrizio Operator

作者: Seham M. Al-Mekhlafi, Ahmed Boudaoui, Matthias Ehrhardt

类别: math.NA, math.DS

发布日期: 2026-06-17

arXiv ID: 2606.19045v1

链接: http://arxiv.org/abs/2606.19045v1

摘要: This paper proposes and analyzes a fractional-order SVIR epidemic model based on a hybrid Mittag-Leffler-Caputo-Fabrizio (MLCF) fractional operator with a nonsingular kernel. This model captures short- and long-term memory effects in epidemic transmission dynamics. The positivity and boundedness of the solutions are proven through an integrated formulation of the MLCF operator and a fractional Gronwall inequality. The basic reproduction number $\mathcal{R}_0$, equilibrium points, and their local and global stability properties are rigorously investigated through Jacobian analysis, logarithmic Lyapunov functionals, and a fractional LaSalle invariance principle. To approximate the model, a $θ$-weighted nonstandard finite difference (NSFD) method is developed. This method preserves the continuous system’s key qualitative properties, including positivity and boundedness, and is unconditionally stable in the fully implicit case. Consistency and first-order convergence are also proven. Numerical experiments, together with sensitivity and bifurcation analyses, illustrate the impact of fractional memory parameters on epidemic evolution and demonstrate the effectiveness of the proposed approach.

5. 定量多模态光学相干光声弹性成像

Quantitative Multi-Modal Optical Coherence Photoacoustic Elastography

作者: Ekaterina Sherina, Lisa Krainz, Wolfgang Drexler, Otmar Scherzer

类别: physics.med-ph, math.NA

发布日期: 2026-06-17

arXiv ID: 2606.18990v1

链接: http://arxiv.org/abs/2606.18990v1

摘要: We present a novel multi-modal optical coherence photoacoustic elastography (OCPE) framework, which combines two imaging modalities, optical coherence tomography (OCT) and photoacoustic tomography (PAT), to enable complementary absorption-scattering measurements for the extraction of quantitative tissue features via quasi-static elastography. For this, we develop a sophisticated hybrid inversion algorithm for merging the complementary information layers contained in both OCT and PAT-based elastography measurements, and perform systematic evaluations to assess the impact of hybrid elastography data on strain and stiffness reconstructions. Studies on a silicone elastomer phantom demonstrate that the combined OCT-PAT approach outperforms single-modality OCT elastography and PAT elastography, yielding higher strain signal-to-noise ratio and improved stiffness estimates. These results establish the advantage of multi-modal complementary imaging and data merging for accurate, high-resolution elastographic strain and stiffness mapping in both scattering and absorbing materials.

6. 具有复多项式非线性的波方程的概率表示与经典解

Probabilistic representation and classical solutions of wave equations with complex polynomial nonlinearities

作者: Joshua J. Y. Chan, Nicolas Privault

类别: math.NA, math.AP, math.PR

发布日期: 2026-06-17

arXiv ID: 2606.18919v1

链接: http://arxiv.org/abs/2606.18919v1

摘要: We review the probabilistic representation of solutions of wave equations with polynomial nonlinearities in spatial dimensions d=1,2,3 using stochastic branching processes. Under regularity assumptions on the initial data, we derive conditions ensuring the integrability of the corresponding Monte Carlo estimator, and the existence and smoothness of mild and classical solutions. We also present numerical results and comparisons with grid-based algorithms for the solution of nonlinear wave equations.

7. 由Lévy噪声驱动的McKean-Vlasov随机微分方程的精确解与数值解的指数遍历性

Exponential ergodicity of exact and numerical solutions for McKean-Vlasov SDEs driven by Lévy noise

作者: Yang Sun, Yuhang Zhang, Minghui Song

类别: math.NA

发布日期: 2026-06-17

arXiv ID: 2606.18815v1

链接: http://arxiv.org/abs/2606.18815v1

摘要: This paper investigates the exponential ergodicity of the exact solution and the tamed Euler solution for McKean-Vlasov stochastic differential equations driven by Lévy noise. First, we establish exponential ergodicity for both the original equation and the tamed Euler method. Then we prove the convergence of the numerical invariant measure to the exact invariant measure, which is obtained by combining the propagation of chaos (PoC) result with the strong convergence of the tamed Euler scheme. Furthermore, we derive a convergence rate for the numerical invariant measure by establishing uniform-in-time PoC and uniform-in-time convergence of the tamed Euler method. Finally, numerical experiments are presented to illustrate the theoretical results.

8. 计算扰动薛定谔方程的共振：应用于Reissner-Norsdtröm-de Sitter黑洞

Computing resonances of perturbed Schrödinger equations: Application to Reissner-Norsdtröm-de Sitter black holes

作者: Valentin Arrigoni, Geneviève Dusson

类别: math.NA

发布日期: 2026-06-17

arXiv ID: 2606.18770v1

链接: http://arxiv.org/abs/2606.18770v1

摘要: We present a numerical method for computing resonances of one-dimensional Schrödinger equations perturbed by a compactly supported potential, via finding zeros of the Wronskian associated with Jost solutions of the reference equation, computed through the resolution of Cauchy problems. All resonances located in a given domain are found efficiently using a defeated Newton algorithm. A key ingredient of the method is the choice of reference potential for which Jost solutions are known, which removes spurious resonances often encountered numerically. We test this method on three types of reference potentials and perturbations thereof: Pöschl-Teller potentials, exponentially decaying potentials, and potentials associated with Reissner-Nordströmde Sitter black holes. In particular we study the impact of perturbations on the resonances, and the stability of small resonances under perturbation. As an illustration, we use the method to numerically study the strong cosmic censorship hypothesis.

9. 一种用于参数曲面上类测地线计算的神经网络框架

A Neural Network Framework for Geodesic-Like Curve Computation on Parametric Surfaces

作者: Sheng-Gwo Chen, Chen-Chang Peng

类别: cs.CG, cs.LG, math.NA

发布日期: 2026-06-17

arXiv ID: 2606.18759v1

链接: http://arxiv.org/abs/2606.18759v1

摘要: The concept of geodesic-like curves was introduced by Chen in 2010 as a method for estimating shortest paths (geodesics) on parametric surfaces, with its convergence established theoretically. However, an efficient numerical computational framework has not yet been developed. In this paper, we propose an elegant and efficient approach for computing geodesic-like curves by leveraging deep learning and Physics-Informed Neural Networks (PINNs). Under the proposed framework, not only can single parametric surfaces be handled efficiently, but a broad class of complex parametric surfaces including multi-surface systems with $C^0$ or higher continuity and surfaces of revolution can also be robustly addressed.

10. 一类趋化驱动的鱼-贻贝系统的整体存在性、爆破行为与数值模拟

Global existence, blow-up behavior and numerical simulations for a class of chemotaxis-driven fish-mussel systems

作者: Gnanasekaran Shanmugasundaram, Jitraj Saha

类别: math.AP, math.NA

发布日期: 2026-06-17

arXiv ID: 2606.18695v1

链接: http://arxiv.org/abs/2606.18695v1

摘要: In this work, we investigate a chemotaxis-driven fish–mussel ecosystem model described by a coupled system of partial differential equations subject to homogeneous Neumann boundary conditions. Under suitable assumptions on the system parameters and initial data, we establish the global existence of classical solutions by employing semigroup methods together with a priori estimates. We also examine the possible blow-up behavior of solutions in a three-dimensional domain. To support the theoretical analysis, a finite element method is developed for the numerical approximation of the system, and convergence studies based on mesh refinement are carried out to verify the accuracy and stability of the proposed numerical scheme. Furthermore, numerical simulations illustrating the blow-up behavior of solutions in the computational domain are presented.

11. 具有随机速度的奇异摄动对流扩散问题的拟蒙特卡罗有限元逼近

Quasi-Monte Carlo finite element approximation for singularly perturbed convection-diffusion problems with random velocity

作者: Seungchan Ko, Guanglian Li, Yi Yu

类别: math.NA

发布日期: 2026-06-17

arXiv ID: 2606.18678v1

链接: http://arxiv.org/abs/2606.18678v1

摘要: This paper studies the numerical approximation of a singularly perturbed convection-diffusion problem over a bounded polygonal domain in $\mathbb{R}^d$ ($d=2,3$), where the velocity field is modeled by a log-uniform random field, a setting typical in uncertainty quantification. We introduce a novel numerical framework for computing the expected value of the linear functionals of the solution. The approach combines a finite element discretization of the problem, a truncated Karhunen–Loève expansion to represent the stochastic velocity field, and a lattice-based quasi-Monte Carlo (QMC) method to estimate expectations over the parameter space. We provide a rigorous error analysis of the proposed scheme, establishing bounds on the mean squared error and demonstrating that the QMC method achieves a nearly linear optimal convergence rate, with a constant independent of the integration dimension. Furthermore, the convergence rate is shown to be independent of the singular perturbation parameter.

12. DTPFI：一种用于恢复相场系统中非线性能量势的稳定算法

DTPFI: A stable algorithm for recovering nonlinear energy potentials in phase field systems

作者: Tianhao Ni, Jun Lai

类别: math.NA

发布日期: 2026-06-17

arXiv ID: 2606.18607v1

链接: http://arxiv.org/abs/2606.18607v1

摘要: This work proposes a Dual Time Phase Field Inversion (DTPFI) method for recovering unknown potential functions in phase field models. The reconstruction is formulated as an optimization problem that minimizes the mismatch between model predictions and observed fields at the final measurement time. We prove the differentiability of the measured field with respect to the unknown potential and establish the local convexity of the regularized objective function, thereby ensuring the existence of a local optimal solution. For numerical implementation, automatic differentiation is employed to compute gradients, avoiding the expensive evaluation of analytic gradients. Extensive numerical experiments demonstrate that DTPFI accurately reconstructs both polynomial and logarithmic potentials and remains robust under measurement noise. The framework is further extended to inverse problems involving field dependent mobility and joint parameter identification in coupled Cahn-Hilliard-Allen-Cahn systems.

13. 面向 GPU 的广义线性模型的混合精度通信避免 SGD

Mixed-Precision Communication-Avoiding SGD for Generalized Linear Models on GPUs

作者: Aditya Devarakonda, Irene Simó Muñoz, Giulia Guidi

类别: cs.DC, cs.LG, math.NA, stat.ML

发布日期: 2026-06-16

arXiv ID: 2606.18463v1

链接: http://arxiv.org/abs/2606.18463v1

摘要: Distributed stochastic gradient descent (SGD) is limited by communication rather than computation, since each iteration requires an AllReduce across processes. Communication-avoiding SGD (CA-SGD) amortizes communication over $s$ iterations by replacing $s$ consecutive AllReduces with a single AllReduce of an $sb\times sb$ Gram matrix, trading more computation and bandwidth for fewer synchronization points. Modern GPUs with matrix hardware and reduced-precision formats offset this by accelerating the Gram GEMM and shrinking BF16 traffic. We study mixed-precision CA-SGD for generalized linear models on NVIDIA GPUs. Our finite-precision analysis decomposes the local rounding error of one CA-SGD outer iteration into nine independent precision choices, depending on the hardware only through its low-precision unit roundoffs, so the resulting recipes transfer in principle across GPU generations. The recipe stores the input matrix and margin vector in low precision, computes the Gram matrix from low-precision inputs with high-precision accumulation, communicates it in high precision, and performs the inner recurrence and weight updates in high precision. On NERSC Perlmutter A100 GPUs, mixed-precision CA-SGD matches FP32 SGD loss within $0.5\%$ on logistic, linear, and Poisson problems and reaches $5.1$–$6.8\times$ speedup over FP32 SGD on epsilon, SUSY, HIGGS, synth, and Poisson-synth. Our software is available at https://doi.org/10.5281/zenodo.20448273

14. 基于混合精度随机预处理的GPU上数值稳定的Cholesky-QR分解

Numerically Stable Cholesky-QR on GPU via Mixed-Precision Randomized Preconditioning

作者: James E. Garrison, Chao Chen, Ilse C. F. Ipsen

类别: math.NA

发布日期: 2026-06-16

arXiv ID: 2606.18411v1

链接: http://arxiv.org/abs/2606.18411v1

摘要: Cholesky-QR is among the fastest algorithms for computing the thin QR factorization of tall-and-skinny matrices on GPUs, relying entirely on BLAS-3 operations. However, it is numerically unstable: forming the Gram matrix squares the condition number, causing breakdown when $κ_2(\boldsymbol{A}) \gtrsim 10^8$. We present MRCQR (Mixed-Precision Randomized Cholesky-QR), a stable GPU algorithm that addresses this limitation. MRCQR uses a subsampled randomized trigonometric transform to construct a preconditioner $\boldsymbol{R}_s$ that reduces $κ_2(\boldsymbol{A}\boldsymbol{R}_s^{-1})$ to near unity with high probability, then applies Cholesky-QR in double precision to the preconditioned matrix. The key insight – supported by perturbation analysis – is that the preconditioner requires far less accuracy than the final result: single (FP32) precision suffices when $κ_2(\boldsymbol{A}) \lesssim 10^8$, and half (FP16) when $κ_2(\boldsymbol{A}) \lesssim 10^4$. MRCQR produces an explicit orthogonal factor $\widehat{\boldsymbol{Q}}$ satisfying $\|\boldsymbol{I} - \widehat{\boldsymbol{Q}}^\top\widehat{\boldsymbol{Q}}\|_2 = \cal O(\mathbf{u})$ ($\mathbf{u} \approx 10^{-16}$, double-precision unit roundoff) for condition numbers up to $10^{16}$, far beyond the $10^8$ limit of CholQR2. Experiments on an NVIDIA H100 GPU show that MRCQR (FP16) outperforms rand-cholQR by $1.4$–$1.8\times$ across all tested column counts and is $1.8$–$13.5\times$ faster than cuSOLVER geqrf, while the FP16 sketch (used when $κ_2(\boldsymbol{A}) \lesssim 10^4$) is $2\times$ cheaper than FP64 at no accuracy cost.