生成时间: 2026年05月27日 06:49:37

重点关注论文数量: 0

了解领域论文数量: 5

不相关论文数量: 13

了解领域论文（摘要翻译）

1. 一种等价于间断Galerkin离散的配置格式

A collocation scheme that is equivalent to discontinuous Galerkin discretizations

作者: Jason Hicken

类别: math.NA

发布日期: 2026-05-26

arXiv ID: 2605.27327v1

链接: http://arxiv.org/abs/2605.27327v1

摘要翻译

中文标题: 一种等价于间断Galerkin离散的配置格式

摘要翻译: Chan 引入了一种具有分部求和性质的谱配置算子，用于发展熵稳定的间断 Galerkin (DG) 半离散 (https://doi.org/10.1016/j.jcp.2018.02.033)。本文表明，基于该配置算子的半离散所产生的解与使用相同底层数值积分的 DG 半离散的解等价。无论配置格式中的自由度数目多少，以及当数值积分不严格正定时，该等价性均成立。配置格式中多余的零空间自由度与算子的零空间相关联，并在整个非定常模拟过程中保持为零。如有必要，可通过引入仅针对多余模态的基于投影的数值耗散来恢复零空间一致性。在三角形网格上针对常系数对流方程和 Burgers 方程，验证了配置解与 DG 解之间的等价性。数值结果表明，对于基于斜对称分裂的 Burgers 方程的熵稳定半离散，该等价性失效，但通过将配置格式的残差投影到相关多项式空间上，可以恢复等价性。除研究等价性外，结果还表明，与常用的分部求和算子构造相比，该配置算子生成的半离散具有更优的谱半径。

2. PINNsur: 用于曲面上偏微分方程的物理信息神经网络

PINNsur: Physics-Informed Neural Networks for PDEs on Curved Surfaces

作者: Pranav Jain, Navami Kairanda, Peter Yichen Chen, Oded Stein

类别: cs.GR, math.NA

发布日期: 2026-05-26

arXiv ID: 2605.27308v1

链接: http://arxiv.org/abs/2605.27308v1

摘要翻译

中文标题: PINNsur: 用于曲面上偏微分方程的物理信息神经网络

摘要翻译: 曲面上的偏微分方程(PDEs)是科学计算和几何处理的基础。求解曲面PDE的一种流行方法是有限元方法(FEM), 该方法将曲面划分为离散的几何单元(通常为三角形)。最近, 物理信息神经网络(PINNs)作为一种连续的、无网格的替代方案出现, 不会受到FEM对网格质量或几何离散化误差的敏感性的影响。我们提出了PINNSur, 一个在曲面上使用PINN的简单框架: 我们训练一个神经场来近似曲面的法向量, 然后利用从$\mathbb{R}^3$到曲面上的投影来表达曲面微分算子。由于每个可定向流形都有定义良好的法向量, 我们的方法适用于所有此类曲面, 无论其曲率或拓扑如何, 从而支持许多几何处理应用。此外, 尽管PINN在平坦欧几里得域中求解PDE的经验成功, 但它们缺乏收敛到基础PDE真解的收敛性保证, 且关于证明这种收敛性的系统实验证据有限。这一差距限制了它们作为可靠求解器被采用, 相比像FEM这样已建立的方法, 后者对真解的收敛性有很好的理解和理论基础。这些曲面PDE特别难以收敛求解, 因为不仅需要处理函数逼近的收敛性, 还要处理曲面本身的几何逼近的收敛性。在这项工作中, 我们通过引入一个简单的经验收敛测试, 对使用PINN求解曲面PDE的收敛行为进行了实证研究。

3. 关于鞍点问题保结构离散的迭代罚方法的收敛性

On the convergence of iterated penalty methods for structure-preserving discretizations of saddle point problems

作者: Patrick E. Farrell, Michael Neilan, Charles Parker, L. Ridgway Scott

类别: math.NA

发布日期: 2026-05-26

arXiv ID: 2605.27069v1

链接: http://arxiv.org/abs/2605.27069v1

摘要翻译

中文标题: 关于鞍点问题保结构离散的迭代罚方法的收敛性

摘要翻译: 我们给出了应用于线性广义鞍点系统保结构离散的迭代罚方法的新的收敛估计。该方法可视为系统增广拉格朗日形式上的Uzawa迭代。作为副产品，我们得到了对罚/扰动鞍点问题更精确的稳定性估计。三个模型有限元应用与理论一致。

4. 使用简单乘子的梯度流隐式-显式线性多步法的能量耗散分析

Energy Dissipation Analysis of Implicit-Explicit Linear Multistep Methods for Gradient Flows Using a Simple Multiplier

作者: Chaoyu Quan, Huaijin Wang, Xuping Wang, Chuanju Xu

类别: math.NA

发布日期: 2026-05-26

arXiv ID: 2605.26592v1

链接: http://arxiv.org/abs/2605.26592v1

摘要翻译

中文标题: 使用简单乘子的梯度流隐式-显式线性多步法的能量耗散分析

摘要翻译: 本文提出一个理论框架，通过构造由原始能量与一个非负二次修正组成的耗散修正能量，建立一般隐式-显式线性多步方法（IMEX-LMMs）用于梯度流的能量耗散性。我们首先用数值解的一阶时间差，即所谓的简单乘子，来检验IMEX-LMMs。然后证明，当且仅当两个生成多项式（对应于LMM）在 $[-1,1]$ 上非负时，可以构造出相应的非负二次修正。在此基础上，在基于生成多项式下界的适度时间步长限制下，证明了修正能量随时间衰减。作为推论，可以直接得到直到五阶的知名向后微分公式方法的能量耗散性。此外，我们首次（据我们所知）构造了一个六阶能量耗散IMEX-LMM，并且在使用简单乘子检验时，证明了能量耗散IMEX-LMM的六阶障碍。最后通过数值实验验证了理论结果。

5. 二维 Poisson 问题的精确曲边 Lagrange 有限元

Exact-curved Lagrange finite elements for the Poisson problem in two dimensions

作者: Hiroki Ishizaka

类别: math.NA

发布日期: 2026-05-26

arXiv ID: 2605.26566v1

链接: http://arxiv.org/abs/2605.26566v1

摘要翻译

中文标题: 二维 Poisson 问题的精确曲边 Lagrange 有限元

摘要翻译: 我们为二维曲边区域上的 Poisson 问题建立了一个精确曲边 Lagrange 有限元框架。单元映射被分解为 $ F_K=Ψ_K\circΦ_{T_K}$，其中 $Φ_{T_K}$ 将参考三角形映射到仿射核，$Ψ_K$ 将仿射核映射到物理曲边单元。这种分解将仿射缩放与曲率效应分离开来，使得插值分析可以先在仿射核上进行，然后转移到精确曲边单元。对于协调线性 Lagrange 元，我们证明了精确曲边三角形上的局部 $L^2$- 和 $H^1$-插值估计。这些估计用物理单元上的输运方向导数表示，并且在所述半正则假设下，常数与仿射核的各向异性形状无关。然后应用这些插值估计推导 Poisson 问题的能量范数和 $L^2$ 误差估计。单位圆盘上的数值结果表明了直边与曲边几何表示之间的差异：曲边几何显著减小了几何误差，而主要的有限元误差仍由 $\mathbb{P}^1$ 逼近控制。

不相关论文（基本信息）

1. 次正态高斯模糊成本下的最短路径问题

Shortest Path Problem with Subnormal Gaussian Fuzzy Costs

作者: Murat Moran, Hande Günay Akdemir

类别: cs.CR, cs.NI, math.NA

发布日期: 2026-05-26

arXiv ID: 2605.27317v1

链接: http://arxiv.org/abs/2605.27317v1

摘要: This paper addresses the fuzzy shortest path problem in directed graphs, where edge costs are modeled as generalized fuzzy numbers with Gaussian membership functions. We interpret height as an indicator of information reliability. Based on this view, we introduce a weighted geometric mean to aggregate heights during the addition of generalized Gaussian fuzzy numbers. We employ a reliability-aware ranking that jointly considers the core, height, and standard deviation of fuzzy edge costs to determine the shortest path, thereby capturing their central tendency, reliability, and variability while keeping Dijkstra-level complexity per relaxation. The method yields routes that are not only cost-efficient but also supported by highly reliable information. To assess robustness, we construct a crisp baseline from the ranking and conduct Monte Carlo alpha-cut sampling–drawing membership levels uniformly and then sampling within the induced intervals–to recompute path costs and quantify sensitivity via the mean percentage deviation and its standard deviation. Finally, a large-scale case study on the FAA air traffic network demonstrates that the proposed GGFN–SPP framework scales efficiently to real-world networks, balances cost and reliability through $α$–cut aggregation and risk-aware ranking, and exhibits stable performance under Monte Carlo simulations with subnormal fuzzy costs.

2. 广义分数阶拉盖尔正交函数：投影与插值估计

Generalized fractional Laguerre orthogonal functions: projection and interpolation estimates

作者: Mahmoud A. Zaky

类别: math.NA

发布日期: 2026-05-26

arXiv ID: 2605.26832v1

链接: http://arxiv.org/abs/2605.26832v1

摘要: Classical Laguerre spectral approximations are highly effective on the half-line when the target function is smooth in the usual polynomial scale. However, their accuracy deteriorates for nonsmooth functions. Such behavior appears naturally in fractional models, weakly singular integral equations, and semi-infinite-domain approximations with limited regularity near the origin. The main contribution of this work is the construction and analysis of a fractional Laguerre approximation framework tailored to nonsmooth functions on the half-line. We establish projection and interpolation error estimates in nonuniformly weighted Sobolev space. These estimates clarify how the fractional parameter adapts the approximation space to the regularity of nonsmooth functions and improves the resulting convergence behavior. We further introduce a generalized fractional Laguerre family with an additional algebraic parameter, which gives greater flexibility in controlling both the approximation space and the underlying weight. Numerical experiments confirm the theoretical estimates and demonstrate the advantage of the proposed functions over standard Laguerre-type approximations.

3. 面向时间依赖偏微分方程的物理信息神经求解器的预测移动样本方法

Predictive Moving Sample Method for Physics-Informed Neural Solvers of Time-Dependent PDEs

作者: Beining Xu, Bocheng Zhang, Haijun Yu, Zhao Zhang, Jiayu Zhai

类别: math.NA

发布日期: 2026-05-26

arXiv ID: 2605.26745v1

链接: http://arxiv.org/abs/2605.26745v1

摘要: Time-dependent partial differential equations (PDEs) often develop sharp fronts, localized peaks, and other moving structures that occupy only a small portion of the space–time domain but dominate the approximation error. This makes fixed or uniformly sampled collocation strategies inefficient for physics-informed neural networks (PINNs), especially in high dimensions and over long-time prediction intervals. We propose the predictive moving sample method (PMSM), which builds on the moving sample method (MSM) in \cite{xu2026moving} by replacing its full time domain iterative training with a progressive time-stepping strategy and simplifying the velocity-field loss to further reduce the per-step cost. To improve practicality for long-time prediction, we further introduce the windowed-reset predictive moving sample method (WR-PMSM), which restricts extension training to an active time window and periodically resets the reference state, thereby reducing the growth of optimization cost while preserving global consistency through a final refinement stage. Across four representative benchmarks, PMSM consistently outperforms both standard PINNs and the original MSM under matched collocation budgets. These results suggest that transporting samples according to residual dynamics provides an effective and practical route to neural network solvers for time-dependent PDEs.

4. FINOM：非均匀网格上的快速Sinkhorn

FINOM: Fast Sinkhorn on Non-uniform Meshes

作者: Qihao Cheng, Qichen Liao, Hao Wu, Shuai Yang

类别: math.NA, math.OC

发布日期: 2026-05-26

arXiv ID: 2605.26659v1

链接: http://arxiv.org/abs/2605.26659v1

摘要: A linear-complexity algorithm for computing the Wasserstein-1 distance on non-uniform meshes is proposed. This work extends the fast Sinkhorn algorithms from [Q. Liao et al., Commun. Math. Sci., 20(2022)] and [Q. Liao et al., J. Sci. Comput., 98 (2024)] to non-uniform meshes. In those prior works, a distinctive collinear structure of the kernel matrix on uniform meshes was identified, enabling (O(N)) acceleration via dynamic programming. While non-uniform meshes are prevalent in practical applications like computational fluid dynamics and finance, their lack of collinearity has hindered direct acceleration. In this paper, we introduce the concept of a ``dividing index’’, which partitions the kernel matrix into two blocks. We demonstrate that each block exhibits a quasi-collinear property, a generalization of the structure found in uniform meshes. Leveraging this insight, we develop \textbf{F}ast S\textbf{I}nkhorn algorithm on \textbf{NO}n-uniform \textbf{M}eshes (\textbf{FINOM}), a dynamic programming approach that reduces the per-iteration complexity of the Sinkhorn algorithm from (O(N^2)) to (O(N)). Extensive numerical experiments on 1D and 2D problems confirm these improvements, achieving speed-ups of several orders of magnitude while maintaining accuracy.

5. 一种求解具有Flory-Huggins势的Allen-Cahn方程的无条件线性收敛ADMM方法

An Unconditionally Linearly Convergent ADMM Approach for the Allen-Cahn Equation with Flory-Huggins Potential

作者: Peng Jiang, Shengtong Liang, Tiao Lu

类别: math.NA

发布日期: 2026-05-26

arXiv ID: 2605.26623v1

链接: http://arxiv.org/abs/2605.26623v1

摘要: The Allen-Cahn equation with Flory-Huggins potential is a fundamental and crucial model in phase field simulation for describing phase separation phenomena, which serves as a core tool in diverse branches of natural sciences. The numerical simulation of the Allen-Cahn equation is of great importance but poses significant challenges due to the strong nonlinearity and the presence of logarithmic singularities at $u=0,1$ in the Flory-Huggins potential. In this paper, we consider convex splitting schemes to %preserve this bound and guarantee unconditional unique solvability, which reduces the numerical simulation to solving a singular nonlinear system arising from spatial discretization at each time step. We propose an iterative solver that is specifically designed for such systems based on the alternating direction method of multipliers (ADMM) approach. The scheme possesses properties such as bound preserving and discrete energy stability. Building upon the recent unconditionally convergent ADMM framework for the Cahn-Hilliard equation (Li et al., 2026), our key theoretical contributions are twofold: (a) a proof of unconditional convergence when the multiplier update step size $α\in (0,\frac{\sqrt{5}+1}{2})$; (b) a rigorous establishment of the linear convergence for the embedded ADMM solver. This effectively liberates the solver from time-step constraints or strict separation conditions. Comprehensive numerical experiments validate our proposed ADMM framework, where its theoretical predictions are fully substantiated in practice, showcasing efficiency and robustness.

6. 减少仅计算特征值的分治三对角特征求解器中的内部状态

Reducing Internal State in Eigenvalue-Only Divide-and-Conquer Tridiagonal Eigensolvers

作者: Ruiyi Zhan, Shaoshuai Zhang

类别: cs.DC, math.NA

发布日期: 2026-05-26

arXiv ID: 2605.26599v1

链接: http://arxiv.org/abs/2605.26599v1

摘要: Divide and Conquer (D&C) is a widely used algorithmic strategy for symmetric eigenvalue decomposition. Its natural parallelism makes D&C attractive on modern multicore CPUs and GPUs, but existing eigenvalue-only routines often default to QR-based methods because conventional D&C still materializes or replays large transformation matrices during the conquer phase. This paper proposes a boundary-row D&C algorithm for eigenvalue-only computation. The key observation is that the conquer phase only needs selected boundary rows/columns rather than the full accumulated eigenvector matrix. By propagating these boundary rows directly through the recursion, the proposed algorithm reduces the memory requirement from quadratic to linear space while also eliminating unnecessary matrix-vector work in the conventional lazy-replay formulation. We provide the algorithm, its time and space complexity analysis, correctness and stability arguments, optimized CPU and GPU implementations, and an evaluation against QR and D&C routines in standard numerical libraries.

7. Nussinov模型中RNA二级结构能量最小构型的超度量性

Ultrametricity of Energy Minimum Configurations of RNA Secondary Structures in the Nussinov Model

作者: A. P. Zubarev

类别: cond-mat.dis-nn, cond-mat.stat-mech, math.NA

发布日期: 2026-05-26

arXiv ID: 2605.26570v1

链接: http://arxiv.org/abs/2605.26570v1

摘要: We present a numerical study of the ultrametric properties of the set of RNA secondary structures with the maximum number of base pairs (energetically degenerate minima) within the maximum matching model (Nussinov algorithm). Using 18 natural small nuclear RNAs as examples, we show that the degree of nontrivial ultrametricity varies widely. We consider the optimization problem for the degree of nontrivial ultrametricity of RNA secondary structures with the maximum number of base pairs under a fixed nucleotide composition. It is found that permuting the nucleotide sequence can strongly change the degree of ultrametricity, indicating the key role of nucleotide order in shaping the hierarchical properties of RNA secondary structures.

8. 递归流匹配

Recursive Flow Matching

作者: Jiahe Huang, Sihan Xu, Sharvaree Vadgama, Rose Yu

类别: cs.LG, cs.AI, cs.CV, math.NA

发布日期: 2026-05-26

arXiv ID: 2605.26535v1

链接: http://arxiv.org/abs/2605.26535v1

摘要: Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental challenge, as existing approaches face a critical speed-fidelity trade-off. In this work, we introduce Recursive Flow Matching (RecFM), a generative framework for forecasting complex spatiotemporal dynamics. RecFM enforces self-consistency to align trajectories across discretization scales, reducing discretization errors and improving performance across metrics for physics-based tasks. To our knowledge, this is the first method to achieve high-fidelity one- and few-step (2-4 step) dynamic generation for scientific systems with performance comparable to state-of-the-art multi-step solvers. Across challenging scientific benchmarks, RecFM achieves up to a 20$\times$ speedup over leading diffusion-based emulators while improving predictive accuracy. Furthermore, RecFM reduces mean squared error by over 15% compared to vanilla flow matching, offering a scalable and efficient solution for real-time scientific emulation.

9. 通过拓扑优化直接工程声子晶体缺陷模式的色散曲线以实现指定频率

Direct Dispersion-Curve Engineering of Phononic Crystal Defect Modes for Prescribed Frequencies via Topology Optimization

作者: Xinlin Xu, Junji Kato

类别: cond-mat.mtrl-sci, math.NA, physics.comp-ph

发布日期: 2026-05-26

arXiv ID: 2605.26435v1

链接: http://arxiv.org/abs/2605.26435v1

摘要: Phononic crystals enable precise manipulation of elastic wave propagation through engineered bandgaps; however, designing defect states within these bandgaps for frequency-selective applications remains a significant challenge. Existing design approaches, including prior optimization formulations, struggle to systematically resolve the competing objectives of attracting desired defect modes to target frequencies while simultaneously repelling unwanted modes from the bandgap region. This inability to suppress competing modes often results in spurious, undesired in-gap resonant modes, thereby limiting design purity. This paper presents a novel two-stage topology optimization framework that addresses this challenge through an innovative multi-objective formulation based on a selection function with Gaussian weighting. In the first stage, the unit cell topology is optimized to create a wide bandgap around a target frequency. In the second stage, a supercell containing a defect is optimized using a specially designed objective function that dynamically balances mode attraction and repulsion via a selection function $S(ω)$ with adaptive $σ$ parameters. This selection mechanism enables the optimizer to automatically identify and selectively attract the most suitable defect mode while repelling competing modes from the bandgap region, eliminating the need for manual mode tracking. Numerical examples demonstrate that the proposed framework successfully generates phononic crystals featuring engineered defect states that yield precisely positioned localized resonant modes at prescribed frequencies within wide bandgaps, with potential applications in frequency-selective filters and elastic wave manipulation devices.

10. 半群一致性作为学习型物理模拟器的诊断工具

Semigroup Consistency as a Diagnostic for Learned Physics Simulators

作者: Lennon J. Shikhman

类别: cs.LG, cs.AI, math.NA

发布日期: 2026-05-25

arXiv ID: 2605.26324v1

链接: http://arxiv.org/abs/2605.26324v1

摘要: Learned physics simulators are often evaluated by one-step or short-horizon prediction error, but these metrics can miss failures in temporal composition and long-horizon rollout. For autonomous, state-complete systems, exact solution maps satisfy a semigroup law: direct evolution over $s+t$ should agree with evolution over $s$ followed by $t$. We propose normalized semigroup error as a post hoc, model-agnostic diagnostic comparing these direct and composed learned predictions. On one-dimensional heat and Burgers dynamics with time-conditioned ConvNet and FNO baselines, semigroup error is positively associated with rollout degradation, with trajectory-level Spearman correlation $ρ= 0.635$ and $95%$ CI $[0.621, 0.649]$. Semigroup regularization has mixed effects, supporting semigroup consistency primarily as an evaluation diagnostic rather than a universally beneficial training objective.

11. 基于斜对称部分的正规矩阵类雅可比算法

A Jacobi-like algorithm for normal matrices by the skew-symmetric part

作者: Simon Mataigne, P. -A. Absil

类别: math.NA

发布日期: 2026-05-25

arXiv ID: 2605.26317v1

链接: http://arxiv.org/abs/2605.26317v1

摘要: We present a fast Jacobi-like algorithm for computing the eigenvalues, and optionally the eigenvectors, of a real normal matrix. The method gains a computational advantage by using Paardekooper’s method for skew-symmetric matrices The method is most efficient for matrices where most eigenvalues are complex, such as random orthogonal matrices arising in the context of statistics on manifolds. In this case, the method is faster than the other Jacobi-like algorithms. In the last section of this paper, we also give explicit formulas for the nearest symmetric skew-Hamiltonian and the nearest ortho-symplectic matrix. These problems arise in the design and the analysis of the algorithm.

12. 基于有理高斯小波神经网络的多无人机分类与检测

Classification and detection of multiple UAVs using rational Gaussian wavelet neural networks

作者: Ungvári Gergő, Ferenc Braun, Attila Ámon, Péter Kackstädter, János Volk, Péter Kovács, Tamás Dózsa

类别: cs.LG, math.NA

发布日期: 2026-05-25

arXiv ID: 2605.26310v1

链接: http://arxiv.org/abs/2605.26310v1

摘要: The detection of unmanned aerial vehicles (UAVs) is important for the protection of civilian and military infrastructure. In this paper we propose a cost effective UAV detection system using sound signals obtained from microphones. The recorded signals are passed through a signal processing pipeline which employs interpretable adaptive feature extractors using so-called rational Gaussian wavelets. These adaptive wavelet transformations are embedded into and trained together with an underlying small neural network which detects and classifies UAVs based on the obtained features. This leads to a physically interpretable machine learning algorithm that in addition to classifying UAVs is also capable of detecting UAV swarms. We demonstrate our results using data collected in indoor studio and noisy outdoor environments. We conclude that the proposed method outperforms traditional machine learning approaches for detecting and classifying single UAVs as well as drone swarms, while retaining a high degree of interpretability. Our implementation of the proposed methods is made publicly available for reproducibility.

13. 学习物理系统种群动力学的双参数流

Two-Parameter Flows for Learning Population Dynamics of Physical Systems

作者: Paul Schwerdtner, Tobias Blickhan, Benjamin Peherstorfer

类别: cs.LG, math.NA

发布日期: 2026-05-25

arXiv ID: 2605.26285v1

链接: http://arxiv.org/abs/2605.26285v1

摘要: This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only sampling-time transports from a base distribution to each marginal and then extract a physics-time velocity by regressing on coupled synthetic trajectories. We prove that the resulting physics-time dynamics are unique and inherit regularity from the sampling-time transports. Because we can build on standard, well-developed conditional flow matching techniques for learning the base-to-marginal transports, our approach scales to high dimensions and avoids per-step optimal-transport couplings, while allowing admissible non-gradient dynamics that can naturally explain rotational or circulating physics phenomena.