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Twin Bounded Least Squares Support Vector Regression 6th

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Twin Bounded Least Squares Support Vector Regression

6th IFIP TC 12 International Conference on Intelligence Science, ICIS 2024

作者： Chen, Ran Liu, Muhan Ma, Jinwen Department of Information and Computational Sciences School of Mathematical Sciences Peking University Beijing100871 China Department of Applied Mathematics China Agricultural University Beijing100083 China

ISBN: (纸本)9783031712524

Support Vector Machine (SVM) has received much attention in machine learning due to its profound theoretical research and practical application results. Support Vector Regression (SVR) has become a powerful tool for solving regression problems. Least Squares Support Vector Regression (LSSVR) has advantages in computing speed but can be prone to overfitting due to its sensitivity to noise and outliers. Additionally, Twin Support Vector Regression (TSVR) shows insufficient flexibility when dealing with large-scale data, and its robustness to noise could be improved. In response to these problems, this paper proposes an innovative solution: Twin Bounded Least Squares Support Vector Regression (TBLSSVR). This model combines the advantages of LSSVR and TSVR and introduces regularization terms to mitigate their limitations effectively. The regularization term helps minimize structural risk, reflecting the advantages of statistical learning theory and ensuring the stability of the solution. Experimental results demonstrate that TBLSSVR improves regression accuracy and significantly accelerates the solution speed, providing new directions and methods for future technology development. © IFIP International Federation for Information Processing 2025.

关键词： Vectors

Learning the Exact Time Integration Algorithm for Initial Value Problems by Randomized Neural Networks

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arXiv 2025年

作者： Dong, Suchuan Ni, Naxian Center for Computational and Applied Mathematics Department of Mathematics Purdue University United States

We present a method leveraging extreme learning machine (ELM) type randomized neural networks (NNs) for learning the exact time integration algorithm for initial value problems. The exact time integration algorithm for non-autonomous (including autonomous) systems can be represented by an algorithmic function in higher dimensions, which satisfies an associated system of partial differential equations with corresponding boundary conditions. Our method learns the algorithmic function by solving this associated system using ELM with a physics informed approach. The trained ELM network serves as the learned algorithm and can be used to solve the initial value problem with arbitrary initial data or arbitrary step sizes from some domain. When the right hand side of the non-autonomous system exhibits a periodicity with respect to any of its arguments, while the solution itself to the problem is not periodic, we show that in this case the algorithmic function is either periodic, or when it is not, satisfies a well-defined relation for different periods. This property can greatly simplify the network training for algorithm learning in many problems. We consider explicit and implicit NN formulations, leading to explicit and implicit time integration algorithms, and discuss how to train the ELM network by the nonlinear least squares method. Extensive numerical experiments with benchmark problems, including non-stiff, stiff and chaotic systems, show that the learned NN algorithm produces highly accurate solutions in long-time simulations, with its time-marching errors decreasing nearly exponentially with increasing degrees of freedom in the neural network. We compare extensively the computational performance (time-marching accuracy vs. time-marching cost) between the current NN algorithm and the leading traditional time integration algorithms. The learned NN algorithm is computationally competitive, markedly outperforming the traditional algorithms in many problems. Copyright ©

关键词： Least squares approximations

Traveling antiferromagnetic domain walls in a magnetic field

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arXiv 2025年

作者： Theodorou, George Komineas, Stavros Department of Mathematics and Applied Mathematics University of Crete Crete Heraklion70013 Greece Institute of Applied and Computational Mathematics FORTH Crete Heraklion Greece

We consider an antiferromagnet in one space dimension with easy-axis anisotropy in a perpendicular magnetic field. We study propagating domain wall solutions that can have a velocity up to a maximum vc. The width of the domain wall is a non-monotonic function of the velocity and it diverges to infinity at vc. Both features are in contrast to the case of the Lorentz invariant model in the absence of the field. We further study the modification of the wall profile when a Dzyaloshinskii-Moriya interaction is added. Finally, we present a propagating spiral expected to form when the system is forced at a velocity higher than the maximum velocity for domain walls and we give numerical results for the effect of the Dzyaloshinskii-Moriya interaction. © 2025, CC BY.

关键词： Magnetic fields

Stability and Lorentzian geometry for an inverse problem of a semilinear wave equation

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Analysis & PDE 2025年第5期18卷 1065-1118页

作者： Matti Lassas Tony Liimatainen Leyter Potenciano-Machado Teemu Tyni Department of Mathematics and Statistics University of Helsinki Helsinki Finland Department of Mathematics and Statistics University of Jyväskylä Jyväskylä Finland Research Unit of Applied and Computational Mathematics University of Oulu Oulu Finland

This paper concerns an inverse boundary value problem for a semilinear wave equation on a globally hyperbolic Lorentzian manifold. We prove a Hölder stability result for recovering an unknown potential ☆q☆ of the nonlinear wave equation ☆□☆g☆u☆+☆q☆u☆m☆=☆0☆, ☆m☆≥☆4☆, from the Dirichlet-to-Neumann map. Our proof is based on the recent higher-order linearization method and use of Gaussian beams. We also extend earlier uniqueness results by removing the assumptions of convex boundary and that pairs of light-like geodesics can intersect only once. For this, we construct special light-like geodesics and other general constructions in Lorentzian geometry. We expect these constructions to be applicable in studies of related problems as well.

关键词： Lorentzian geometry nonlinear wave equations inverse problems

Discontinuous Galerkin Finite Element Methods for Linear Port-Hamiltonian Dynamical Systems

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Journal of Scientific Computing 2025年第1期104卷 1-47页

作者： Cheng, Xiaoyu van der Vegt, J. J. W. Xu, Yan Zwart, H. J. School of Mathematics University of Science and Technology of China Anhui Hefei China Department of Applied Mathematics Mathematics of Computational Science Group University of Twente Enschede The Netherlands Department of Applied Mathematics Mathematics of Systems Theory Group University of Twente Enschede The Netherlands Department of Mechanical Engineering Dynamics and Control Group Eindhoven University of Technology Eindhoven The Netherlands

In this paper, we present discontinuous Galerkin (DG) finite element discretizations for a class of linear hyperbolic port-Hamiltonian dynamical systems. The key point in constructing a port-Hamiltonian system is a Stokes-Dirac structure. Instead of following the traditional approach of defining the strong form of the Dirac structure, we define a Dirac structure in weak form, specifically in the input-state-output form. This is implemented within broken Sobolev spaces on a tessellation with polyhedral elements. After that, we state the weak port-Hamiltonian formulation and prove that it relates to a Poisson bracket. In our work, a crucial aspect of constructing the above-mentioned Dirac structure is that we provide a conservative relation between the boundary ports. Next, we state DG discretizations of the port-Hamiltonian system by using the weak form of the Dirac structure and broken polynomial spaces of differential forms, and we provide a priori error estimates for the structure-preserving port-Hamiltonian discontinuous Galerkin (PHDG) discretizations. The accuracy and capability of the methods developed in this paper are demonstrated by presenting several numerical experiments.

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A flow-kick model of dryland vegetation patterns: the impact of rainfall variability on resilience

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arXiv 2025年

作者： Gandhi, Punit Oline, Matthew Silber, Mary Department of Mathematics and Applied Mathematics Virginia Commonwealth University RichmondVA23284 United States Computational and Applied Mathematics University of Chicago ChicagoIL60637 United States Department of Statistics and Committee on Computational and Applied Mathematics University of Chicago ChicagoIL60637 United States

In many drylands around the globe, vegetation self-organizes into regular spatial patterns in response to aridity stress. We consider the regularly-spaced vegetation bands, on gentle hill-slopes, that survive low rainfall conditions by harvesting additional stormwater from upslope low-infiltration bare zones. We are interested in the robustness of this pattern formation survival mechanism to changes in rainfall variability. For this, we use a flow-kick modeling framework that treats storms as instantaneous kicks to the soil water. The positive feedbacks in the storm-level hydrology, that act to concentrate water within the vegetation bands, are captured through the spatial profiles of the soil water kicks. Between storms, the soil water and vegetation, modeled by a two-component reaction-diffusion system, evolve together. We use a combination of linear stability analysis and numerical simulation to compare predictions of idealized periodic rainfall, with no variability, to predictions when there is randomness in the timing and magnitude of water input from storms. We show that including these random elements leads to a decrease in the parameter range over which patterns appear. This suggests that an increase in storm variability, even with the same mean annual rainfall, may negatively impact the resilience of these pattern-forming dryland ecosystems. Copyright © 2025, The Authors. All rights reserved.

关键词： Vegetation

Radiative Vlasov-Maxwell Equations

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arXiv 2025年

作者： Constantin, Peter Grayer, Hezekiah Department of Mathematics Princeton University PrincetonNJ08544 United States Program in Applied an Computational Mathematics Princeton University PrincetonNJ08544 United States

In the radiative Vlasov-Maxwell equations, the Lorentz force is modified by the addition of radiation reaction forces. The radiation forces produce damping of particle energy but the forces are no longer divergence-free in momentum space, which has an effect of concentration to zero momentum. We prove unconditional global regularity of solutions for a class of radiative Vlasov-Maxwell equations with large initial *** Codes 35Q70, 35Q83 © 2025, CC BY.

关键词： Maxwell equations

Axisymmetric type II blowup solutions to the three dimensional Keller-Segel system

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arXiv 2025年

作者： Hou, Thomas Y. Nguyen, Van Tien Song, Peicong Applied and Computational Mathematics Caltech PasadenaCA United States Department of Mathematics National Taiwan University Taiwan

We construct axisymmetric solutions to the three-dimensional parabolic-elliptic Keller-Segel system that blows up in finite time. In particular, the singularity is of type II, which admits locally a leading order profile of the rescaled stationary solution of the two-dimensional system. Additionally, mass concentration occurs along a one-dimensional ring in the plane. In the analysis, we rely on an approximate solution of the eigenproblem associated with the linearized operator around the stationary solution as well as the modulation dynamics to control the perturbation function and derive the accurate blowup rate. © 2025, CC BY.

关键词： Eigenvalues and eigenfunctions

Structure stability of steady supersonic shear flow with inflow boundary conditions

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arXiv 2025年

作者： Jiang, Song Zhou, Chunhui Department of Mathematics Southeast University Nanjing210096 China Institute of Applied Physics and Computational Mathematics Beijing China

We study the existence and zero viscous limit of smooth solutions to steady compressible Navier-Stokes equations near plane shear flow between two moving parallel walls. Under the assumption 0 0 = (µ(x2), 0), there exist smooth solutions near U0 to steady compressible Navier-Stokes equations in a 2-dimension domain Ω = (0, L) × (0, 2). Moreover, based on the uniform-in-Ε estimates, we establish the zero viscosity limit of the solutions obtained above to the solutions of the steady Euler equations. © 2025, CC BY-NC-ND.

关键词： Navier Stokes equations