arXiv subjects

Weiwen Wang

Publications and source records attributed to Weiwen Wang.

3 recordsLinked to original sources

arXiv2026

A fully-decoupled arbitrarily high-order time-stepping scheme based on matrix diagonalization for the anisotropic phase-field dendritic crystal growth model

We propose a fully-decoupled arbitrarily high-order time-stepping scheme for the anisotropic phase-field dendritic crystal growth model. The scheme combines an auxiliary-variable formulation with algebraically stable Runge-Kutta methods and satisfies a discrete energy dissipation law. To address the computational bottleneck arising from the coupled linear system in existing high-order schemes, a matrix diagonalization technique is introduced to transform the coupled linear elliptic system into a set of independent constant-coefficient elliptic equations. The resulting equations can be solved separately and in parallel, thereby improving computational efficiency. Numerical experiments in both two and three dimensions are presented to verify the convergence, energy stability, and efficiency of the proposed scheme. Comparisons with the original coupled formulation demonstrate the effectiveness of the matrix diagonalization strategy, while additional tests illustrate the advantages of high-order temporal discretizations. Simulations under different anisotropy coefficients, latent heat parameters, rotation angles, and initial nucleus shapes are also presented to investigate their effects on dendritic morphology.

math.NA↗

arXiv2025

An efficient fully explicit scheme for stochastic Navier-Stokes equations driven by multiplicative noise

This work proposes an efficient, linear, and fully decoupled pressure-correction scheme for the 2D stochastic Navier-Stokes equations with multiplicative noise and Dirichlet boundary condition. Leveraging the auxiliary variable approach, the scheme is fully explicit yet unconditionally stable. At each time step, it only requires solving Poisson-type equations with constant coefficients. To the best of our knowledge, this is the first application of the auxiliary variable method to stochastic Navier-Stokes equations. We provide a detailed strong convergence analysis for the linearized equation under standard assumptions.

math.NA↗

arXiv2024

Invariant Risk Minimization Is A Total Variation Model

Invariant risk minimization (IRM) is an arising approach to generalize invariant features to different environments in machine learning. While most related works focus on new IRM settings or new application scenarios, the mathematical essence of IRM remains to be properly explained. We verify that IRM is essentially a total variation based on $L^2$ norm (TV-$\ell_2$) of the learning risk with respect to the classifier variable. Moreover, we propose a novel IRM framework based on the TV-$\ell_1$ model. It not only expands the classes of functions that can be used as the learning risk and the feature extractor, but also has robust performance in denoising and invariant feature preservation based on the coarea formula. We also illustrate some requirements for IRM-TV-$\ell_1$ to achieve out-of-distribution generalization. Experimental results show that the proposed framework achieves competitive performance in several benchmark machine learning scenarios.

cs.LG↗