English(EN) Nonlinear elliptic homogenization with the parametric Deep Ritz method

深度Ritz方法解决非线性均匀化问题

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-10 04:00

研究人员开发了一种使用参数化深度Ritz方法来解决非线性椭圆均匀化中胞问题的新方法。该方法使用神经网络对胞响应进行离散化，提供了一种连续且可微的表示，可以在宏观状态范围内同时求解。参数化深度Ritz方法显示出准确性和效率，与传统的FE$^2$方案相比，显著加快了宏观尺度的求解速度。 AI

影响该方法为解决复杂的材料属性模拟提供了一种更有效且可微的方法，可能对计算材料科学和工程产生影响。

排序理由该集群包含一篇学术论文，详细介绍了一种用于求解特定类型偏微分方程的新计算方法。[lever_c_demoted from research: ic=1 ai=0.7]

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arXiv cs.LG TIER_1 English(EN) · Conor Rowan · 2026-09-10 04:00

参数化深度Ritz方法下的非线性椭圆均匀化

arXiv:2609.05778v1 Announce Type: new Abstract: Elliptic homogenization is used to determine coarse-grained properties of materials with features on small scales. When these small scale features have rapid, periodic fluctuations, the solution field corresponding to a homogenized …