使用科尔莫戈罗夫-阿诺德网络准确地建模了物理反应和结构之间的关系
Yang Wang1, Changliang Zhu2, Shuzhe Zhang3
1State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi'an Jiaotong University, Xi'an, 710049, P. R. China.
Advanced science (Weinheim, Baden-Wurttemberg, Germany)
|February 8, 2025
概括
本研究使用科尔莫戈罗夫-阿诺德网络 (KAN) 预测六角格子中的Poisson比率转换. KAN阐明了几何性质与波桑比率从正变为负的转变之间的联系.
科学领域:
- * 物理与材料科学 物理与材料科学
- * 计算机科学和人工智能
背景情况:
- *当前科学中的机器学习方法往往缺乏可解释性,阻碍了对潜在的物理机制的理解.
- * 了解像弹性网络中的Poisson比率这样的现象对于科学进步至关重要.
研究的目的:
- * 在结构变形过程中研究六角格子弹性网络的波桑比率.
- * 利用Kolmogorov-Arnold网络 (KAN) 来进行可解释的AI驱动的物理现象分析.
- *阐明几何性质和波桑比率过渡之间的数学关系.
主要方法:
- * 应用科尔莫戈罗夫-阿诺德网络 (KAN) 来建模一个六角格子弹性网络.
- * 分析结构变形及其对网络Poisson比率的影响.
- * 数学框架开发使用KAN来描述从正到负的波桑比率的过渡.
主要成果:
- * 准确预测波桑比率从正变为负的转变.
- *确定Poisson比率等于零的关键几何参数.
- * 展示KAN揭示几何与材料行为之间的联系的能力.
结论:
- * 科尔莫戈罗夫-阿诺德网络 (KAN) 为理解复杂的物理行为提供了一种可解释的方法.
- * 这项研究突出了KAN在澄清管理结构反应的数学关系方面的潜力.
- * KAN有助于更深入地了解几何变化如何影响像波桑比率这样的材料特性.
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