数据驱动的组织力学与多凸的神经普通微分方程
Vahidullah Tac1, Francisco Sahli Costabal2, Adrian B Tepole1,3
1School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA.
概括
神经常规微分方程 (N-ODEs) 创建符合物理学的数据驱动材料模型. 这种方法确保了多凸性,在模拟中优于复杂材料 (如皮肤) 的传统模型.
科学领域:
- 计算力学 计算力学 计算力学
- 材料科学 材料科学 材料科学
- 应用数学 应用数学 应用数学
背景情况:
- 数据驱动的方法在计算力学中比传统的材料建模提供了优势.
- 深度神经网络可以学习复杂的物质反应,但往往缺乏基于物理的约束,如多凸性.
- 多凸性对于确保在弹性边界值问题中存在最小化器至关重要.
研究的目的:
- 开发数据驱动的材料模型,使用神经常规微分方程 (N-ODEs) 本质上满足多凸性.
- 解决当前数据驱动方法在执行基本数学要求方面的局限性.
- 创建一个用于建模各种材料,特别是软生物组织的一般框架.
主要方法:
- 利用神经常规微分方程 (N-ODEs) 来构建数据驱动的材料模型.
- 利用ODEs的杆性质来产生近似应变能量导数的单调函数.
- 通过保证这些衍生物在变形不变方面具有单调性来确保多凸性.
主要成果:
- N-ODE材料模型成功地从已建立的材料模型中捕获了合成数据.
- 与传统模型相比,使用来自非线性,异质性皮肤组织的实验数据显示出更高的性能.
- 成功地将N-ODE模型集成到用于重建手术的有限元模拟中.
结论:
- 基于N-ODE的数据驱动材料模型自动满足多凸性,这是一个关键的物理要求.
- 拟议的方法显示了复杂材料,特别是生物软组织的建模的巨大潜力.
- 这一框架预计将推动数据驱动方法在计算力学中的应用.
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