VpROM:一种新的变量自编码器增强的减少顺序模型,用于处理非线性系统中的参数依赖性
Thomas Simpson1, Konstantinos Vlachas2, Anthony Garland3
1Department of Civil, Environmental, and Geomatic Engineering, ETH Zürich, Stefano-Franscini Platz 5, 8049, Zürich, Switzerland. simpson@ibk.baug.ethz.ch.
Scientific reports
|March 14, 2024
概括
本研究介绍了变量自编码器 (VAE),以创建更可通用的减少顺序模型 (ROM) 用于工程模拟. 这种方法提高了准确性,并允许在复杂的参数模型中量化不确定性.
科学领域:
- 计算工程和应用数学应用数学
- 模型订单减少 模型订单减少
- 在工程领域的机器学习.
背景情况:
- 减少订单模型 (ROM) 对于计算密集型工程问题至关重要.
- 传统的基于投影的方法,如正确直角分解,对线性运算符和参数依赖性有局限性.
- 现有的技术通常需要大量的局部ROM来进行参数变化,从而限制了概括性.
研究的目的:
- 为生成模型开发参数输入和减少基数之间的更可概括的映射.
- 提出变量自编码器 (VAE) 用于推断基本模式和近似模型响应模组.
- 为了提高ROM的精度和适用性,用于复杂的多模式动态行为.
主要方法:
- 使用变量自编码器 (VAE) 来推断基本模式 (向量) 接近模型响应变量组.
- 开发了一个新的ROM,将投影基与VAE近似系数矩阵结合起来.
- 这个矩阵通过参数输入将本地样本对全球现象的反应与参数输入联系起来.
主要成果:
- 实现了高精度,低序表示,适用于多参数依赖和多个响应模式的问题.
- 证明了VAE对任何输入状态的系数的近似能力,使不确定性定量化成为可能.
- 验证了基准方法,包括歇斯底里,多参数依赖和非线性风力轮塔模型.
结论:
- 拟议的VAE增强ROM为复杂的工程模拟提供了可概括和准确的方法.
- 由于VAE的概率性,可以对不确定性进行强有力的量化,从而提高模型的可靠性.
- 这种方法有效地解决了传统ROM在处理参数变化和非线性动态方面的局限性.
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