基于物理的双层神经网络,用于非线性模型的减少顺序
Yankun Hong1, Harshit Bansal1, Karen Veroy1
1Centre for Analysis, Scientific Computing and Applications, Eindhoven University of Technology, Eindhoven, 5600MB The Netherlands.
Advanced modeling and simulation in engineering sciences
|November 18, 2024
概括
本研究介绍了一种新的基于物理的双层深度网络 (TTDN),用于基于机器学习的高效模型订单减少 (MOR). TTDN 方法降低了计算成本,并改善了复杂非线性问题的概括性.
科学领域:
- 计算科学与工程 计算科学与工程
- 机器学习应用 机器学习应用
- 基于物理的建模模型
背景情况:
- 机器学习 (ML) 显著影响非侵入性模型订单减少 (MOR),但面临着高的线下培训成本和泛化问题.
- 当前的方法往往忽略了物理信息,并与效率作斗争,一些技术是侵入性的或计算昂贵的.
- 对于高效的在线阶段而言,现有的超缩减方法要么是侵入性的,要么需要大量的离线计算.
研究的目的:
- 提出一种非侵入性的,基于物理的,双层深度网络 (TTDN) 方法,以解决目前基于ML的MOR技术的局限性.
- 开发一种方法,降低离线计算成本,增强泛化能力.
- 将物理定律直接集成到神经网络培训过程中,以改善MOR.
主要方法:
- 建议采用双层深度网络 (TTDN) 架构,其灵感来源于基于物理学的神经网络.
- 第一个层执行利息量的回归,而第二层重建物理构成法.
- 该网络使用预培训和半监督学习策略进行培训.
主要成果:
- TTDN 方法在处理具有挑战性的非线性和非同源性问题的过程中表现出了效率.
- 数字实验证实了拟议的基于物理学的方法的有效性.
- 该方法成功地解决了与线下培训阶段相关的高计算成本.
结论:
- 拟议的非侵入性,基于物理的TTDN方法为计算昂贵的基于ML的MOR提供了有效的解决方案.
- 通过纳入物理定律,TTDN提高了概括性,并降低了培训成本.
- 这种方法对复杂的多尺度力学问题和其他非线性系统有希望.
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