时间一致的koopman自动编码器用于预测动态系统
Indranil Nayak1,2,3, Ananda Chakrabarti2, Mrinal Kumar1,4
1ElectroScience Laboratory, The Ohio State University, Columbus, OH, 43212, USA.
Scientific reports
|July 1, 2025
概括
一个新的时间一致的库普曼自编码器 (tcKAE) 改善了复杂系统的长期预测,即使数据有限或杂. 这种方法通过时间一致性规范化提高了模型的稳定性和通用性.
科学领域:
- 动态系统和控制理论.
- 机器学习和人工智能的人工智能
- 科学计算科学计算
背景情况:
- 高维时空系统的数据驱动建模因数据质量不足而面临挑战.
- 库普曼自动编码器 (KAE) 结合了深度神经网络,自动编码器和库普曼运算符理论,用于减少顺序的建模,但在有限/杂的数据上扎.
- 现有 KAE 的普遍性较差,阻碍了它们在现实场景中的应用.
研究的目的:
- 引入一种新的时间一致的库普曼自动编码器 (tcKAE) 以提高长期预测.
- 通过使用有限和杂的数据集来提高 KAE 的稳定性和通用性.
- 为tcKAE方法提供分析和经验验证.
主要方法:
- 通过结合一致性规范化术语,开发了临时一致的库普曼自编码器 (tcKAE).
- 正规化强制执行跨时间步骤的预测连贯性,增强模型稳定性.
- 从库普曼光谱理论得出的分析理由.
主要成果:
- 与最先进的KAE模型相比,tcKAE表现出卓越的性能.
- 该模型甚至在有限和杂的训练数据的情况下也能实现准确的长期预测.
- 在各种测试案例中进行经验验证,包括摆动振荡,动力等离子体和流体流.
结论:
- 在数据稀缺的环境中,tcKAE有效地解决了传统 KAE 的局限性.
- 拟议的时间一致性规范化显著提高了模型的稳定性和预测准确性.
- tcKAE为模拟复杂的时空动态系统提供了一个有前途的方法.
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