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基于辛格式的深度哈密尔顿神经网络

本站小编 Free考研考试/2021-12-27

祝爱卿, 金鹏展, 唐贻发
LSEC, 中国科学院数学与系统科学研究院, 计算数学与科学工程计算研究所, 北京 100190;中国科学院大学, 数学科学学院, 北京 100049
收稿日期:2020-03-28出版日期:2020-08-15发布日期:2020-08-15
通讯作者:唐贻发,Email:tyf@lsec.cc.ac.cn

基金资助:科技部“新一代人工智能”重大专项(2018AAA0101002)和国家自然科学基金项目(11771438).


DEEP HAMILTONIAN NEURAL NETWORKS BASED ON SYMPLECTIC INTEGRATORS

Zhu Aiqing, Jin Pengzhan, Tang Yifa
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Received:2020-03-28Online:2020-08-15Published:2020-08-15







摘要



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HNN是一类基于物理先验学习哈密尔顿系统的神经网络.本文通过误差分析解释使用不同积分器作为超参数对HNN的影响.如果我们把网络目标定义为在任意训练集上损失为零的映射,那么传统的积分器无法保证HNN存在网络目标.我们引进反修正方程,并严格证明基于辛格式的HNN具有网络目标,且它与原哈密尔顿量之差依赖于数值格式的精度.数值实验表明,由辛HNN得到的哈密尔顿系统的相流不能精确保持原哈密尔顿量,但保持网络目标;网络目标在训练集、测试集上的损失远小于原哈密尔顿量的损失;在预测问题上辛HNN较非辛HNN具备更强大的泛化能力和更高的精度.因此,辛格式对于HNN是至关重要的.
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