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Aug, 2024
基于动力系统的辛神经网络
Symplectic Neural Networks Based on Dynamical Systems
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Benjamin K Tapley
TL;DR
本研究针对传统神经网络在哈密尔顿微分方程中的局限性，提出了一种基于几何积分器的辛神经网络（SympNets）框架。该框架具有非消失梯度的特性，并能够完全参数化与二次哈密尔顿对应的辛映射，实验结果表明其在表现力和准确性上显著优于现有架构，尤其是在训练成本上更具优势。
Abstract
We present and analyze a framework for designing
Symplectic Neural Networks
(SympNets) based on
Geometric Integrators
for Hamiltonian differential equations. The SympNets are universal approximators in the space
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