论文标题
神经DAE：受约束的神经网络
Neural DAEs: Constrained neural networks
论文作者
论文摘要
本文研究了明确将辅助代数轨迹信息添加到动态系统的神经网络中的效果。尽管存在一些根本的情况差异，但我们从差分方程和差分方程的领域中汲取灵感，并在残留神经网络中实现相关方法。约束或辅助信息效应是通过稳定和投影方法纳入的，我们显示何时根据涉及涉及多体摆和分子动力学情景的实验的方法使用该方法。我们的几种方法在现有代码中易于实施，并且对培训性能的影响有限，同时在推理方面具有重大的提升。
This article investigates the effect of explicitly adding auxiliary algebraic trajectory information to neural networks for dynamical systems. We draw inspiration from the field of differential-algebraic equations and differential equations on manifolds and implement related methods in residual neural networks, despite some fundamental scenario differences. Constraint or auxiliary information effects are incorporated through stabilization as well as projection methods, and we show when to use which method based on experiments involving simulations of multi-body pendulums and molecular dynamics scenarios. Several of our methods are easy to implement in existing code and have limited impact on training performance while giving significant boosts in terms of inference.
