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.

翻译：本文研究了在动态系统神经网络中显式添加辅助代数轨迹信息的效果。我们从微分代数方程及流形上微分方程领域汲取灵感，将相关方法应用于残差神经网络中，尽管两者在基本场景上存在差异。通过稳定化方法和投影方法融入约束或辅助信息的影响，并基于多体摆模拟与分子动力学场景的实验，展示了何时应使用何种方法。我们提出的多种方法易于在现有代码中实现，对训练性能影响有限，同时在推理阶段带来显著提升。