In this article we investigate the effect of explicitly adding auxiliary 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 similar methods in residual neural networks. We discuss constraints through stabilization as well as projection methods, and 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:在本条中,我们调查在动态系统神经网络中明确增加辅助轨迹信息的效果。我们从不同代数方程式和元数差异方程式领域得到启发,并在残余神经网络中采用类似方法。我们讨论通过稳定以及预测方法的制约因素,并表明何时使用基于多体钟和分子动态情景模拟实验的方法。我们的一些方法很容易在现有代码中实施,对培训绩效的影响有限,同时在推论方面给予显著的推动。