The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically requires mathematical proficiency and manual analytical work. In this paper, we present a neural network that can simultaneously learn the dynamics of the system and the constants of motion from data. By exploiting the discovered constants of motion, it can produce better predictions on dynamics and can work on a wider range of systems than Hamiltonian-based neural networks. In addition, the training progresses of our method can be used as an indication of the number of constants of motion in a system which could be useful in studying a novel physical system.
翻译:物理学的美丽之处在于,在一个始终变化的系统中,通常会有一个被保存的数量,称为运动的常态。发现运动的常态对于了解系统的动态非常重要,但通常需要数学熟练度和人工分析工作。在本文中,我们提出了一个神经网络,可以同时学习系统的动态和数据运动的常数。通过利用所发现的运动常数,它可以对动态产生更好的预测,并且可以对更广泛的系统进行比汉密尔顿神经网络更多的工作。此外,我们方法的培训进展可以用来表明一个系统内运动常数的数量,这个系统可用于研究新的物理系统。