论文标题
时间反转对称ode网络
Time-Reversal Symmetric ODE Network
论文作者
论文摘要
时间反转对称性要求系统的动力学不应随时间轴的逆转而改变，它是经常在经典和量子力学中具有的基本属性。在本文中，我们提出了一种新颖的损失函数，该功能衡量了我们的普通微分方程（ODE）网络符合此时间反转对称性的很好。它是由前向和向后动力学之间的ode网络的时间演变中的差异正式定义的。然后，我们设计了一个新框架，我们将其命名为时间反转对称ode网络（TRS-odens），可以通过使用建议的损失函数来学习实体系统的动态。我们在几种经典的动力学上评估了TRS-末代，并发现它们可以从观察到的嘈杂和复杂的轨迹中学习所需的时间演变。我们还表明，即使对于没有全职反转对称性的系统，TRS-odens也可以实现比基础的更好的预测性能。
Time-reversal symmetry, which requires that the dynamics of a system should not change with the reversal of time axis, is a fundamental property that frequently holds in classical and quantum mechanics. In this paper, we propose a novel loss function that measures how well our ordinary differential equation (ODE) networks comply with this time-reversal symmetry; it is formally defined by the discrepancy in the time evolutions of ODE networks between forward and backward dynamics. Then, we design a new framework, which we name as Time-Reversal Symmetric ODE Networks (TRS-ODENs), that can learn the dynamics of physical systems more sample-efficiently by learning with the proposed loss function. We evaluate TRS-ODENs on several classical dynamics, and find they can learn the desired time evolution from observed noisy and complex trajectories. We also show that, even for systems that do not possess the full time-reversal symmetry, TRS-ODENs can achieve better predictive performances over baselines.
