时间延迟对称ODE网络
Time-Reversal Symmetric ODE Network
摘要：
时间反演对称性要求系统的动力学不应随着时间轴的反转而改变，这是经典力学和量子力学中经常存在的基本性质。在本文中，我们提出了一种新的损失函数，衡量我们的常微分方程（ODE）网络遵守这种时间反演对称性的程度;它是由ODE网络的前向和后向动态之间的时间演化差异正式定义的。然后，我们设计了一个新的框架，我们称之为时间延迟对称ODE网络（TRS-ODENs），它可以学习物理系统的动力学更有效的样本通过学习与建议的损失函数。我们评估TRS-ODENS在几个经典的动力学，并发现他们可以学习所需的时间演化从观察到的嘈杂和复杂的轨迹。我们还表明，即使对于不具有完整的时间反演对称性的系统，TRS-ODENS可以实现更好的预测性能超过基线。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
