论文标题
与信息瓶颈中混乱的双摆中的信息丢失表征
Characterizing information loss in a chaotic double pendulum with the Information Bottleneck
论文作者
论文摘要
混乱动态的标志是随着时间的流逝而失去信息。尽管信息丢失通常是通过与Lyapunov指数的连接来表示的 - 在有关系统状态的高信息的限制下有效，但该图片却错过了各种粒度级别的信息衰减的丰富范围。在这里，我们展示了机器学习如何为研究混乱动态中信息丢失的新机会，并用双摆充当模型系统。我们将信息瓶颈用作神经网络的培训目标，以从系统状态中提取信息状态，这些信息在规定的时间范围后可以最佳地预测未来状态。然后，我们通过向每个状态变量分配瓶颈来分解最佳预测性信息，从而恢复变量在确定未来演变中的相对重要性。我们开发的框架广泛适用于混沌系统，并务实应用，利用数据和机器学习来监视可预测性的限制并绘制出信息丢失。
A hallmark of chaotic dynamics is the loss of information with time. Although information loss is often expressed through a connection to Lyapunov exponents -- valid in the limit of high information about the system state -- this picture misses the rich spectrum of information decay across different levels of granularity. Here we show how machine learning presents new opportunities for the study of information loss in chaotic dynamics, with a double pendulum serving as a model system. We use the Information Bottleneck as a training objective for a neural network to extract information from the state of the system that is optimally predictive of the future state after a prescribed time horizon. We then decompose the optimally predictive information by distributing a bottleneck to each state variable, recovering the relative importance of the variables in determining future evolution. The framework we develop is broadly applicable to chaotic systems and pragmatic to apply, leveraging data and machine learning to monitor the limits of predictability and map out the loss of information.
