Universidad de San Andrés, Buenos Aires 1644, Argentina.
Physics Department, University of Buenos Aires and Buenos Aires Physics Institute, Buenos Aires 1428, Argentina.
Phys Rev Lett. 2020 Dec 4;125(23):238101. doi: 10.1103/PhysRevLett.125.238101.
We consider the problem of encoding pairwise correlations between coupled dynamical systems in a low-dimensional latent space based on few distinct observations. We use variational autoencoders (VAEs) to embed temporal correlations between coupled nonlinear oscillators that model brain states in the wake-sleep cycle into a two-dimensional manifold. Training a VAE with samples generated using two different parameter combinations results in an embedding that encodes the repertoire of collective dynamics, as well as the topology of the underlying connectivity network. We first follow this approach to infer the trajectory of brain states measured from wakefulness to deep sleep from the two end points of this trajectory; then, we show that the same architecture was capable of representing the pairwise correlations of generic Landau-Stuart oscillators coupled by complex network topology.
我们考虑基于少数几个不同观测值，在低维潜在空间中对耦合动力系统之间的成对相关性进行编码的问题。我们使用变分自编码器 (VAEs) 将模型睡眠-觉醒周期中大脑状态的耦合非线性振荡器之间的时间相关性嵌入到二维流形中。使用两种不同参数组合生成的样本训练 VAE 会导致嵌入编码集体动力学的曲目，以及基础连通性网络的拓扑结构。我们首先采用这种方法从轨迹的两个端点推断出从清醒到深度睡眠测量的脑状态的轨迹;然后，我们表明相同的架构能够表示通过复杂网络拓扑耦合的通用 Landau-Stuart 振荡器的成对相关性。
