论文标题
神经Langevin动力学：朝向可解释的神经随机微分方程
Neural Langevin Dynamics: towards interpretable Neural Stochastic Differential Equations
论文作者
论文摘要
神经随机微分方程（NSDE）已被培训为两种变异自动编码器和gan。但是，由于漂移和扩散场的通用性质，因此很难解释或分析所得的随机微分方程。通过将我们的NSDE限制为Langevin Dynamics的形式，并以VAE进行训练，我们获得了NSDE，可以比一般的NSDE进行更精细的分析和更广泛的可视化技术。更具体地说，我们获得了一个能量景观，其最小值是与所用数据的潜在状态一对一的对应关系。这不仅允许我们以无监督的方式检测数据动态的基础状态，而且还可以根据学习的SDE推断在每个状态上所花费的时间的分布。通常，将NSDE限制为langevin Dynamics可以从计算分子动力学中使用大量工具来分析获得的结果。
Neural Stochastic Differential Equations (NSDE) have been trained as both Variational Autoencoders, and as GANs. However, the resulting Stochastic Differential Equations can be hard to interpret or analyse due to the generic nature of the drift and diffusion fields. By restricting our NSDE to be of the form of Langevin dynamics, and training it as a VAE, we obtain NSDEs that lend themselves to more elaborate analysis and to a wider range of visualisation techniques than a generic NSDE. More specifically, we obtain an energy landscape, the minima of which are in one-to-one correspondence with latent states underlying the used data. This not only allows us to detect states underlying the data dynamics in an unsupervised manner, but also to infer the distribution of time spent in each state according to the learned SDE. More in general, restricting an NSDE to Langevin dynamics enables the use of a large set of tools from computational molecular dynamics for the analysis of the obtained results.
