Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are however difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended $\beta$-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables for the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.

翻译：随机过程在科学中有着广泛的应用，常用于模拟各种自然现象。然而，由于其固有的随机性和不确定性，对其进行表征较为困难。本文引入了一种无监督机器学习方法，用于确定有效描述随机过程动力学所需的最小参数集。该方法基于扩展的$\beta$-变分自编码器架构。通过使用对应于典型扩散模型的模拟数据集，我们展示了该方法在提取准确描述这些动力学的最小相关参数方面的有效性。此外，该方法还能够生成忠实再现预期随机行为的新轨迹。总体而言，我们的方法能够自主发现描述随机过程的未知参数，从而增强对跨领域复杂现象的理解。