Recent years have seen a surge of interest in the algorithmic estimation of stochastic entropy production (EP) from trajectory data via machine learning. A crucial element of such algorithms is the identification of a loss function whose minimization guarantees the accurate EP estimation. In this study, we show that there exists a host of loss functions, namely those implementing a variational representation of the $\alpha$-divergence, which can be used for the EP estimation. By fixing $\alpha$ to a value between $-1$ and $0$, the $\alpha$-NEEP (Neural Estimator for Entropy Production) exhibits a much more robust performance against strong nonequilibrium driving or slow dynamics, which adversely affects the existing method based on the Kullback-Leibler divergence ($\alpha = 0$). In particular, the choice of $\alpha = -0.5$ tends to yield the optimal results. To corroborate our findings, we present an exactly solvable simplification of the EP estimation problem, whose loss function landscape and stochastic properties give deeper intuition into the robustness of the $\alpha$-NEEP.

翻译：近年来，通过机器学习从轨迹数据中估计随机熵产生的研究引起了广泛关注。这类算法的关键要素是确定一个损失函数，其最小化能保证熵产生的准确估计。本研究表明，存在一系列损失函数（即实现$α$-散度变分表示的损失函数）可用于熵产生估计。通过将$α$固定为-1到0之间的值，$α$-NEEP（熵产生神经估计器）在强非平衡驱动或慢动力学条件下表现出更稳健的性能，而这些条件会对基于Kullback-Leibler散度（$α=0$）的现有方法产生不利影响。特别地，选择$α=-0.5$往往能获得最优结果。为验证上述发现，我们提出了熵产生估计问题的精确可解简化模型，其损失函数景观和随机特性为$α$-NEEP的稳健性提供了更深刻的直观认识。