Many living and complex systems exhibit second order emergent dynamics. Limited experimental access to the configurational degrees of freedom results in data that appears to be generated by a non-Markovian process. This poses a challenge in the quantitative reconstruction of the model from experimental data, even in the simple case of equilibrium Langevin dynamics of Hamiltonian systems. We develop a novel Bayesian inference approach to learn the parameters of such stochastic effective models from discrete finite length trajectories. We first discuss the failure of naive inference approaches based on the estimation of derivatives through finite differences, regardless of the time resolution and the length of the sampled trajectories. We then derive, adopting higher order discretization schemes, maximum likelihood estimators for the model parameters that provide excellent results even with moderately long trajectories. We apply our method to second order models of collective motion and show that our results also hold in the presence of interactions.

中文翻译：

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从离散数据集构建通用Langevin模型

许多有生命的和复杂的系统表现出二阶突发动力学。对配置自由度的有限实验访问会导致数据似乎是由非马尔可夫过程生成的。即使在哈密顿系统的平衡兰格文动力学的简单情况下，这也对从实验数据定量重建模型提出了挑战。我们开发了一种新颖的贝叶斯推理方法，以从离散有限长度轨迹中学习此类随机有效模型的参数。我们首先讨论基于有限差分估计导数的幼稚推理方法的失败，而不考虑时间分辨率和采样轨迹的长度。然后，我们采用高阶离散化方案，模型参数的最大似然估计器即使在中等长的轨迹下也能提供出色的结果。我们将我们的方法应用于集体运动的二阶模型，并表明我们的结果在交互作用下也成立。