Building General Langevin Models from Discrete Datasets
Building General Langevin Models from Discrete Datasets
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DOI：
10.1103/physrevx.10.031018
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发表时间：
2020-07-23
影响因子：
12.5
通讯作者：
Giardina, Irene
中科院分区：
文献类型：
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作者：
Ferretti, Federica;Chardes, Victor;Giardina, Irene
许多生命和复杂系统都表现出二阶涌现动力学。有限的实验访问配置自由度的结果，似乎是由一个非马尔可夫过程产生的数据。这种限制构成了一个挑战，在定量重建的模型从实验数据，即使在简单的情况下，平衡朗之万动力学的哈密顿系统。我们开发了一种新的贝叶斯推理方法，从离散的有限长度的轨迹学习这样的随机有效模型的参数。我们首先讨论了失败的天真的推断方法的基础上估计的衍生物，通过有限的差异，无论时间分辨率和采样轨迹的长度。然后，我们推导出，采用高阶离散化方案，最大似然估计的模型参数，提供了良好的结果，即使有适度长的轨迹。我们将我们的方法应用于集体运动的二阶模型，并表明我们的结果也适用于存在相互作用。
Many living and complex systems exhibit second-order emergent dynamics. Limited experimental access to the configurational degrees of freedom results in data that appear to be generated by a non-Markovian process. This limitation 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.