Inferring dynamical models from low-resolution temporal data continues to be
a significant challenge in biophysics, especially within transcriptomics, where
separating molecular programs from noise remains an important open problem. We
explore a common scenario in which we have access to an adequate amount of
cross-sectional samples at a few time-points, and assume that our samples are
generated from a latent diffusion process. We propose an approach that relies
on the probability flow associated with an underlying diffusion process to
infer an autonomous, nonlinear force field interpolating between the
distributions. Given a prior on the noise model, we employ score-matching to
differentiate the force field from the intrinsic noise. Using relevant
biophysical examples, we demonstrate that our approach can extract
non-conservative forces from non-stationary data, that it learns equilibrium
dynamics when applied to steady-state data, and that it can do so with both
additive and multiplicative noise models.

从低分辨率时间数据推断动力学模型在生物物理学中仍然是一个重要的挑战，我们提出了一种方法，利用与潜在扩散过程相关的概率流来推断插值分布之间的自主的非线性力场，通过使用得分匹配来区分力场和固有噪声，我们的方法可以从非平稳数据中提取非守恒力，在应用于稳态数据时学习均衡动力学，无论是添加型噪声模型还是乘法型噪声模型。

通过密度估计的随机力推断

Stochastic force inference via density estimation

Parameter inference for stochastic differential equations is challenging due
to the presence of a latent diffusion process. Working with an Euler-Maruyama
discretisation for the diffusion, we use variational inference to jointly learn
the parameters and the diffusion paths. We use a standard mean-field
variational approximation of the parameter posterior, and introduce a recurrent
neural network to approximate the posterior for the diffusion paths conditional
on the parameters. This neural network learns how to provide Gaussian state
transitions which bridge between observations in a very similar way to the
conditioned diffusion process. The resulting black-box inference method can be
applied to any SDE system with light tuning requirements. We illustrate the
method on a Lotka-Volterra system and an epidemic model, producing accurate
parameter estimates in a few hours.

本文介绍了一种使用欧拉 - 马鲁雅马方法对扩散过程离散化，并应用变分推断方法共同学习参数和扩散路径的方法。这种方法使用平均场变分近似参数后验分布，并引入递归神经网络来近似参数条件下扩散路径的后验分布，所得结果可用于具有轻微调整需求的任何 SDE 系统，并在短短几个小时内产生准确的参数估计。

随机微分方程的黑匣子变分推理

Black-box Variational Inference for Stochastic Differential Equations

We present a probabilistic language model for time-stamped text data which
tracks the semantic evolution of individual words over time. The model
represents words and contexts by latent trajectories in an embedding space. At
each moment in time, the embedding vectors are inferred from a probabilistic
version of word2vec [Mikolov et al., 2013]. These embedding vectors are
connected in time through a latent diffusion process. We describe two scalable
variational inference algorithms--skip-gram smoothing and skip-gram
filtering--that allow us to train the model jointly over all times; thus
learning on all data while simultaneously allowing word and context vectors to
drift. Experimental results on three different corpora demonstrate that our
dynamic model infers word embedding trajectories that are more interpretable
and lead to higher predictive likelihoods than competing methods that are based
on static models trained separately on time slices.

该研究提出了一种基于概率的语言模型，可以跟踪个别单词随时间的语义演变，并通过嵌入空间中的潜在轨迹表示单词和上下文。研究发现，该动态模型推断的单词嵌入轨迹更易解释，并且具有更高的预测性可能性。