Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

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学习单个和集体细胞迁移的动态模型：回顾

单细胞和集体细胞迁移是对从胚胎发育和免疫反应到伤口愈合和癌症转移等生理现象至关重要的基本过程。为了从物理角度理解细胞迁移，已经开发了控制细胞运动的潜在物理机制的多种模型。开发此类模型的一个关键挑战是如何将它们与实验观察联系起来，而实验观察通常表现出复杂的随机行为。在这篇综述中，我们讨论了数据驱动的理论方法的最新进展，这些方法直接与实验数据联系起来，推断随机细胞迁移的动力学模型。利用纳米制造、图像分析和跟踪技术的进步，实验研究现在提供了前所未有的关于细胞动力学的大型数据集。与此同时，理论工作致力于将这些数据集整合到从单细胞到组织尺度的物理模型中，目的是概念化细胞的新兴行为。我们首先回顾一下如何在自由迁移和受限细胞中解决这个推理问题。接下来，我们讨论为什么这些动力学通常采用欠阻尼随机运动方程的形式，以及如何从数据推断出此类方程。然后，我们回顾了数据驱动推理和机器学习方法在细胞行为异质性、亚细胞自由度以及多细胞系统集体动力学方面的应用。在这些应用中，我们强调数据驱动的方法如何与迁移细胞的物理活性物质模型相结合，并帮助揭示潜在的分子机制如何控制细胞行为。总之，这些数据驱动的方法是直接从实验数据构建细胞迁移物理模型以及提供不同长度描述之间的概念联系的有前途的途径。