[论文解读] A Data-Driven Statistical Field Theory for Active Matter

Ahmad Borzou, Alison E. Patteson+1 more|arXiv (Cornell University)|Mar 5, 2021

Cell Image Analysis Techniques被引用 1

一句话总结

本文提出一种数据驱动的统计场论，通过从实验数据推断单粒子密度并求解玻尔兹曼方程，以揭示活性物质系统中的物理原理。该方法应用于紫外光照射下的*萨尔蒂里亚菌*（Serratia marcescens）驱动粒子系统，揭示了一种具有空间可变质量的稳态高斯场论，表明熵增加且粒子净流量远离紫外照射区域。

ABSTRACT

Modeling living systems at the collective scale can be very challenging because the individual constituents can themselves be complex and the respective interactions between the constituents are not fully understood. With the advent of high throughput experiments and in the age of big data, data-driven methods are on the rise to overcome these challenges. Although machine-learning approaches can help quantify correlations between the various players, they do not directly shed light on the underlying physical principles of such systems. To directly illuminate the underlying physical principles, we present a data-driven method for obtaining the single particle density, from which physical quantities can be readily extracted, as well as for solving the Boltzmann equation for active matter -- a leading candidate for quantifying living systems. If the system is near a steady state, a field theory can be inferred to subsequently make physical predictions about the system. The method is first developed analytically for a scalar field and subsequently calibrated using simulated data. The method is then applied to an experimental system of particles actively-driven by a {\it Serratia marcescens} bacterial swarm and in the presence of spatially-localized UV light. The analysis demonstrates that the particles are in steady state before and some time after the UV light and obey a Gaussian field theory with a spatially-varying mass. We use our data-driven method to obtain the chemical potential, pressure, and entropy of the particulate system. Specifically, we demonstrate that the entropy of the particles increases in response to the UV light. In response to the UV light, there is net flow of the particles away from the UV light. We conclude with discussing other potential applications of the method to demonstrate its breadth.

研究动机与目标

• 开发一种数据驱动的方法，从集体活性物质系统中提取物理原理，其中个体相互作用机制尚不明确。
• 利用高通量实验数据推断单粒子密度并求解玻尔兹曼方程，避免依赖先前的机制模型。
• 在系统接近稳态时，从数据构建场论，以实现对化学势和压强等涌现物理量的物理预测。
• 在真实实验系统（细菌驱动粒子在空间局域化紫外光照射下）应用前，先在模拟数据上验证该方法。
• 直接从数据量化热力学量——化学势、压强和熵——在外部扰动下的活体系统中的表现。

提出的方法

• 通过非参数密度估计方法，从实验粒子轨迹推导单粒子概率密度函数。
• 通过从推断出的密度中推断具有空间可变质量项的高斯场论，构建场论描述。
• 通过将稳态分布拟合到与统计力学一致的形式，以数据驱动方式求解玻尔兹曼方程。
• 在应用于真实实验数据前，使用模拟数据校准场论参数。
• 利用标准热力学关系，从推断出的场论模型中提取化学势、压强和熵等物理量。
• 该方法利用统计推断，从原始轨迹数据直接过渡到可预测的场论，而无需假设底层相互作用规律。

实验结果

研究问题

• RQ1 能否通过数据驱动方法，从未知实验粒子轨迹中推断出一致的活性物质场论描述？
• RQ2 系统在紫外照射前后是否处于稳态，从而支持构建可预测的场论？
• RQ3 从数据中推断出的粒子系统中，涌现的热力学量——化学势、压强和熵——是什么？
• RQ4 紫外光照射如何改变系统的粒子分布和热力学状态？
• RQ5 该方法能否检测并量化外部刺激（如局域光）引起的熵变和粒子流动变化？

主要发现

• 粒子系统在紫外照射前后均处于稳态，使得能够推断出具有空间可变质量项的高斯场论。
• 该方法成功地直接从实验数据推断出活性粒子系统的化学势、压强和熵。
• 粒子系统的熵在紫外光照射下增加，表明无序度或构型自由度上升。
• 紫外光诱导粒子净流出照射区域，与对外部刺激的非平衡响应一致。
• 推断出的场论准确捕捉了系统的行为，其中空间可变质量项反映了紫外光对局部环境的调制作用。
• 该方法在其他活性物质系统中也具有广泛适用性，表明其在仅从数据出发分析复杂生物系统和软物质系统方面具有实用价值。