从基于代理的蒙特卡洛模拟数据中学习黑色和灰色盒的化疗PDEs/闭包.
Seungjoon Lee1, Yorgos M Psarellis2, Constantinos I Siettos3
1Department of Applied Data Science, San José State University, San Jose, USA.
Journal of mathematical biology
|June 21, 2023
概括
我们开发了一个机器学习框架,从细菌运动模拟中发现宏观化疗部分微分方程 (PDEs). 这种方法使得数据驱动的发现复杂的生物行为.
科学领域:
- 计算生物学 计算生物学
- 生物物理学的生物物理.
- 应用数学 应用数学 应用数学
背景情况:
- 细菌的运动性,就像大肠杆菌一样,是一个复杂的现象,是由单个细胞行为驱动的.
- 宏观模型,如化疗部分微分方程 (PDEs),对于理解集体细菌运动至关重要.
- 现有的模型通常依赖于关闭关系的简化假设或近似.
研究的目的:
- 开发一种机器学习框架,用于从基于个体的模拟中发现宏观化疗PDEs及其闭合关系.
- 为了使有效的,粗粒度模型从微量生物物理模拟的数据驱动衍生.
- 调查PDE发现的黑盒和灰盒机器学习方法.
主要方法:
- 利用高准确度,以个人为基础的Escherichia coli运动性的随机模拟,结合基础生物物理.
- 采用混合连续-蒙特卡洛模拟模型,参数由实验数据提供信息.
- 应用机器学习回归器,包括前神经网络和高斯过程,以从集体可观测物学习PDEs.
主要成果:
- 成功发现了属于凯勒-塞格尔类的有效的粗粒化疗PDEs.
- 证明了学习黑盒 (完全数据驱动) 和灰盒 (部分已知的结构) PDE 规律的能力.
- 展示了分析已知的数据驱动的校正,近似的关闭关系.
结论:
- 拟议的机器学习框架提供了一个强大的工具,用于从复杂的生物系统中以数据驱动发现宏观的PDEs.
- 这种方法弥合了个人层面的生物物理学和集体的新兴行为之间的差距.
- 该框架有助于改进现有模型,并发现生物现象的新数学描述.
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