Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic geometry methods can be used to identify the conservation laws. Our work focuses on using data-driven methods to identify the conservation law(s) in the absence of the knowledge of system dynamics. Building in part upon the ideas proposed in [arXiv:1811.00961], we develop a robust data-driven computational framework that automates the process of identifying the number and type of the conservation law(s) while keeping the amount of required data to a minimum. We demonstrate that due to relative stability of singular vectors to noise we are able to reconstruct correct conservation laws without the need for excessive parameter tuning. While we focus primarily on biological examples, the framework proposed herein is suitable for a variety of data science applications and can be coupled with other machine learning approaches.

翻译：守恒律是许多现实世界现象建模系统中的固有特征，尤其是那些建模生物和化学系统的模型。若底层动力系统的形式已知，可利用线性代数和代数几何方法识别守恒律。我们的工作聚焦于在系统动力学未知的情况下，采用数据驱动方法识别守恒律。部分基于文献[arXiv:1811.00961]提出的思路，我们开发了一个稳健的数据驱动计算框架，可自动化识别守恒律的数量和类型，同时将所需数据量降至最低。我们证明，由于奇异向量对噪声的相对稳定性，能够在无需过多参数调优的情况下重建正确的守恒律。尽管我们主要关注生物学示例，但本文提出的框架适用于多种数据科学应用，并可与其它机器学习方法结合使用。