CDI-Type I: Distilling Freeform Natural Laws from Experimental Data

该奖项是根据2009年美国复苏和再投资法案(公法111-5)资助的。这项研究的目标是开发通用算法，自动识别从物理到生物等领域所观察到的现象背后的原理。几个世纪以来，科学家们一直试图识别和记录自然界中物理现象背后的分析定律。尽管在科学研究中普遍存在计算能力，但寻找自然规律及其对应的方程式一直抵制自动化。该方法基于符号回归方法，可以在时间序列数据中搜索描述不变量的方程。寻找不变量通常会比单纯的预测带来更深层次的洞察：例如，寻找钟摆运动中的不变量会导致发现能量守恒。在智力方面，研究寻找新的算法来自动搜索在数据上守恒的隐含模型，同时搜索导致竞争模型预测之间最大不一致的新实验。自动寻找分析关系的一个关键挑战是在算法上定义是什么使观察到的数据中的相关性变得重要和不重要。最终的里程碑将是所提出的方法在生物等新系统中识别未知的规律，其中自然规律和守恒定律很难找到。从更广泛的影响来看，该研究解决了许多领域中自动和动态综合非线性系统模型的结构和参数的方法的需求。从行为主动推断模型的能力可以应用于创建从机器人到生物网络再到人类行为的工程系统和自然系统的模型。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The objective of this research is to develop general-purpose algorithms for automatically identifying principles underlying observed phenomena, in fields ranging from physics to biology. For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power in scientific inquiry, finding natural laws and their corresponding equations has resisted automation. The approach is based on symbolic regression methods that can search for equations that describe invariant quantities in time-series data. Seeking invariants usually leads to deeper insights than prediction alone: For example, seeking invariant quantities in a pendulum motion leads to discovery of the conservation of energy.With respect to intellectual merit, the research seeks new algorithms to automatically search for implicit models that are conserved over the data and, simultaneously, search for new experiments that cause maximum disagreement between competing model predictions. A key challenge to finding analytic relationships automatically is defining algorithmically what makes a correlation in observed data significant and non-trivial. The ultimate milestone will be for the proposed method to identify yet-unknown laws in new systems such as biology, where natural laws and conservations are difficult to find.With respect to broader impact, the research addresses the need for methods to automatically and dynamically synthesize both the structure and parameters of models of nonlinear systems in many fields. The ability to actively infer models from behavior can be applied to create models of both engineered and natural systems from robotics to biological networks to human behavior.