The project of physics discovery is often equivalent to finding the most concise description of a physical system. The description with optimum predictive capability for a dataset generated by a physical system is one that minimizes both predictive error on the dataset and the complexity of the description. The discovery of the governing physics of a system can therefore be viewed as a mathematical optimization problem. We outline here a method to optimize the description of arbitrarily complex physical systems by minimizing the entropy of the description of the system. The Recursive Domain Partitioning (RDP) procedure finds the optimum partitioning of each physical domain into subdomains, and the optimum predictive function within each subdomain. Penalty functions are introduced to limit the complexity of the predictive function within each domain. Examples are shown in 1D and 2D. In 1D, the technique effectively discovers the elastic and plastic regions within a stress-strain curve generated by simulations of amorphous carbon material, while in 2D the technique discovers the free-flow region and the inertially-obstructed flow region in the simulation of fluid flow across a plate.
翻译:物理发现项目往往相当于找到物理系统最简明的描述。物理系统生成的数据集的最佳预测能力描述是将数据集的预测错误和描述复杂性最小化的描述。因此,发现一个系统的管辖物理学可被视为数学优化问题。我们在此概述一种通过将系统描述的酶最小化来优化任意复杂物理系统描述的方法。再分层(RDP)程序发现每个物理域在子域中的最佳分隔,以及每个子域内的最佳预测功能。引入惩罚功能是为了限制每个域内预测功能的复杂性。示例见1D和2D。在1D中,该技术有效地发现在不固定碳材料模拟产生的压力-压力-压力曲线内弹性和塑料区域,而在2D中,该技术发现自由流区和惯性-渗透流区域,以模拟流过板块的液体流动。