论文标题
测谎仪
The Lie Detector
论文作者
论文摘要
我们真的需要多少个自由变量来构建物理系统的可靠模型？目前没有系统的方法。我们通过与规范案例进行比较来呼吁一些物理原则，调整无变量，并希望我们之间的现实应用程序在它们之间插值。在这项工作中，我们结合了两个开创性和完全不同的数学作品：Sophus的百年技术谎言，用于解决差异率，以及Field的奖牌获得者Terence Tao在将NP完整组合问题转换为相邻的convex优化的最新工作。我们提出了一个新颖且完全系统的程序，用于设计具有必要且恰好复杂性的物理系统模型，与神经网络和其他当前机器学习方法采用的功能近似方法形成鲜明对比。我们的方法替代了从观察性，实验或模拟数据中恢复结构和理解的模型的临时开发。从本质上讲，我们的方法旨在找到称为Lie对称性的微分方程的不变属性，因此，我们称我们的算法为Lie ottecter。
How many free variables do we really need to build a credible model of a physical system? Currently there is no systematic approach; we appeal to some physical principles, tune free variables by comparing with canonical cases, and hope our real-world applications interpolate between them. In this work we combine two pioneering and entirely disparate pieces of mathematics: the century-old techniques of Sophus Lie for solving differential equtions and recent work initiated by Field's medallist Terence Tao on converting NP-complete combinatorical problems into neighbouring convex optimisations. We present a novel and fully systematic procedure for designing models of physical systems with necessary and just-sufficient complexity, in marked contrast with the approach to function approximation taken by neural networks and other current approaches to machine learning. Our methodology replaces the ad-hoc development of models to recover structure and understanding from observational, experimental or simulated data. At its core, our method seeks to find invariant properties of differential equations known as Lie symmetries, and for this reason we have called our algorithm the Lie Detector.
