arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2011.14442hep-thmath.AGphysics.hist-ph
收藏

宇宙作为大数据

Universes as Big Data

Yang-Hui He

摘要:

我们简要地回顾一下,从历史上看,弦论是如何首先将理论物理引向代数几何和微分几何中的精确问题,然后在过去十年左右的时间里引向计算几何,现在,在过去几年里,又引向数据科学。使用Calabi-Yau景观-由物理学家,数学家和计算机科学家在过去40年中的合作积累-作为起点和具体的游乐场,我们回顾了机器学习应用于从紧化筛选可能的宇宙的一些最新进展,以及量子场论几何工程中更广泛的问题。同时,我们讨论了机器学习数学结构的程序,并解决了它如何帮助做数学的诱人问题,从数学物理,几何,表示论,组合数学和数论。

英文摘要:

We briefly overview how, historically, string theory led theoretical physics first to precise problems in algebraic and differential geometry, and thence to computational geometry in the last decade or so, and now, in the last few years, to data science. Using the Calabi-Yau landscape -- accumulated by the collaboration of physicists, mathematicians and computer scientists over the last 4 decades -- as a starting-point and concrete playground, we review some recent progress in machine-learning applied to the sifting through of possible universes from compactification, as well as wider problems in geometrical engineering of quantum field theories. In parallel, we discuss the programme in machine-learning mathematical structures and address the tantalizing question of how it helps doing mathematics, ranging from mathematical physics, to geometry, to representation theory, to combinatorics, and to number theory.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑