通过将数据和背景知识与AI (希尔伯特人工智能) 统一,发展科学发现.
Ryan Cory-Wright1, Cristina Cornelio2, Sanjeeb Dash3
1Department of Analytics, Marketing and Operations, Imperial College Business School, London, UK. r.cory-wright@imperial.ac.uk.
Nature communications
|July 14, 2024
概括
科学家现在可以通过将实验数据整合到方程发现过程中来发现自然规律. 这种新方法使用多项式优化来导出科学定律,提高效率和准确性.
科学领域:
- 科学发现是科学发现.
- 计算科学是一种计算科学.
- 数学物理学的数学物理.
背景情况:
- 发现科学规律传统上涉及对基于现有知识的方程进行操纵,通常不包括实验数据.
- 这种间接方法可能是低效的,可能无法充分利用现有信息.
研究的目的:
- 开发一种原则性的科学发现方法,直接结合实验数据.
- 为了证明这种方法用于推导已知的科学规律的适用性.
主要方法:
- 将科学定律建模为多项式,并使用二进制变量和逻辑约束.
- 通过混合整数线性或半确定的优化解决多项式优化问题.
- 使用Positivstellensatz证书验证发现的科学规律.
主要成果:
- 成功地从公理和实验数据中推导出开普勒的行星运动定律.
- 使用拟议的方法推导出辐射引力波功率方程.
- 证明该方法对多项式科学定律具有广泛适用性.
结论:
- 拟议的方法通过整合实验数据,提供了一种更有效和更有原则的方式来发现科学规律.
- 这种计算方法可以加速科学发现,并揭示对自然现象的新见解.
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