无需预设项式库，用基础函数自动发现物理方程
Equation discovery framework EPDE: Towards a better equation discovery
- 用基本函数和微分项自动生成方程候选，摆脱固定项式库限制
- 多目标优化提升搜索效率，在含噪数据下仍能准确提取方程
- 适合需要从复杂实验数据中挖掘物理规律的研究者
方程发现方法在从物理相关数据中提取知识方面具有潜力。然而，现有方法通常需要大量先验信息，显著降低了可提取的知识量。本文改进了基于进化优化的EPDE算法。与依赖预定义项式库和线性的SINDy等方法不同，本方法使用基本函数和独立微分项作为构建块生成方程项。在进化优化中，我们改进了适应度函数计算方式，类似梯度方法，并优化了整体搜索算法。通过引入多目标优化，有效探索搜索空间，即使在复杂实验数据下也能实现更鲁棒的方程提取。我们通过与最先进框架SINDy的对比，验证了该算法在抗噪声性和整体性能上的优势。
原文摘要 · Abstract (English)
Equation discovery methods hold promise for extracting knowledge from physics-related data. However, existing approaches often require substantial prior information that significantly reduces the amount of knowledge extracted. In this paper, we enhance the EPDE algorithm -- an evolutionary optimization-based discovery framework. In contrast to methods like SINDy, which rely on pre-defined libraries of terms and linearities, our approach generates terms using fundamental building blocks such as elementary functions and individual differentials. Within evolutionary optimization, we may improve the computation of the fitness function as is done in gradient methods and enhance the optimization algorithm itself. By incorporating multi-objective optimization, we effectively explore the search space, yielding more robust equation extraction, even when dealing with complex experimental data. We validate our algorithm's noise resilience and overall performance by comparing its results with those from the state-of-the-art equation discovery framework SINDy.
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