方程发现框架 EPDE：迈向更好的方程发现
Equation discovery framework EPDE: Towards a better equation discovery
AI总结：
本文增强了基于进化优化的方程发现框架EPDE，利用初等函数和微分等基本构建块生成项，并引入多目标优化来有效探索搜索空间，相比SINDy等现有方法，在处理复杂实验数据时实现了更稳健的方程提取和更好的噪声鲁棒性。
摘要：
方程发现方法有望从物理相关数据中提取知识。然而，现有方法通常需要大量先验信息，这显著减少了提取的知识量。在本文中，我们增强了 EPDE 算法——一个基于进化优化的发现框架。与 SINDy 等依赖于预定义项库和线性关系的方法不同，我们的方法使用基本构建块（如初等函数和单个微分）来生成项。在进化优化中，我们可以像梯度方法那样改进适应度函数的计算，并增强优化算法本身。通过引入多目标优化，我们有效地探索了搜索空间，即使在处理复杂的实验数据时，也能产生更稳健的方程提取。我们通过将算法结果与最先进的方程发现框架 SINDy 的结果进行比较，验证了算法的噪声鲁棒性和整体性能。
英文摘要：
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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