The discovery of equations with knowledge of the process origin is a tempting prospect. However, most equation discovery tools rely on gradient methods, which offer limited control over parameters. An alternative approach is the evolutionary equation discovery, which allows modification of almost every optimization stage. In this paper, we examine the modifications that can be introduced into the evolutionary operators of the equation discovery algorithm, taking inspiration from directed evolution techniques employed in fields such as chemistry and biology. The resulting approach, dubbed directed equation discovery, demonstrates a greater ability to converge towards accurate solutions than the conventional method. To support our findings, we present experiments based on Burgers', wave, and Korteweg--de Vries equations.

翻译：利用过程起源知识进行方程发现是一个引人期待的前景。然而，大多数方程发现工具依赖梯度方法，这类方法对参数的控制能力有限。另一种替代方案是进化式方程发现，它能够修改优化过程的几乎所有阶段。本文受化学和生物学等领域中采用的定向进化技术启发，研究了方程发现算法进化算子中可引入的改进方案。由此产生的被称为"定向方程发现"的方法，相比传统方法展现出更强的收敛至精确解的能力。为支撑研究结果，我们基于Burgers方程、波动方程及Korteweg-de Vries方程开展了实验验证。