Evolutionary differential equation discovery proved to be a tool to obtain equations with less a priori assumptions than conventional approaches, such as sparse symbolic regression over the complete possible terms library. The equation discovery field contains two independent directions. The first one is purely mathematical and concerns differentiation, the object of optimization and its relation to the functional spaces and others. The second one is dedicated purely to the optimizational problem statement. Both topics are worth investigating to improve the algorithm's ability to handle experimental data a more artificial intelligence way, without significant pre-processing and a priori knowledge of their nature. In the paper, we consider the prevalence of either single-objective optimization, which considers only the discrepancy between selected terms in the equation, or multi-objective optimization, which additionally takes into account the complexity of the obtained equation. The proposed comparison approach is shown on classical model examples -- Burgers equation, wave equation, and Korteweg - de Vries equation.

翻译：演化微分方程发现已被证明是一种工具，能够以比传统方法（如基于完整可能项库的稀疏符号回归）更少的先验假设来获得方程。方程发现领域包含两个独立方向。第一个方向纯粹是数学性的，涉及微分、优化对象及其与函数空间的关系等。第二个方向则专门致力于优化问题的陈述。这两个主题都值得研究，以提升算法以更接近人工智能的方式处理实验数据的能力，无需显著的预处理及其性质的先验知识。在本文中，我们考虑了单目标优化（仅考虑方程中选定项之间的偏差）或多目标优化（额外考虑所得方程的复杂度）中哪一种更占优势。所提出的比较方法在经典模型示例——伯格斯方程、波动方程和科特韦格-德弗里斯方程上进行了展示。