Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and appropriate differential terms, algorithms can autonomously uncover equations from data. This paper explores the prerequisites and tools for independent equation discovery without expert input, eliminating the need for equation form assumptions. We focus on addressing the challenge of assessing the adequacy of discovered equations when the correct equation is unknown, with the aim of providing insights for reliable equation discovery without prior knowledge of the equation form.

翻译：微分方程发现作为机器学习的一个子领域，用于开发可解释模型，尤其在自然相关应用中。通过专业地整合运动方程的一般参数形式和适当的微分项，算法可以自主从数据中挖掘出方程。本文探讨了无需专家输入即可独立发现方程的前提条件和工具，消除了对方程形式假设的需求。我们重点解决在未知正确方程的情况下评估所发现方程充分性的挑战，旨在为无需事先知道方程形式即可可靠发现方程提供见解。