Abstract—

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.

中文翻译：

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走向微分方程的发现

摘要-

微分方程发现是机器学习的一个子领域，用于开发可解释的模型，特别是在与自然相关的应用中。通过熟练地结合运动方程的一般参数形式和适当的微分项，算法可以自动从数据中揭示方程。本文探讨了无需专家输入即可发现独立方程的先决条件和工具，从而消除了对方程形式假设的需要。我们专注于解决在正确方程未知时评估所发现方程的充分性的挑战，目的是在不先了解方程形式的情况下为可靠的方程发现提供见解。