这篇综述为做物理建模或AI for Science的研究者提供了一个清晰的领域地图和思考框架，看完能快速理解不同方法适合解决什么问题，建议点开看看。
这篇综述论文提出了一个面向问题的视角来理解数据驱动微分方程发现领域。作者首先引入了一个二维相图，根据结构复杂度和系数复杂度对发现问题进行组织，展示了该领域如何从发现稀疏方程发展到更复杂的物理定律。然后提出了表示-评估-优化（REO）框架作为发现过程的基本抽象，将讨论从具体算法转向决定可发现性的基本原则。论文还讨论了这些视角在物理学及相关科学中的应用，并指出下一个挑战不仅是恢复方程，而是利用它们修正现有理论、提炼机制和形成新的科学概念。
Data-driven discovery of governing differential equations across physical systems
Differential equations play a critical role in scientific discovery because they provide a mathematical framework to describe the behaviour of physical phenomena. As a promising alternative to traditional first principles, data-driven differential equation discovery has attracted increasing attention for its ability to infer governing laws directly from experimental or simulated data, especially when the underlying physics is unclear. However, the field has expanded rapidly along diverse methodological directions, particularly with the emergence of AI-based approaches, and still lacks a clear organizing perspective. In this Review, we propose a problem-oriented perspective on data-driven differential equation discovery. We first introduce a two-dimensional phase diagram of equation discoverability, where discovery problems are organized according to structural complexity and coefficient complexity. This phase diagram shows how the field has moved from the discovery of sparse equations with simple coefficients toward more complex governing laws with richer structures and more flexible parameterizations. It also clarifies why different methodological families succeed or fail in different problem settings. We then present the representation-evaluation-optimization (REO) framework as a fundamental abstraction of the discovery process. By identifying the core problems of equation discovery that persist across algorithmic variations, REO shifts the discussion from individual algorithms to the fundamental principles that determine discoverability. We connect these perspectives to applications across physics and adjacent sciences, and argue that the next challenge is not merely recovering equations, but using them to revise existing theories, distil mechanisms and form new scientific concepts.