Determining whether a dynamical system is integrable is generally a difficult task which is currently done on a case by case basis requiring large human input. Here we propose and test an automated method to search for the existence of relevant structures, the Lax pair and Lax connection respectively. By formulating this search as an optimization problem, we are able to identify appropriate structures via machine learning techniques. We test our method on standard systems of classical integrability and find that we can single out some integrable deformations of a system. Due to the ambiguity in defining a Lax pair our algorithm identifies novel Lax pairs which can be easily verified analytically.

中文翻译：

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可集成性 Ex Machina

确定动态系统是否可积通常是一项艰巨的任务，目前需要大量人力投入，逐案完成。在这里，我们提出并测试了一种自动化方法来搜索相关结构的存在，分别是 Lax 对和 Lax 连接。通过将此搜索公式化为优化问题，我们能够通过机器学习技术识别合适的结构。我们在经典可积性的标准系统上测试我们的方法，发现我们可以挑出系统的一些可积变形。由于定义 Lax 对的模糊性，我们的算法识别了新的 Lax 对，可以轻松地进行分析验证。