透過學習不同相中的物理量，人們認為機器學習能夠給出其中相變的位置來幫助我們更加了解物理系統. 然而，常見的方法需要預先假設相變的存在，並使用監督式學習來判斷相變。這不太符合實際的情況，因為我們不應該先知道相變是否真的存在，也不應該知道如何為物理量標記它所對應的相。 在這篇論文裡，我們指出了以往監督式學習應用的缺點與問題，並且透過八個不同的測試來驗證它們。

此外，我們提出了新的非監督式學習方法。在不需要預先假設相變的存在之下，它依然能夠給出精確的相變點。 更特別的是，它有能力區分判斷出的相變點是否為真。這在以往的機器學習方法是不可能做到的。 這代表說我們的方法確實不需要任何的先備知識，並且可以應用在新的多體系統上。

It has been believed that the phase boundary between two different quantum states can be determined by a machine learning model which is trained by the physical observable in the deep regimes of these two phases. However, the common method may not be reliable because it is still based on a theoretical work that a phase transition must exist somewhere in between. In this work, we indicate several shortcomings of the common method, which is supervised learning technique, and verify them through eight different tests, two physical systems with four kinds of data.

Besides, we develop a new unsupervised learning method, which can determine phase boundary exactly even without assuming its existence. Moreover, it has an ability to distinguish whether the phase transition really occurs or not, which is impossible for the typical machine learning model. This implies that our approach could be in principle applied to discover new many-body states without any priori theoretical works.

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