The high dimesionality, non-linearity and emergent properties of complex systems pose a challenge to identifying general laws in the same manner that has been so successful in simpler physical systems. In the seminal work of Anderson on why more is different he pointed to how emergent, macroscale patterns break symmetries of the underlying microscale laws. Yet, less recognized is that these large scale, emergent patterns must also retain some symmetries of the microscale rules. Here we introduce a new, relational macrostate theory (RMT) that defines macrostates in terms of symmetries between two mutually predictive observations, and develop a machine learning architecture, MacroNet, that identifies which symmetries are preserved during the mapping from micro-to-macro. Using this framework, we show how macrostates can be identifed across systems ranging in complexity from the simplicity of the simple harmonic oscillator to the much more complex spatial patterning characteristic of Turing instabilities. Furthermore, we show how our framework can be used for the inverse design of microstates consistent with a given macroscale property - in Turing patterns this allows us to design microstates with a given specification of macroscale spatial patterning, and to identify which parameters most control these patterns. By demonstrating a general theory for how macroscale properties emerge from conservation of symmetries in the mapping from micro-to-macro, we provide a machine learning framework that allows a unified approach to identifying macrostates in systems from the simple to complex, and allows the design of new examples consistent with a given macroscale property.

提出了一个新的关系性宏观状态理论（RMT），并开发了一个机器学习架构 MacroNet，该电子框架可用于简单到复杂系统中的宏观状态的识别和设计微观状态。

基于关系的宏观状态理论指导人工智能学习宏观及设计微观