Relational Macrostate Theory Guides Artificial Intelligence to Learn Macro and Design Micro

A central focus of science is the identification and application of laws, which are often represented as macrostates that capture invariant properties associated with symmetries. However, complex systems can be challenging to study due to their high-dimensionality, non-linearity, and emergent properties. To address this challenge, we propose the relational macrostate theory (RMT) that defines macrostates in terms of symmetries between mutually predictive observations. Additionally, we have developed a machine learning architecture, MacroNet, that can learn these macrostates and invertibly sample from them, allowing for the design of new microstates consistent with conserved properties. By utilizing this framework, we have studied how macrostates can be identified in systems ranging from simple harmonic oscillators to complex spatial patterns known as Turing instabilities. Our results demonstrate how emergent properties can be designed by identifying the unbroken symmetries that give rise to invariants, bypassing Anderson's "more is different" by showing that "more is the same" in complex systems.