A Relational Macrostate Theory Guides Artificial Intelligence to Learn Macro and Design Micro
This work provides a unified machine learning framework for analyzing and designing complex systems, addressing a foundational problem in physics and AI, though it appears incremental in building on symmetry concepts.
The authors tackled the challenge of identifying general laws in complex systems by introducing a relational macrostate theory (RMT) and a machine learning architecture called MacroNet, which successfully identified macrostates across systems from simple harmonic oscillators to Turing patterns and enabled inverse design of microstates with specified macroscopic properties.
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 Anderson's seminal work 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 macrostates. 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 macroscopic property -- in Turing patterns this allows us to design underlying rule with a given specification of spatial patterning, and to identify which rule parameters most control these patterns. By demonstrating a general theory for how macroscopic properties emerge from conservation of symmetries in the mapping between observations, 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 macroscopic property.