English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The high-dimesionality, non-linearity and emergent properties of complexsystems pose a challenge to identifying general laws in the same manner thathas been so successful in simpler physical systems. In Anderson's seminal workon why "more is different" he pointed to how emergent, macroscale patternsbreak symmetries of the underlying microscale laws. Yet, less recognized isthat these large-scale, emergent patterns must also retain some symmetries ofthe microscale rules. Here we introduce a new, relational macrostate theory(RMT) that defines macrostates in terms of symmetries between two mutuallypredictive observations, and develop a machine learning architecture, MacroNet,that identifies macrostates. Using this framework, we show how macrostates canbe identifed across systems ranging in complexity from the simplicity of thesimple harmonic oscillator to the much more complex spatial patterningcharacteristic of Turing instabilities. Furthermore, we show how our frameworkcan be used for the inverse design of microstates consistent with a givenmacroscopic property -- in Turing patterns this allows us to design underlyingrule with a given specification of spatial patterning, and to identify whichrule parameters most control these patterns. By demonstrating a general theoryfor how macroscopic properties emerge from conservation of symmetries in themapping between observations, we provide a machine learning framework thatallows a unified approach to identifying macrostates in systems from the simpleto complex, and allows the design of new examples consistent with a givenmacroscopic property.

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