We address the intricate dynamics of self-organized pattern-forming systems that span multiple spatial and temporal scales, and demonstrate an approach that enables us to reconstruct and forecast the dynamics at small scales from a reduced dynamics at large length and time scales. Our work provides a new route to deal with complex multiscale dynamics that emerge in a broad range of physical systems.
Spatiotemporal patterns are vital for the organization of many biological processes such as cell division, collective cell migration, and morphogenesis. Although commonly assumed in theoretical approaches on pattern-forming systems, patterns generally do not emerge from homogeneity, but rather transition from one pattern to another over time and across different spatial regions – a key scientific challenge, as Turing pointed out in his seminal paper on pattern formation. Coarse-graining methods allow the dynamics of such multiscale systems to be reduced to the essential degrees of freedom at large scales. However, a drawback of traditional coarse-graining approaches is that information about the patterns at small scales, that are integrated out, are lost and cannot be reconstructed from the dynamics at large scales.