Hanqiao Yu, Shusen Yang, Xuebin Ren, Cong Zhao
Deflex combines neural networks and lambda calculus to automatically discover scale-specific formulas in complex systems.
Complex systems exhibit different formula forms (invariants, distributions) across scales, but existing AI methods are limited to single-scale systems, hindering multiscale discovery.
Deflex consists of two subsystems: Deflexpressor, a lambda-calculus symbolic regression model for higher-order formulas, and Deflexformer, a decomposable deep energy model for learning unified representations across scales. Deflexpressor generates synthetic data to pre-train Deflexformer, which then guides formula discovery by decoupling multiscale latent relationships.
On six representative complex systems, Deflex achieves up to 7x higher efficiency than state-of-the-art methods while enabling automated multiscale discovery. This work could be a useful tool for scientific discovery across disciplines.