做复杂系统建模或科学发现的团队，终于有了能自动提取多尺度公式的工具——Deflex比现有方法快7倍，做物理、生物、工程等跨学科研究的可以直接试试。
Deflex是一种端到端AI方法，能从多尺度复杂系统中自动提取不同形式的数学公式（如不变量和分布）。它由两个子系统组成：Deflexpressor（基于Lambda演算的符号回归模型）和Deflexformer（可分解深度能量模型）。Deflexpressor生成合成数据预训练Deflexformer，后者通过解耦多尺度潜在关系引导公式发现。在六个代表性复杂系统上，Deflex比现有方法效率提升高达7倍，实现了自动化多尺度发现。这项工作有望成为跨学科科学发现的有用工具。
Discovering Multiscale Deep Formulas in Complex Systems via Neural-Guided Lambda Calculus
A fundamental problem in science is identifying underlying patterns of complex systems in the form of concise mathematical formulas. Current Artificial Intelligence (AI)-based methods have shown strong performance in single-scale systems, yet remain limited in identifying scale-specific formulas in multiscale complex systems. We present Deflex, an end-to-end AI method to automatically extract multiscale formulas with potentially different forms, including invariants and distributions, from complex systems. Deflex consists of two subsystems named Deflexformer and Deflexpressor. Deflexpressor is a lambda-calculus symbolic regression model for higher-order formulas. Deflexformer is 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. Across six representative complex systems with diverse behaviors, Deflex achieves up to 7-fold higher efficiency than the state-of-the-art methods while enabling automated multiscale discovery. Our work could be a useful tool for scientific discovery across disciplines.