Title: Learning Causal Structures from Mixed Dynamics via Polynomial Chaos Expansion
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Causal Discovery, Nonlinear Systems, Polynomial Chaos Expansion, Residual Analysis, Uncertainty Quantification

Abstract: Real-world systems are rarely purely linear or nonlinear, but are instead a complex mixture of both. This heterogeneity makes them exceedingly difficult for standard causal discovery algorithms, which are typically designed for one regime and are brittle when applied to the other. Linear models miss critical nonlinear effects, while general nonlinear methods are computationally expensive and notoriously prone to discovering spurious relationships. We propose a new framework that robustly learns causal structures from such mixed-dynamics systems by learning from a spectral representation of model residuals. Our approach first identifies a sparse linear backbone and then systematically evaluates candidate nonlinear additions through a novel multi-criteria decision process. This validation mechanism, which requires convergent evidence from multiple independent tests, is powered by a new application of Polynomial Chaos Expansion (PCE) to detect latent structure in model residuals with high sensitivity. On a complex industrial process dataset, our method achieves a state-of-the-art 88.9% F1-score, correctly identifying the mixed-type causal graph while drastically reducing the false discoveries that plague other nonlinear methods.