Learning regime-dependent governing equations: A symbolic decision tree approach

Abstract

Many chemical engineering systems are governed by mechanisms that switch across operating regimes, making the data-driven discovery of regime-dependent governing equations essential for predictive modeling, optimization, and control. We propose symbolic decision trees for the data-driven discovery of regime-dependent governing equations. The method simultaneously learns interpretable splitting conditions to partition the input domain and local governing equations that describe each regime. To improve tractability, both the splitting conditions and governing equations are parametrized using basis functions, resulting in a mixed-integer optimization learning problem. We use the proposed approach to learn hybrid dynamical models and a constitutive equation for the zero-shear viscosity of polymer melts. Symbolic decision trees identify physically interpretable regimes and local governing equations while improving predictive accuracy relative to approaches that learn a single global model or use existing decision tree models. This framework provides an interpretable and generalizable route for discovering regime-dependent models in chemical engineering systems.