Discovery of Differential Equations Using Probabilistic Grammars

Ordinary differential equations (ODEs) are a widely used formalism for mathematical modeling of dynamical systems, a task omnipresent in many scientific domains. The paper introduces a novel method for inferring ODEs from data. It extends ProGED, a method for equation discovery that employs probabilistic context-free grammars for constraining the space of candidate equations. The proposed method can discover ODEs from partial observations of dynamical systems, where only a subset of state variables can be observed. The new method's empirical evaluation shows it can reconstruct the ODEs of the well-known Van der Pol oscillator from synthetic simulation data. In terms of reconstruction performance, improved ProGED compares favorably to state-of-the-art methods for inferring ODEs from data.