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.

Automated summary

The paper presents a novel method for inferring ODEs from data, which extends an existing equation discovery method. It can infer ODEs from partial observations of dynamical systems and has shown improved reconstruction performance compared to state-of-the-art methods.