Dynamic System Identification from Scarce and Noisy Data using Symbolic Regression

A framework for dynamic system model identification from scarce and noisy data is proposed. This framework uses symbolic regression via genetic programming with a gradient-based parameter estimation step to identify a differential equation model and its parameters from available system data. The effectiveness of the method is demonstrated by identifying four synthetic systems: an ideal plug flow reactor (PFR) with an irreversible chemical reaction, an ideal continuously stirred tank reactor (CSTR) with an irreversible chemical reaction, a system described by Burgers' Equation, and an ideal PFR with a reversible chemical reaction. The results show that this framework can identify PDE models of systems from broadly spaced and noisy data. When the data was not sufficiently rich, the framework discovered a surrogate model that described the observations in equal or fewer terms than the true system model. Additionally, the method can select relevant physics terms to describe a system from a list of candidate arguments, providing valuable models for use in controls applications.