Physics-informed genetic programming for discovery of partial differential equations from scarce and noisy data

A novel framework is proposed that utilizes symbolic regression via genetic programming to identify free-form partial differential equations from scarce and noisy data. The framework successfully identified ground truth models for four synthetic systems (an isothermal plug flow reactor, a continuously stirred tank reactor, a nonisothermal reactor, and viscous flow governed by Burgers' equation) from time-variant data collected at one location. A comparative analysis against the so-called weak Sparse Identification of Nonlinear Dynamics (SINDy) demonstrated the proposed framework's superior ability to identify meaningful partial differential equation (PDE) models when data was scarce. The framework was further tested for robustness to noise and scarcity, showing successful model recovery from as few as eight time series data points collected at a single point in space with 50% noise. These results emphasize the potential of the proposed framework for the discovery of PDE models when data collection is expensive or otherwise difficult.