A Bayesian algorithm for data driven Equation Discovery (BED). This algorithm utilises Gaussian Process (GP) Regression and Markov Chain Monte Carlo (MCMC) with a horseshoe prior for discovering the governing equations of systems of ODE's and PDE's.
An example of using the algorithm for candidate functions of polynomials upto the 4th order and derivatives up to the 4th order and includeing interactions:
# Data X Response U
model = BED(X, U, p_ord=4, d_ord=4, interact=True)
An example output for the Van der pol oscillator with parameter value 2.5:
Discovered Equation(s):
dU[0]/dt = 1.03 U[1]^1
dU[1]/dt = -1.02 U[0]^1 + 2.52 U[1]^1 + -2.50 U[0]^2*U[1]^1