This repository is associated with the preprint of "Gaussian process learning of nonlinear dynamics".
This repository presents the implementation of four scenarios, including identification and estimation with an affine parametrization, nonlinear parametric approximation without prior knowledge, and general parameter estimation for a given dynamical system. Each scenario is corresponding to the numerical examples presented in the paper:
Example 1 - Parameter estimation for Lotka–Volterra model (with analytical posterior)
LotkaVolterra_model.py: contain the function of Lotka Volterra model.data_generation.py: execute the generate the data to train a data-driven model.Scene1.py: execute to perform Gaussian process learning. It also includes the implementation of the comparison method FD+LinReg.plot_compare.py: visualize the comparison result.
Example 2 - Sparse identification for Lotka-Volterra model
LotkaVolterra_model.py: contain the function of Lotka Volterra model.data_generation.py: execute the generate the data to train a data-driven model.Scene2.py: execute to perform Gaussian process learning. It also includes the implementation of the comparison method SINDy.plot_compare.py: visualize the comparison result (corresponding to figure 6).plot_error.py: visualize the error under different noise and data density (corresponding to figure 5).visualization.py: contain the visualization function for the posterior distributions of candidate parameters.
Example 3 - A neural network surrogate for 1D ODE system
dynamical_system.py: contain the function of 1D ODE system.data_generation.py: execute the generate the data to train a data-driven model.Scene3.py: execute to perform Gaussian process learning.Scene3_IC.py: execute to perform Gaussian process learning with data from multiple trajectories.
Example 4 - Parameter estimation for binary black-hole system (with MCMC)
dynamical_system.py: contain the function of 1D ODE system.data_generation.py: execute the generate the data to train a data-driven model.Scene4.py: execute to perform Gaussian process learning.
Note that some minor changes in hyperparameters/visualization are required for different data conditions. For those details, see the comments in the code.