mfmodeling

Multi-fidelity modeling using Gaussian process regression

Purpose of this project

This project is motivated to apply multi-fidelity data fusion algorithms to the regression problem in turbulent transport modeling in magnetic fusion plasma. The developed module will be available as a general tool for multi-fidelity regression problems.

Usage

mfmodeling module requires external packages: numpy, GPy.

The following is an explanation on the simple usage of NARGP (Nonlinear AutoRegressive Gaussian Process regression [P. Perdikaris (2017)]) as a multi-fidelity regression algorithm. See also tests/NARGP_example_2d/Demo_May2024_NARGP_example_2d.ipynb.

1. Prepare multi-fidelity datasets as a list of each fidelity data.

    data_list = [[data_lowfid_x,  data_lowfid_y],
                 [data_highfid_x, data_highfid_y]]

2. Instantiate the NARGP object using the above dataset.

    from mfmodeling import NARGP
    model_nargp = NARGP(data_list = data_list)

3. Optimize hyperparameters of the kernel function in NARGP.

    model_nargp.optimize()

4. Make a prediction.

    mean, var = model_nargp.prediction(x_pred)

where mean and var are the prediction of posterior mean and variance at your evaluating position x_pred.

Reference

S. Maeyama, M. Honda, E. Narita, S. Toda, "Multi-Fidelity Information Fusion for Turbulent Transport Modeling in Magnetic Fusion Plasma", Scientific Reports 14, 28242 (2024).