Generating the numerical results included in

Chris Vales, David C. Freeman, Joanna Slawinska & Dimitrios Giannakis.
Quantum mechanical closure of partial differential equations with
symmetries.

- Run the "swe_datagen.py" file to generate the true simulation results,
choosing the appropriate value for the initial condition parameter
and trajectory ID.

- (Optional) Run the "swe_param.py" file with the appropriate trajectory
ID to generate the simulation results on the coarse grid using the
true subgrid fluxes for each trajectory.
This is done to verify that the subgrid fluxes have been generated
correctly in the previous step.

- Run the "swe_preproc_single.py" file with the appropriate trajectory ID
to process the true simulation results for each trajectory, generating the
corresponding training data. 

- Run the "swe_autotune_basis.py" file to calibrate the bandwidth parameter
for the eigenfunction basis kernel for each individual trajectory, using
the appropriate trajectory ID.

- Run the "swe_basis_single.py" file to compute the eigenfunction basis
corresponding to each trajectory, using the appropriate trajectory ID.

- Run the "swe_basis_multi.py" file to combine the individual bases into
one basis matrix.

- Run the "swe_preproc_multi.py" file to process the true simulation results,
generating the training data combining all trajectories.

- Run the "swe_offline.py" file to generate the matrices required by the
QMCl scheme.

- Run the "swe_varbandwidth_cond.py" file to generate the variable bandwidth
values used for the bayesian conditioning kernel function.

- Run the "swe_autotune_cond.py" file to calibrate the bandwidth parameter
for the conditioning kernel function (including the variable bandwidth).

- Run the "swe_online.py" file to run the QMCl surrogate model with the
appropriate initial condition.

- Use the "swe_plots.ipynb" notebook to generate the plots based on the
numerical results.