Note
Click here to download the full example code
Algorithm: MEStatic#
# Windows users have to encapsulate the code into a main function to avoid multiprocessing errors.
# def main():
import pygpc
from collections import OrderedDict
fn_results = 'tmp/mestatic' # filename of output
save_session_format = ".pkl" # file format of saved gpc session ".hdf5" (slow) or ".pkl" (fast)
Loading the model and defining the problem#
# define model
model = pygpc.testfunctions.SurfaceCoverageSpecies()
# define problem
parameters = OrderedDict()
parameters["rho_0"] = pygpc.Beta(pdf_shape=[1, 1], pdf_limits=[0, 1])
parameters["beta"] = pygpc.Beta(pdf_shape=[1, 1], pdf_limits=[0, 20])
parameters["alpha"] = 1.
problem = pygpc.Problem(model, parameters)
Setting up the algorithm#
# gPC options
options = dict()
options["method"] = "reg"
options["solver"] = "Moore-Penrose"
options["settings"] = None
options["order"] = [10, 10]
options["order_max"] = 10
options["interaction_order"] = 2
options["matrix_ratio"] = 2
options["n_cpu"] = 0
options["gradient_enhanced"] = True
options["gradient_calculation"] = "FD_2nd"
options["gradient_calculation_options"] = {"dx": 0.05, "distance_weight": -2}
options["error_type"] = "loocv"
options["qoi"] = "all"
options["classifier"] = "learning"
options["classifier_options"] = {"clusterer": "KMeans",
"n_clusters": 2,
"classifier": "MLPClassifier",
"classifier_solver": "lbfgs"}
options["fn_results"] = fn_results
options["save_session_format"] = save_session_format
options["grid"] = pygpc.Random
options["grid_options"] = {"seed": 1}
options["n_grid"] = 1000
options["adaptive_sampling"] = False
# define algorithm
algorithm = pygpc.MEStatic(problem=problem, options=options)
Running the gpc#
# Initialize gPC Session
session = pygpc.Session(algorithm=algorithm)
# run gPC algorithm
session, coeffs, results = session.run()
Out:
Creating initial grid (<class 'pygpc.Grid.Random'>) with n_grid=1000
Determining gPC approximation for QOI #0:
=========================================
Performing 1000 simulations!
It/Sub-it: 10/2 Performing simulation 0001 from 1000 [ ] 0.1%
Total function evaluation: 0.740556001663208 sec
Gradient evaluation: 0.04762625694274902 sec
Determine gPC coefficients using 'Moore-Penrose' solver (gradient enhanced)...
Determine gPC coefficients using 'Moore-Penrose' solver (gradient enhanced)...
LOOCV 01 from 25 [= ] 4.0%
LOOCV 02 from 25 [=== ] 8.0%
LOOCV 03 from 25 [==== ] 12.0%
LOOCV 04 from 25 [====== ] 16.0%
LOOCV 05 from 25 [======== ] 20.0%
LOOCV 06 from 25 [========= ] 24.0%
LOOCV 07 from 25 [=========== ] 28.0%
LOOCV 08 from 25 [============ ] 32.0%
LOOCV 09 from 25 [============== ] 36.0%
LOOCV 10 from 25 [================ ] 40.0%
LOOCV 11 from 25 [================= ] 44.0%
LOOCV 12 from 25 [=================== ] 48.0%
LOOCV 13 from 25 [==================== ] 52.0%
LOOCV 14 from 25 [====================== ] 56.0%
LOOCV 15 from 25 [======================== ] 60.0%
LOOCV 16 from 25 [========================= ] 64.0%
LOOCV 17 from 25 [=========================== ] 68.0%
LOOCV 18 from 25 [============================ ] 72.0%
LOOCV 19 from 25 [============================== ] 76.0%
LOOCV 20 from 25 [================================ ] 80.0%
LOOCV 21 from 25 [================================= ] 84.0%
LOOCV 22 from 25 [=================================== ] 88.0%
LOOCV 23 from 25 [==================================== ] 92.0%
LOOCV 24 from 25 [====================================== ] 96.0%
LOOCV 25 from 25 [========================================] 100.0%
LOOCV computation time: 0.12640595436096191 sec
-> relative loocv error = 0.015283703141592631
LOOCV 01 from 25 [= ] 4.0%
LOOCV 02 from 25 [=== ] 8.0%
LOOCV 03 from 25 [==== ] 12.0%
LOOCV 04 from 25 [====== ] 16.0%
LOOCV 05 from 25 [======== ] 20.0%
LOOCV 06 from 25 [========= ] 24.0%
LOOCV 07 from 25 [=========== ] 28.0%
LOOCV 08 from 25 [============ ] 32.0%
LOOCV 09 from 25 [============== ] 36.0%
LOOCV 10 from 25 [================ ] 40.0%
LOOCV 11 from 25 [================= ] 44.0%
LOOCV 12 from 25 [=================== ] 48.0%
LOOCV 13 from 25 [==================== ] 52.0%
LOOCV 14 from 25 [====================== ] 56.0%
LOOCV 15 from 25 [======================== ] 60.0%
LOOCV 16 from 25 [========================= ] 64.0%
LOOCV 17 from 25 [=========================== ] 68.0%
LOOCV 18 from 25 [============================ ] 72.0%
LOOCV 19 from 25 [============================== ] 76.0%
LOOCV 20 from 25 [================================ ] 80.0%
LOOCV 21 from 25 [================================= ] 84.0%
LOOCV 22 from 25 [=================================== ] 88.0%
LOOCV 23 from 25 [==================================== ] 92.0%
LOOCV 24 from 25 [====================================== ] 96.0%
LOOCV 25 from 25 [========================================] 100.0%
LOOCV computation time: 0.12137627601623535 sec
LOOCV 01 from 25 [= ] 4.0%
LOOCV 02 from 25 [=== ] 8.0%
LOOCV 03 from 25 [==== ] 12.0%
LOOCV 04 from 25 [====== ] 16.0%
LOOCV 05 from 25 [======== ] 20.0%
LOOCV 06 from 25 [========= ] 24.0%
LOOCV 07 from 25 [=========== ] 28.0%
LOOCV 08 from 25 [============ ] 32.0%
LOOCV 09 from 25 [============== ] 36.0%
LOOCV 10 from 25 [================ ] 40.0%
LOOCV 11 from 25 [================= ] 44.0%
LOOCV 12 from 25 [=================== ] 48.0%
LOOCV 13 from 25 [==================== ] 52.0%
LOOCV 14 from 25 [====================== ] 56.0%
LOOCV 15 from 25 [======================== ] 60.0%
LOOCV 16 from 25 [========================= ] 64.0%
LOOCV 17 from 25 [=========================== ] 68.0%
LOOCV 18 from 25 [============================ ] 72.0%
LOOCV 19 from 25 [============================== ] 76.0%
LOOCV 20 from 25 [================================ ] 80.0%
LOOCV 21 from 25 [================================= ] 84.0%
LOOCV 22 from 25 [=================================== ] 88.0%
LOOCV 23 from 25 [==================================== ] 92.0%
LOOCV 24 from 25 [====================================== ] 96.0%
LOOCV 25 from 25 [========================================] 100.0%
LOOCV computation time: 0.09618401527404785 sec
Postprocessing#
# read session
session = pygpc.read_session(fname=session.fn_session, folder=session.fn_session_folder)
# Post-process gPC
pygpc.get_sensitivities_hdf5(fn_gpc=options["fn_results"],
output_idx=None,
calc_sobol=True,
calc_global_sens=True,
calc_pdf=True,
algorithm="sampling",
n_samples=1e3)
Out:
> Loading gpc session object: tmp/mestatic.pkl
> Loading gpc coeffs: tmp/mestatic.hdf5
> Adding results to: tmp/mestatic.hdf5
Validation#
Validate gPC vs original model function (2D-surface)#
pygpc.validate_gpc_plot(session=session,
coeffs=coeffs,
random_vars=list(problem.parameters_random.keys()),
n_grid=[51, 51],
output_idx=[0],
fn_out=None,
folder=None,
n_cpu=session.n_cpu)
Validate gPC vs original model function (Monte Carlo)#
nrmsd = pygpc.validate_gpc_mc(session=session,
coeffs=coeffs,
n_samples=int(1e4),
output_idx=[0],
fn_out=None,
folder=None,
plot=True,
n_cpu=session.n_cpu)
print("> Maximum NRMSD (gpc vs original): {:.2}%".format(max(nrmsd)))
# On Windows subprocesses will import (i.e. execute) the main module at start.
# You need to insert an if __name__ == '__main__': guard in the main module to avoid
# creating subprocesses recursively.
#
# if __name__ == '__main__':
# main()
Out:
> Maximum NRMSD (gpc vs original): 0.0068%
Total running time of the script: ( 0 minutes 14.086 seconds)