def test_loo_error_singular_values(self):
pod = POD()
rbf = RBF()
db = Database(param, snapshots.T)
rom = ROM(db, pod, rbf).fit()
valid_svalues = rom.reduction.singular_values
rom.loo_error()
np.testing.assert_allclose(valid_svalues, rom.reduction.singular_values)
def test_loo_error(self):
pod = POD()
rbf = RBF()
db = Database(param, snapshots.T)
rom = ROM(db, pod, rbf)
err = rom.loo_error()
np.testing.assert_allclose(
err,
np.array([421.299091, 344.571787, 48.711501, 300.490491]),
rtol=1e-4)
def test_loo_error_01(self):
pod = POD()
rbf = RBF()
db = Database(param, snapshots.T)
rom = ROM(db, pod, rbf)
err = rom.loo_error()
np.testing.assert_allclose(
err,
np.array([0.540029, 1.211744, 0.271776, 0.919509]),
rtol=1e-4)
def test_loo_error_02(self):
pod = POD()
gpr = GPR()
db = Database(param, snapshots.T)
rom = ROM(db, pod, gpr)
err = rom.loo_error(normalizer=False)
np.testing.assert_allclose(
err[0],
np.array(0.639247),
rtol=1e-3)
from ipywidgets import interact
def plot_solution(mu0, mu1):
new_mu = [mu0, mu1]
pred_sol = rom.predict(new_mu)
plt.figure(figsize=(8, 7))
plt.triplot(triang, 'b-', lw=0.1)
plt.tripcolor(triang, pred_sol)
plt.colorbar()
interact(plot_solution, mu0=8, mu1=1)
# ## Error Approximation & Improvement
#
# At the moment, we used a database which is composed by 8 files. we would have an idea of the approximation accuracy we are able to reach with these high-fidelity solutions. Using the *leave-one-out* strategy, an error is computed for each parametric point in our database and these values are returned as array.
# In[12]:
for pt, error in zip(rom.database.parameters, rom.loo_error()):
print(pt, error)
# Moreover, we can use the information about the errors to locate the parametric points where we have to compute the new high-fidelity solutions and add these to the database in order to optimally improve the accuracy.
# In[13]:
rom.optimal_mu()
# These function can be used to achieve the wanted (estimated) accuracy.