def cost(x, axis=None, samples=Ns):
"""lower bound on expected model output
Inputs:
x: list of NoisyModel hyperparameters
axis: int, the index of y on which to find bound (all, by default)
samples: int, number of samples, for a non-deterministic OUQ model
Returns:
lower bound on expected value of model output
"""
# build a model, F(x|a), and tune "a" for optimal F.
kwds = dict(mu=x[0], sigma=0.0, zmu=x[1], zsigma=0.0,
# uid=False, cached=True) # active updates enabled
uid=True, cached=False) # active updates disabled
#print('building model F(x|a)...')
model = NoisyModel('model', model=toy, nx=nx, ny=ny, **kwds)
rnd = Ns if model.rnd else None
#print('building UQ objective of expected model output...')
b = ExpectedValue(model, bnd, constraint=scons, cvalid=is_cons, samples=rnd)
i = counter.count()
#print('solving for lower bound on expected model output...')
solver = b.lower_bound(axis=axis, id=i, **param)
if type(solver) is not tuple:
solver = (solver,) #FIXME: save solver to DB (or pkl)
if axis is None:
results = tuple(-s.bestEnergy for s in solver) #NOTE: -1 for GLB
#print('[id: %s] %s' % (i, tuple(s.bestSolution for s in solver)))
else:
results = -solver[axis].bestEnergy #NOTE: -1 for GLB
#print('[id: %s] %s' % (i, solver[axis].bestSolution))
return results
model = NoisyModel('model', model=toy, nx=nx, ny=ny, **approx)
#print('building estimator G(x) from truth data...')
kwds = dict(smooth=0.0, noise=0.0, method='thin_plate', extrap=False)
surrogate = InterpModel('surrogate', nx=nx, ny=ny, data=truth, **kwds)
#print('building UQ model of model error...')
error = ErrorModel('error', model=model, surrogate=surrogate)
rnd = Ns if error.rnd else None
#print('building UQ objective of expected model error...')
b = ExpectedValue(error,
bnd,
constraint=scons,
cvalid=is_cons,
samples=rnd)
#print('solving for lower bound on expected model error...')
b.lower_bound(axis=None, id=0, **param)
print("lower bound per axis:")
for axis, solver in b._lower.items():
print("%s: %s @ %s" % (axis, solver.bestEnergy, solver.bestSolution))
#print('solving for upper bound on expected model error...')
param['opts']['termination'] = COG(1e-10, 200) #NOTE: short stop?
param['npop'] = 160 #NOTE: increase if poor convergence
param['stepmon'] = VerboseLoggingMonitor(1,
20,
filename='log.txt',
label='upper')
b.upper_bound(axis=None, id=1, **param)
print("upper bound per axis:")
for axis, solver in b._upper.items():
print("%s: %s @ %s" % (axis, -solver.bestEnergy, solver.bestSolution))
# build a model that approximates 'truth'
#print('building model F(x|a) of truth...')
approx = dict(mu=-.05, sigma=0., zmu=.05, zsigma=0.)
model = NoisyModel('model', model=toy, nx=nx, ny=ny, **approx)
#print('building UQ model of model error...')
error = ErrorModel('error', model=truth, surrogate=model)
rnd = Ns if error.rnd else None
#print('building UQ objective of expected model error...')
b = ExpectedValue(error,
bnd,
constraint=scons,
cvalid=is_cons,
samples=rnd)
#print('solving for lower bound on expected model error...')
solver = b.lower_bound(axis=None, **param)
if type(solver) is not tuple:
solver = (solver, )
for s in solver:
print("lower bound:\n%s @ %s" % (s.bestEnergy, s.bestSolution))
#print('solving for upper bound on expected model error...')
param['opts']['termination'] = COG(1e-10, 200) #NOTE: short stop?
param['npop'] = 160 #NOTE: increase if poor convergence
param['stepmon'] = VerboseLoggingMonitor(1,
20,
filename='log.txt',
label='upper')
solver = b.upper_bound(axis=None, id=1, **param)
if type(solver) is not tuple:
solver = (solver, )