UM-Bridge with QMCPy

Using QMCPy to evaluate the UM-Bridge Cantilever Beam Function and approximate the expectation with respect to a uniform random variable.

Imports

import umbridge
import qmcpy as qp

Start Docker Container

See the UM-Bridge Documentation for image options.

!docker run --name muqbp -d -it -p 4243:4243 linusseelinger/benchmark-muq-beam-propagation:latest

57a43d7926cf9838fd7273725b2415a5e6c1fe5d131fc5012a8bfbad4f531c0a

Problem Setup

Initialize a QMCPy sampler and distribution.

sampler = qp.DigitalNetB2(dimension=3,seed=7) # DISCRETE DISTRIBUTION
distribution = qp.Uniform(sampler,lower_bound=1,upper_bound=1.05) # TRUE MEASURE

Initialize a UM-Bridge model and wrap it into a QMCPy compatible Integrand

model = umbridge.HTTPModel('http://localhost:4243','forward')
umbridge_config = {"d": sampler.d}
integrand = qp.UMBridgeWrapper(distribution,model,umbridge_config,parallel=False) # INTEGRAND

Model Evaluation

x = sampler(16) # same as sampler.gen_samples(16)
y = integrand.f(x)
print(y.shape)
print(type(y))
print(y.dtype)

(16, 31)
<class 'numpy.ndarray'>
float64

Automatically Approximate the Expectation

qmc_stop_crit = qp.CubQMCNetG(integrand,abs_tol=2.5e-2) # QMC STOPPING CRITERION
solution,data = qmc_stop_crit.integrate()
print(data)

LDTransformData (AccumulateData Object)
    solution        [  0.      3.855  14.69  ... 898.921 935.383 971.884]
    comb_bound_low  [  0.      3.854  14.688 ... 898.901 935.363 971.863]
    comb_bound_high [  0.      3.855  14.691 ... 898.941 935.404 971.906]
    comb_flags      [ True  True  True ...  True  True  True]
    n_total         2^(11)
    n               [1024. 1024. 1024. ... 2048. 2048. 2048.]
    time_integrate  25.311
CubQMCNetG (StoppingCriterion Object)
    abs_tol         0.025
    rel_tol         0
    n_init          2^(10)
    n_max           2^(35)
UMBridgeWrapper (Integrand Object)
Uniform (TrueMeasure Object)
    lower_bound     1
    upper_bound     1.050
DigitalNetB2 (DiscreteDistribution Object)
    d               3
    dvec            [0 1 2]
    randomize       LMS_DS
    graycode        0
    entropy         7
    spawn_key       ()

from matplotlib import pyplot
pyplot.style.use('../qmcpy/qmcpy.mplstyle')
fig,ax = pyplot.subplots(figsize=(6,3))
ax.plot(solution,'-o')
ax.set_xlim([0,len(solution)-1]); ax.set_xlabel(r'$x$')
ax.set_ylim([1000,-10]);  ax.set_ylabel(r'$u(x)$');

Parallel Evaluation

QMCPy can automatically multi-threaded requests to the model by setting parallel=p where p is the number of processors used by multiprocessing.pool.ThreadPool. Setting parallel=True is equivalent to setting paralle=os.cpu_count().

import os
print('Available CPUs: %d'%os.cpu_count())

Available CPUs: 12

integrand = qp.UMBridgeWrapper(distribution,model,umbridge_config,parallel=8)
solution,data = qp.CubQMCNetG(integrand,abs_tol=2.5e-2).integrate()
data

LDTransformData (AccumulateData Object)
    solution        [  0.      3.855  14.69  ... 898.921 935.383 971.884]
    comb_bound_low  [  0.      3.854  14.688 ... 898.901 935.363 971.863]
    comb_bound_high [  0.      3.855  14.691 ... 898.941 935.404 971.906]
    comb_flags      [ True  True  True ...  True  True  True]
    n_total         2^(11)
    n               [1024. 1024. 1024. ... 2048. 2048. 2048.]
    time_integrate  14.785
CubQMCNetG (StoppingCriterion Object)
    abs_tol         0.025
    rel_tol         0
    n_init          2^(10)
    n_max           2^(35)
UMBridgeWrapper (Integrand Object)
Uniform (TrueMeasure Object)
    lower_bound     1
    upper_bound     1.050
DigitalNetB2 (DiscreteDistribution Object)
    d               3
    dvec            [0 1 2]
    randomize       LMS_DS
    graycode        0
    entropy         7
    spawn_key       ()

Shut Down Docker Image

!docker rm -f muqbp

muqbp