parPE example: steadystate model - model simulation, optimization, analysis¶
This notebooks demonstrates basic use of parPE for parameter estimation.
Prerequisites¶
This notebook requires:
a successful parPE with CMake options
BUILD_EXAMPLES=ON(default).an installation of the parPE Python package (
${PARPE_SOURCE_DIR}/python/) in the Python environment in which this notebook is run (ideally thebuild/venv/virtual environment)
This notebook assumes that this file is used from its default location and that parPE was built inside ${PARPE_SOURCE_DIR}/build/. If this is not the case, adapt parpe_source_root and parpe_build_root in the following block correspondingly.
[26]:
import amici
import os
import sys
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import h5py
from importlib import reload
import parpe
# set paths
parpe_source_root = os.path.abspath('../../../')
parpe_build_root = os.path.join(parpe_source_root, 'build')
model_source_dir = f'{parpe_build_root}/examples/parpeamici/steadystate/steadystate_scaled-prefix/src/steadystate_scaled/model_steadystate_scaled'
example_binary_dir = f'{parpe_build_root}/examples/parpeamici/steadystate/'
example_data_dir = f'{parpe_build_root}/examples/parpeamici/steadystate/steadystate_scaled-prefix/src/steadystate_scaled'
optimization_options_py = f'{parpe_source_root}/misc/optimizationOptions.py'
# MPI launcher and options
mpiexec = "mpiexec -n 4 --allow-run-as-root --oversubscribe"
[27]:
# rebuild example
!cd {parpe_build_root} && make
-- Found Git: /usr/bin/git (found version "2.25.1")
-- Building version parPE-v0.4.3-37-g5bf1-dirty
[ 0%] Built target get_version
[ 10%] Built target parpecommon
[ 21%] Built target parpeoptimization
[ 25%] Built target parpeloadbalancer
[ 37%] Built target parpeamici
[ 39%] Built target parpe
[ 45%] Built target unittests_common
[ 50%] Built target unittests_loadbalancer
[ 58%] Built target unittests_optimization
Setting up virtual environment...
[ 58%] Built target setup_venv
[ 59%] Creating test data using hierarchicalOptimizationTest.py
...
----------------------------------------------------------------------
Ran 3 tests in 0.000s
OK
[ 59%] Built target prepare_test_hierarchical_optimization
[ 67%] Built target unittests_amici
[ 69%] Built target example_loadbalancer
[ 81%] Built target steadystate_scaled
[ 84%] Built target example_steadystate
[ 88%] Built target example_steadystate_multi
[ 92%] Built target example_steadystate_multi_simulator
[100%] Built target test_steadystate
[28]:
# run make test to generated all output files required below
!cd {parpe_build_root} && make test
Running tests...
Test project /home/dweindl/src/parPE_2/build
Start 1: testingMisc.testTenToMinusInf
1/80 Test #1: testingMisc.testTenToMinusInf .................................................. Passed 0.00 sec
Start 2: testingMisc.testWithinTolerance
2/80 Test #2: testingMisc.testWithinTolerance ................................................ Passed 0.00 sec
Start 3: testingMisc.testCheckEqualArray
3/80 Test #3: testingMisc.testCheckEqualArray ................................................ Passed 0.00 sec
Start 4: testingMisc.testRandInt
4/80 Test #4: testingMisc.testRandInt ........................................................ Passed 0.01 sec
Start 5: commonMisc.testBacktrace
5/80 Test #5: commonMisc.testBacktrace ....................................................... Passed 0.00 sec
Start 6: commonMisc.testFilexists
6/80 Test #6: commonMisc.testFilexists ....................................................... Passed 0.00 sec
Start 7: commonMisc.testCreateDirectoryIfNotExists
7/80 Test #7: commonMisc.testCreateDirectoryIfNotExists ...................................... Passed 0.00 sec
Start 8: commonMisc.testRecursiveMkpath
8/80 Test #8: commonMisc.testRecursiveMkpath ................................................. Passed 0.00 sec
Start 9: commonMisc.testRandDouble
9/80 Test #9: commonMisc.testRandDouble ...................................................... Passed 0.01 sec
Start 10: commonMisc.testFillArrayRandomDoubleSameInterval
10/80 Test #10: commonMisc.testFillArrayRandomDoubleSameInterval ............................... Passed 0.00 sec
Start 11: commonMisc.testFillArrayRandomDoubleIndividualInterval
11/80 Test #11: commonMisc.testFillArrayRandomDoubleIndividualInterval ......................... Passed 0.01 sec
Start 12: commonMisc.testMpi
12/80 Test #12: commonMisc.testMpi ............................................................. Passed 0.30 sec
Start 13: commonMisc.runInParallelAndWaitForFinish
13/80 Test #13: commonMisc.runInParallelAndWaitForFinish ....................................... Passed 0.01 sec
Start 14: commonMisc.strFormatCurrentLocaltime
14/80 Test #14: commonMisc.strFormatCurrentLocaltime ........................................... Passed 0.00 sec
Start 15: logging.printDebugInfoAndWait
15/80 Test #15: logging.printDebugInfoAndWait .................................................. Passed 0.01 sec
Start 16: logging.misc
16/80 Test #16: logging.misc ................................................................... Passed 0.00 sec
Start 17: logging.printMPIInfo
17/80 Test #17: logging.printMPIInfo ........................................................... Passed 0.00 sec
Start 18: logging.logProcessStats
18/80 Test #18: logging.logProcessStats ........................................................ Passed 0.01 sec
Start 19: costFunction.mseZero
19/80 Test #19: costFunction.mseZero ........................................................... Passed 0.01 sec
Start 20: costFunction.mseNonzero
20/80 Test #20: costFunction.mseNonzero ........................................................ Passed 0.01 sec
Start 21: costFunction.linearModel
21/80 Test #21: costFunction.linearModel ....................................................... Passed 0.00 sec
Start 22: costFunction.linearModel2
22/80 Test #22: costFunction.linearModel2 ...................................................... Passed 0.01 sec
Start 23: costFunction.linearModel3
23/80 Test #23: costFunction.linearModel3 ...................................................... Passed 0.01 sec
Start 24: hdf5Misc.testOpenExistingFileNoOverwrite
24/80 Test #24: hdf5Misc.testOpenExistingFileNoOverwrite ....................................... Passed 0.01 sec
Start 25: hdf5Misc.testOpenExistingFileOverwrite
25/80 Test #25: hdf5Misc.testOpenExistingFileOverwrite ......................................... Passed 0.01 sec
Start 26: hdf5Misc.testMutexGetLock
26/80 Test #26: hdf5Misc.testMutexGetLock ...................................................... Passed 0.01 sec
Start 27: hdf5Misc.testErrorStackWalker
27/80 Test #27: hdf5Misc.testErrorStackWalker .................................................. Passed 0.01 sec
Start 28: hdf5Misc.testCreateGroup
28/80 Test #28: hdf5Misc.testCreateGroup ....................................................... Passed 0.01 sec
Start 29: hdf5Misc.testCreateExistingGroup
29/80 Test #29: hdf5Misc.testCreateExistingGroup ............................................... Passed 0.01 sec
Start 30: hdf5Misc.testEnsureGroupExists
30/80 Test #30: hdf5Misc.testEnsureGroupExists ................................................. Passed 0.01 sec
Start 31: hdf5Misc.testStringAttribute
31/80 Test #31: hdf5Misc.testStringAttribute ................................................... Passed 0.01 sec
Start 32: hdf5Misc.testDatasetDimensions
32/80 Test #32: hdf5Misc.testDatasetDimensions ................................................. Passed 0.01 sec
Start 33: unittests_loadbalancer
33/80 Test #33: unittests_loadbalancer ......................................................... Passed 0.00 sec
Start 34: multiStartOptimization.testMultiStartOptimization
34/80 Test #34: multiStartOptimization.testMultiStartOptimization .............................. Passed 2.20 sec
Start 35: minibatchOptimization.getBatches
35/80 Test #35: minibatchOptimization.getBatches ............................................... Passed 0.01 sec
Start 36: minibatchOptimization.updateParameters
36/80 Test #36: minibatchOptimization.updateParameters ......................................... Passed 0.01 sec
Start 37: minibatchOptimizationLinearModel.testCostWithTrueParametersIsZeroIndivdually
37/80 Test #37: minibatchOptimizationLinearModel.testCostWithTrueParametersIsZeroIndivdually ... Passed 0.01 sec
Start 38: minibatchOptimizationLinearModel.testCostWithTrueParametersIsZeroFull
38/80 Test #38: minibatchOptimizationLinearModel.testCostWithTrueParametersIsZeroFull .......... Passed 0.01 sec
Start 39: minibatchOptimizationLinearModel.testMinibatchSucceedFromOptimum
39/80 Test #39: minibatchOptimizationLinearModel.testMinibatchSucceedFromOptimum ............... Passed 0.01 sec
Start 40: minibatchOptimizationLinearModel.linearModelCheckCostGradient
40/80 Test #40: minibatchOptimizationLinearModel.linearModelCheckCostGradient .................. Passed 0.01 sec
Start 41: minibatchOptimizationLinearModel.linearModelTestBatchOptimizerSucceeds
41/80 Test #41: minibatchOptimizationLinearModel.linearModelTestBatchOptimizerSucceeds ......... Passed 0.05 sec
Start 42: minibatchOptimizationLinearModel.linearModel
42/80 Test #42: minibatchOptimizationLinearModel.linearModel ................................... Passed 0.02 sec
Start 43: optimizationResultWriter.testResultWriter
43/80 Test #43: optimizationResultWriter.testResultWriter ...................................... Passed 0.02 sec
Start 44: optimizationOptions.setGetOptionStr
44/80 Test #44: optimizationOptions.setGetOptionStr ............................................ Passed 0.01 sec
Start 45: optimizationOptions.setGetOptionInt
45/80 Test #45: optimizationOptions.setGetOptionInt ............................................ Passed 0.01 sec
Start 46: optimizationOptions.setGetOptionDouble
46/80 Test #46: optimizationOptions.setGetOptionDouble ......................................... Passed 0.01 sec
Start 47: optimizationOptions.getNonExistingOption
47/80 Test #47: optimizationOptions.getNonExistingOption ....................................... Passed 0.01 sec
Start 48: optimizationOptions.setIpOptOptions
48/80 Test #48: optimizationOptions.setIpOptOptions ............................................ Passed 0.01 sec
Start 49: optimizationOptions.setCeresOptions
49/80 Test #49: optimizationOptions.setCeresOptions ............................................ Passed 0.01 sec
Start 50: optimizationOptions.fromHDF5
50/80 Test #50: optimizationOptions.fromHDF5 ................................................... Passed 0.02 sec
Start 51: optimizationProblem.quadraticTestFunction
51/80 Test #51: optimizationProblem.quadraticTestFunction ...................................... Passed 0.01 sec
Start 52: optimizationProblem.gradientChecker
52/80 Test #52: optimizationProblem.gradientChecker ............................................ Passed 0.01 sec
Start 53: optimizationProblem.linearModel
53/80 Test #53: optimizationProblem.linearModel ................................................ Passed 0.01 sec
Start 54: optimizationProblem.linearModelToGradientFun
54/80 Test #54: optimizationProblem.linearModelToGradientFun ................................... Passed 0.01 sec
Start 55: optimizationProblem.linearModelToGradientFunOptimization
55/80 Test #55: optimizationProblem.linearModelToGradientFunOptimization ....................... Passed 0.03 sec
Start 56: localOptimizationIpopt.testOptimizationResult
56/80 Test #56: localOptimizationIpopt.testOptimizationResult .................................. Passed 0.04 sec
Start 57: localOptimizationIpopt.testReporterCalled
57/80 Test #57: localOptimizationIpopt.testReporterCalled ...................................... Passed 0.02 sec
Start 58: localOptimizationCeres.testOptimization
58/80 Test #58: localOptimizationCeres.testOptimization ........................................ Passed 0.01 sec
Start 59: localOptimizationCeres.testReporterCalled
59/80 Test #59: localOptimizationCeres.testReporterCalled ...................................... Passed 0.01 sec
Start 60: simulationWorkerAmici.testSerializeResultPackageMessage
60/80 Test #60: simulationWorkerAmici.testSerializeResultPackageMessage ........................ Passed 0.01 sec
Start 61: simulationResultWriter.testResultWriter
61/80 Test #61: simulationResultWriter.testResultWriter ........................................ Passed 0.02 sec
Start 62: simulationResultWriter.testResultWriterNewExistingFile
62/80 Test #62: simulationResultWriter.testResultWriterNewExistingFile ......................... Passed 0.02 sec
Start 63: hierarchicalOptimization1.reader
63/80 Test #63: hierarchicalOptimization1.reader ............................................... Passed 0.01 sec
Start 64: hierarchicalOptimization1.spliceParameters
64/80 Test #64: hierarchicalOptimization1.spliceParameters ..................................... Passed 0.02 sec
Start 65: hierarchicalOptimization1.spliceParametersNothingToDo
65/80 Test #65: hierarchicalOptimization1.spliceParametersNothingToDo .......................... Passed 0.01 sec
Start 66: hierarchicalOptimization1.fillFilteredParams
66/80 Test #66: hierarchicalOptimization1.fillFilteredParams ................................... Passed 0.01 sec
Start 67: hierarchicalOptimization1.likelihoodOfMatchingData
67/80 Test #67: hierarchicalOptimization1.likelihoodOfMatchingData ............................. Passed 0.01 sec
Start 68: hierarchicalOptimization.hierarchicalOptimization
68/80 Test #68: hierarchicalOptimization.hierarchicalOptimization .............................. Passed 0.02 sec
Start 69: hierarchicalOptimization.testNoAnalyticalParameters
69/80 Test #69: hierarchicalOptimization.testNoAnalyticalParameters ............................ Passed 0.01 sec
Start 70: hierarchicalOptimization.testComputeAnalyticalScalings
70/80 Test #70: hierarchicalOptimization.testComputeAnalyticalScalings ......................... Passed 0.02 sec
Start 71: hierarchicalOptimization.testComputeAnalyticalOffsets
71/80 Test #71: hierarchicalOptimization.testComputeAnalyticalOffsets .......................... Passed 0.01 sec
Start 72: hierarchicalOptimization.applyOptimalScaling
72/80 Test #72: hierarchicalOptimization.applyOptimalScaling ................................... Passed 0.01 sec
Start 73: hierarchicalOptimization.applyOptimalOffset
73/80 Test #73: hierarchicalOptimization.applyOptimalOffset .................................... Passed 0.01 sec
Start 74: hierarchicalOptimization.testScaling
74/80 Test #74: hierarchicalOptimization.testScaling ........................................... Passed 0.01 sec
Start 75: hierarchicalOptimization.testWrappedFunIsCalledWithGradient
75/80 Test #75: hierarchicalOptimization.testWrappedFunIsCalledWithGradient .................... Passed 0.01 sec
Start 76: hierarchicalOptimization.problemWrapper
76/80 Test #76: hierarchicalOptimization.problemWrapper ........................................ Passed 0.01 sec
Start 77: example_loadbalancer
77/80 Test #77: example_loadbalancer ........................................................... Passed 0.35 sec
Start 78: parpe_python_package_tests
78/80 Test #78: parpe_python_package_tests ..................................................... Passed 2.78 sec
Start 79: pytest_steadystate_example
79/80 Test #79: pytest_steadystate_example ..................................................... Passed 8.22 sec
Start 80: test_steadystate
80/80 Test #80: test_steadystate ............................................................... Passed 0.02 sec
100% tests passed, 0 tests failed out of 80
Total Test time (real) = 14.70 sec
Model and data¶
This parameter estimation is specified as set of PEtab files which are generated automatically during the build process (see ${PARPE_SOURCE_ROOT}/examples/parpeamici/steadystate). They consist of an SBML model and set of tabular files describing model parameters, model inputs and measurements (training data). The model is automatically converted to C++ code and compiled and linked with parPE during the CMake-based build. The data has been converted to
a HDF5 parPE input file.
The model is loosely based on an AMICI example. It describes the dynamics of three species. The model has six outputs with respective measurements. The measurements are based on model simulations to which artificial noise has been added. Data was simulated to represent four different experimental conditions, each with different model inputs. Some outputs represent model states directly, others are offsetted or scaled. For all outputs additive normally distributed noise is assumed, the standard deviation is known for some measurements and is to be estimated for others.
Here we use libsbml to show the reactions and species described by the model:
[29]:
import libsbml
sbml_file = f'{example_data_dir}/model_steadystate_scaled.sbml'
sbml_reader = libsbml.SBMLReader()
sbml_doc = sbml_reader.readSBML(sbml_file)
sbml_model = sbml_doc.getModel()
dir(sbml_doc)
print('Species: ', [s.getId() for s in sbml_model.getListOfSpecies()])
print('\nReactions:')
for reaction in sbml_model.getListOfReactions():
reactants = ' + '.join(['%s %s'%(int(r.getStoichiometry()) if r.getStoichiometry() > 1 else '', r.getSpecies()) for r in reaction.getListOfReactants()])
products = ' + '.join(['%s %s'%(int(r.getStoichiometry()) if r.getStoichiometry() > 1 else '', r.getSpecies()) for r in reaction.getListOfProducts()])
reversible = '<' if reaction.getReversible() else ''
print('%3s: %10s %1s->%10s\t\t[%s]' % (reaction.getId(),
reactants,
reversible,
products,
libsbml.formulaToL3String(reaction.getKineticLaw().getMath())))
Species: ['x1', 'x2', 'x3']
Reactions:
r1: 2 x1 -> x2 [p1 * x1^2]
r2: x1 + x2 -> x3 [p2 * x1 * x2]
r3: x2 -> 2 x1 [p3 * x2]
r4: x3 -> x1 + x2 [p4 * x3]
r5: x3 -> [k0 * x3]
r6: -> x1 [p5]
Test simulation¶
Performing an exemplary model simulation and plotting state and output trajectories:
[30]:
# load model
model_module = amici.import_model_module("model_steadystate_scaled", model_source_dir)
model = model_module.getModel()
model.setTimepoints(amici.DoubleVector(np.logspace(-5, 1, 20)))
solver = model.getSolver()
rdata = amici.runAmiciSimulation(model, solver)
default_parameters = np.array(model.getParameters())
# Default model parameters: print(default_parameters)
# Result fields reported by AMICI: list(rdata.keys())
[31]:
from amici.plotting import plotStateTrajectories
from amici.plotting import plotObservableTrajectories
plotStateTrajectories(rdata)
plotObservableTrajectories(rdata)
Standard optimization Ipopt¶
In this section, model parameters are estimated. parPE supports different optimization algorithms, available algorithms depend on the build configuration. In this section we will use Ipopt, which worked the best in our experience (https://academic.oup.com/bioinformatics/article/36/2/594/5538985).
Based on the parPE template files, a executable for parameter estimation has been built. By default, these executables are named estimate_${MODEL_NAME}. These files require a HDF5 file containing training data and optimization options. All those files have been generated automatically for this example.
This part of the example requires a parPE build with PARPE_ENABLE_IPOPT=ON.
Set parameter estimation options¶
Parameter estimation settings specified inside an HDF5 file. Those can be changed from any programming language with HDF5 bindings, with hdfview (https://www.hdfgroup.org/downloads/hdfview/), or with a helper script included in parPE, as demonstrated here:
[32]:
# enable derivative checker
input_file = f'{example_data_dir}/example_data.h5'
#!{optimization_options_py} {input_file} -s ipopt/derivative_test first-order
#!{optimization_options_py} {input_file} -s ipopt/derivative_test_print_all yes
# Use Ipopt
!{optimization_options_py} {input_file} -s optimizer 0
# Perform one optimizer runs from different starting points
!{optimization_options_py} {input_file} -s numStarts 1
# Run for 20 iterations
!{optimization_options_py} {input_file} -s ipopt/max_iter 30
# Disable hierarchical optimization (see below)
!{optimization_options_py} {input_file} -s hierarchicalOptimization 0
# Print settings
!{optimization_options_py} {input_file}
hierarchicalOptimization 0
numStarts 1
optimizer 0
retryOptimization 1
ceres/max_num_iterations 100
fmincon/GradObj b'on'
fmincon/MaxFunEvals 10000000.0
fmincon/MaxIter 100
fmincon/TolFun 0
fmincon/TolX 1e-08
fmincon/algorithm b'interior-point'
fmincon/display b'iter'
ipopt/acceptable_iter 1
ipopt/acceptable_obj_change_tol 1e-12
ipopt/acceptable_tol 1e+20
ipopt/hessian_approximation b'limited-memory'
ipopt/limited_memory_update_type b'bfgs'
ipopt/max_iter 30
ipopt/tol 1e-09
ipopt/watchdog_shortened_iter_trigger 0
toms611/mxfcal 100000000.0
Gradient check¶
Before starting the optimization, we can shortly compare the objective function gradients computed by AMICI/parPE with finite differences:
[33]:
# use three random starting points:
for i in range(3):
!PARPE_NO_DEBUG=1 {example_binary_dir}/example_steadystate_multi -t gradient_check -o deletemegc/ {input_file}
print()
[2020-06-24 17:41:30] [INF] [-1:140407870474176/] 0 g: -3.07804e+14 fd_c: -3.07834e+14 Δ/ff: 1.820688e-04 f: 1.61202e+14
[2020-06-24 17:41:30] [INF] [-1:140407870474176/] 1 g: -2.22547e+13 fd_c: -2.23559e+13 Δ/ff: 6.276508e-04 f: 1.61205e+14
[2020-06-24 17:41:30] [INF] [-1:140407870474176/] 2 g: 2.23191e+13 fd_c: 2.23727e+13 Δ/ff: -3.327962e-04 f: 1.61205e+14
[2020-06-24 17:41:30] [INF] [-1:140407870474176/] 3 g: 1.44004e+13 fd_c: 1.43986e+13 Δ/ff: 1.096761e-05 f: 1.61205e+14
[2020-06-24 17:41:30] [INF] [-1:140407870474176/] 4 g: 3.92648e+14 fd_c: 3.92711e+14 Δ/ff: -3.915439e-04 f: 1.61209e+14
[2020-06-24 17:41:30] [INF] [-1:140407870474176/] 5 g: 7.22972e+14 fd_c: 7.22972e+14 Δ/ff: -1.633158e-09 f: 1.61212e+14
[2020-06-24 17:41:30] [INF] [-1:140407870474176/] 6 g: 1.48764e+07 fd_c: 1.48766e+07 Δ/ff: -8.200509e-13 f: 1.61205e+14
[2020-06-24 17:41:30] [INF] [-1:140407870474176/] 7 g: -4.32827e+10 fd_c: -4.32827e+10 Δ/ff: -9.508153e-12 f: 1.61205e+14
[2020-06-24 17:41:30] [INF] [-1:140407870474176/] 8 g: 1.82786e+08 fd_c: 1.82784e+08 Δ/ff: 7.928618e-12 f: 1.61205e+14
[2020-06-24 17:41:30] [INF] [-1:140407870474176/] Walltime on master: 0.357358s, CPU time of all processes: 1.190509s
[2020-06-24 17:41:31] [INF] [-1:140118083160000/] 0 g: -6.21971e+09 fd_c: -6.21836e+09 Δ/ff: -7.588395e-08 f: 1.77565e+13
[2020-06-24 17:41:31] [INF] [-1:140118083160000/] 1 g: -1.01378e+10 fd_c: -1.01431e+10 Δ/ff: 3.019935e-07 f: 1.77565e+13
[2020-06-24 17:41:31] [INF] [-1:140118083160000/] 2 g: 1.01916e+10 fd_c: 1.01875e+10 Δ/ff: 2.299636e-07 f: 1.77565e+13
[2020-06-24 17:41:31] [INF] [-1:140118083160000/] 3 g: 1.01496e+10 fd_c: 1.01498e+10 Δ/ff: -1.220489e-08 f: 1.77565e+13
[2020-06-24 17:41:31] [INF] [-1:140118083160000/] 4 g: 7.63243e+08 fd_c: 7.61412e+08 Δ/ff: 1.030921e-07 f: 1.77565e+13
[2020-06-24 17:41:31] [INF] [-1:140118083160000/] 5 g: 3.5914e+10 fd_c: 3.5914e+10 Δ/ff: -1.675128e-12 f: 1.77565e+13
[2020-06-24 17:41:31] [INF] [-1:140118083160000/] 6 g: 8.66367e+07 fd_c: 8.66367e+07 Δ/ff: -1.943272e-12 f: 1.77565e+13
[2020-06-24 17:41:31] [INF] [-1:140118083160000/] 7 g: 121.481 fd_c: 195.312 Δ/ff: -4.158002e-12 f: 1.77565e+13
[2020-06-24 17:41:31] [INF] [-1:140118083160000/] 8 g: 3.66721e+08 fd_c: 3.66721e+08 Δ/ff: -2.067021e-11 f: 1.77565e+13
[2020-06-24 17:41:31] [INF] [-1:140118083160000/] Walltime on master: 0.420946s, CPU time of all processes: 1.274342s
[2020-06-24 17:41:32] [INF] [-1:140466688518080/] 0 g: 3.0421e+07 fd_c: 3.04203e+07 Δ/ff: 4.257906e-11 f: 1.62622e+13
[2020-06-24 17:41:32] [INF] [-1:140466688518080/] 1 g: -766.774 fd_c: 195.312 Δ/ff: -5.916097e-11 f: 1.62622e+13
[2020-06-24 17:41:32] [INF] [-1:140466688518080/] 2 g: -9.463e+06 fd_c: -9.46338e+06 Δ/ff: 2.347750e-11 f: 1.62622e+13
[2020-06-24 17:41:32] [INF] [-1:140466688518080/] 3 g: 4.0764e+07 fd_c: 4.07931e+07 Δ/ff: -1.786592e-09 f: 1.62622e+13
[2020-06-24 17:41:32] [INF] [-1:140466688518080/] 4 g: 5.7084e+07 fd_c: 5.7084e+07 Δ/ff: -1.569356e-12 f: 1.62622e+13
[2020-06-24 17:41:32] [INF] [-1:140466688518080/] 5 g: -1.73506 fd_c: 0 Δ/ff: -1.066930e-13 f: 1.62622e+13
[2020-06-24 17:41:32] [INF] [-1:140466688518080/] 6 g: 3.40035e+08 fd_c: 3.40035e+08 Δ/ff: -7.920917e-12 f: 1.62622e+13
[2020-06-24 17:41:32] [INF] [-1:140466688518080/] 7 g: -2.35915e+06 fd_c: -2.35918e+06 Δ/ff: 1.758269e-12 f: 1.62622e+13
[2020-06-24 17:41:32] [INF] [-1:140466688518080/] 8 g: 1.20306e+08 fd_c: 1.20307e+08 Δ/ff: -7.991474e-12 f: 1.62622e+13
[2020-06-24 17:41:32] [INF] [-1:140466688518080/] Walltime on master: 0.363544s, CPU time of all processes: 1.217862s
Optimize¶
Now we can run the actual optimization.
[34]:
# !(cd {parpe_build_root} && exec make -j12) # rebuild
!rm -rf deleteme # delete old result files
# optimize (using a single process)
!PARPE_NO_DEBUG=1 {example_binary_dir}/example_steadystate_multi -o deleteme/ {example_data_dir}/example_data.h5
[2020-06-24 17:41:33] [INF] [-1:140425994618816/] Reading random initial theta 0 from /optimizationOptions/randomStarts
List of user-set options:
Name Value used
acceptable_iter = 1 yes
acceptable_obj_change_tol = 1e-12 yes
acceptable_tol = 1e+20 yes
hessian_approximation = limited-memory yes
limited_memory_update_type = bfgs yes
max_iter = 30 yes
print_level = 5 yes
print_user_options = yes yes
tol = 1e-09 yes
watchdog_shortened_iter_trigger = 0 yes
******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
Ipopt is released as open source code under the Eclipse Public License (EPL).
For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************
This is Ipopt version 3.12.12, running with linear solver ma27.
Number of nonzeros in equality constraint Jacobian...: 0
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 0
Total number of variables............................: 9
variables with only lower bounds: 0
variables with lower and upper bounds: 9
variables with only upper bounds: 0
Total number of equality constraints.................: 0
Total number of inequality constraints...............: 0
inequality constraints with only lower bounds: 0
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 0
[2020-06-24 17:41:33] [INF] [-1:140425699804928/] [o0i0] iter: 0 cost: 532.303 time_iter: wall: 0.137419s cpu: 0.127829s time_optim: wall: 0.137419s cpu: 0.127829s
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 5.3230269e+02 0.00e+00 1.00e+02 0.0 0.00e+00 - 0.00e+00 0.00e+00 0
[2020-06-24 17:41:33] [INF] [-1:140425699804928/] [o0i1] iter: 1 cost: 820.034 time_iter: wall: 0.090377s cpu: 0.0783326s time_optim: wall: 0.227797s cpu: 0.206162s
1 8.2003355e+02 0.00e+00 4.00e+01 2.0 5.98e+01 - 9.91e-01 2.66e-02f 2
[2020-06-24 17:41:33] [INF] [-1:140425699804928/] [o0i2] iter: 2 cost: 776.643 time_iter: wall: 0.117079s cpu: 0.106627s time_optim: wall: 0.344876s cpu: 0.312788s
2 7.7664256e+02 0.00e+00 5.20e+01 2.2 5.80e-01 - 1.00e+00 1.00e+00f 1
[2020-06-24 17:41:33] [INF] [-1:140425699804928/] [o0i3] iter: 3 cost: -166.319 time_iter: wall: 0.0932628s cpu: 0.0802567s time_optim: wall: 0.438139s cpu: 0.393045s
3 -1.6631926e+02 0.00e+00 4.12e+01 1.5 2.34e+00 - 1.00e+00 2.50e-01f 3
[2020-06-24 17:41:33] [INF] [-1:140425699804928/] [o0i4] iter: 4 cost: -267.208 time_iter: wall: 0.0768777s cpu: 0.0693811s time_optim: wall: 0.515016s cpu: 0.462426s
4 -2.6720761e+02 0.00e+00 3.92e+00 0.2 1.85e-01 - 9.91e-01 1.00e+00f 1
[2020-06-24 17:41:33] [INF] [-1:140425699804928/] [o0i5] iter: 5 cost: -325.047 time_iter: wall: 0.0737827s cpu: 0.0664222s time_optim: wall: 0.588799s cpu: 0.528848s
5 -3.2504664e+02 0.00e+00 4.86e+00 -1.2 1.59e-01 - 9.84e-01 1.00e+00f 1
[2020-06-24 17:41:33] [INF] [-1:140425699804928/] [o0i6] iter: 6 cost: -336.398 time_iter: wall: 0.0699238s cpu: 0.0622717s time_optim: wall: 0.658723s cpu: 0.59112s
6 -3.3639830e+02 0.00e+00 1.12e+01 -1.9 8.74e-01 - 1.00e+00 1.00e+00f 1
[2020-06-24 17:41:34] [INF] [-1:140425699804928/] [o0i7] iter: 7 cost: -389.279 time_iter: wall: 0.0860524s cpu: 0.0719065s time_optim: wall: 0.744776s cpu: 0.663026s
7 -3.8927856e+02 0.00e+00 6.91e+00 -1.8 7.08e-01 - 1.00e+00 2.50e-01f 3
[2020-06-24 17:41:34] [INF] [-1:140425699804928/] [o0i8] iter: 8 cost: -417.125 time_iter: wall: 0.0824051s cpu: 0.0701718s time_optim: wall: 0.827181s cpu: 0.733198s
8 -4.1712507e+02 0.00e+00 2.72e+00 -2.7 5.18e-01 - 1.00e+00 5.00e-01f 2
[2020-06-24 17:41:34] [INF] [-1:140425699804928/] [o0i9] iter: 9 cost: -425.124 time_iter: wall: 0.0837048s cpu: 0.0707955s time_optim: wall: 0.910886s cpu: 0.803994s
9 -4.2512435e+02 0.00e+00 2.77e+00 -4.1 1.14e-01 - 1.00e+00 5.00e-01f 2
[2020-06-24 17:41:34] [INF] [-1:140425699804928/] [o0i10] iter: 10 cost: -431.91 time_iter: wall: 0.0717744s cpu: 0.0638436s time_optim: wall: 0.982661s cpu: 0.867837s
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 -4.3191005e+02 0.00e+00 9.02e-01 -5.5 4.63e-02 - 1.00e+00 1.00e+00f 1
[2020-06-24 17:41:34] [INF] [-1:140425699804928/] [o0i11] iter: 11 cost: -432.548 time_iter: wall: 0.0821081s cpu: 0.0695296s time_optim: wall: 1.06477s cpu: 0.937367s
11 -4.3254817e+02 0.00e+00 7.07e-01 -7.2 3.94e-02 - 1.00e+00 5.00e-01f 2
[2020-06-24 17:41:34] [INF] [-1:140425699804928/] [o0i12] iter: 12 cost: -433.253 time_iter: wall: 0.0700837s cpu: 0.0621244s time_optim: wall: 1.13485s cpu: 0.999491s
12 -4.3325317e+02 0.00e+00 5.07e-01 -8.8 3.00e-02 - 1.00e+00 1.00e+00f 1
[2020-06-24 17:41:34] [INF] [-1:140425699804928/] [o0i13] iter: 13 cost: -434.385 time_iter: wall: 0.0719023s cpu: 0.0637952s time_optim: wall: 1.20676s cpu: 1.06329s
13 -4.3438479e+02 0.00e+00 6.25e-01 -10.3 4.40e-02 - 1.00e+00 1.00e+00f 1
[2020-06-24 17:41:34] [INF] [-1:140425699804928/] [o0i14] iter: 14 cost: -438.759 time_iter: wall: 0.0663257s cpu: 0.0583022s time_optim: wall: 1.27308s cpu: 1.12159s
14 -4.3875867e+02 0.00e+00 3.98e+00 -11.0 5.21e-01 - 1.00e+00 1.00e+00f 1
[2020-06-24 17:41:34] [INF] [-1:140425699804928/] [o0i15] iter: 15 cost: -440.48 time_iter: wall: 0.09416s cpu: 0.0771593s time_optim: wall: 1.36724s cpu: 1.19875s
15 -4.4047967e+02 0.00e+00 4.39e+00 -11.0 2.61e+00 - 1.00e+00 6.22e-02f 5
[2020-06-24 17:41:34] [INF] [-1:140425699804928/] [o0i16] iter: 16 cost: -442.029 time_iter: wall: 0.0896711s cpu: 0.0733529s time_optim: wall: 1.45691s cpu: 1.2721s
16 -4.4202943e+02 0.00e+00 2.94e+00 -11.0 4.38e-01 - 1.00e+00 1.25e-01f 4
[2020-06-24 17:41:34] [INF] [-1:140425699804928/] [o0i17] iter: 17 cost: -443.967 time_iter: wall: 0.0669892s cpu: 0.0584416s time_optim: wall: 1.5239s cpu: 1.33054s
17 -4.4396683e+02 0.00e+00 1.78e+00 -11.0 1.93e-01 - 1.00e+00 1.00e+00f 1
[2020-06-24 17:41:34] [INF] [-1:140425699804928/] [o0i18] iter: 18 cost: -446.323 time_iter: wall: 0.0676223s cpu: 0.0592318s time_optim: wall: 1.59153s cpu: 1.38977s
18 -4.4632309e+02 0.00e+00 1.06e+00 -11.0 9.67e-02 - 1.00e+00 1.00e+00f 1
[2020-06-24 17:41:34] [INF] [-1:140425699804928/] [o0i19] iter: 19 cost: -446.807 time_iter: wall: 0.0673716s cpu: 0.0595199s time_optim: wall: 1.6589s cpu: 1.44929s
19 -4.4680666e+02 0.00e+00 7.12e-01 -11.0 1.64e-01 - 1.00e+00 1.00e+00f 1
[2020-06-24 17:41:35] [INF] [-1:140425699804928/] [o0i20] iter: 20 cost: -446.911 time_iter: wall: 0.098772s cpu: 0.0806446s time_optim: wall: 1.75767s cpu: 1.52994s
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
20 -4.4691082e+02 0.00e+00 5.78e-01 -11.0 5.12e-01 - 1.00e+00 3.12e-02f 6
[2020-06-24 17:41:35] [INF] [-1:140425699804928/] [o0i21] iter: 21 cost: -447.227 time_iter: wall: 0.066089s cpu: 0.0577964s time_optim: wall: 1.82376s cpu: 1.58774s
21 -4.4722745e+02 0.00e+00 4.61e-02 -11.0 6.51e-02 - 1.00e+00 1.00e+00f 1
[2020-06-24 17:41:35] [INF] [-1:140425699804928/] [o0i22] iter: 22 cost: -447.228 time_iter: wall: 0.0922707s cpu: 0.0758644s time_optim: wall: 1.91603s cpu: 1.6636s
22 -4.4722816e+02 0.00e+00 4.07e-02 -11.0 3.33e-02 - 1.00e+00 1.25e-01f 4
[2020-06-24 17:41:35] [INF] [-1:140425699804928/] [o0i23] iter: 23 cost: -447.228 time_iter: wall: 0.0955807s cpu: 0.0783362s time_optim: wall: 2.01161s cpu: 1.74194s
23 -4.4722838e+02 0.00e+00 5.88e-02 -11.0 3.66e-02 - 1.00e+00 6.25e-02f 5
[2020-06-24 17:41:35] [INF] [-1:140425699804928/] [o0i24] iter: 24 cost: -447.23 time_iter: wall: 0.0814274s cpu: 0.0682416s time_optim: wall: 2.09304s cpu: 1.81018s
24 -4.4723019e+02 0.00e+00 2.31e-02 -11.0 3.32e-03 - 1.00e+00 5.00e-01f 2
[2020-06-24 17:41:35] [INF] [-1:140425699804928/] [o0i25] iter: 25 cost: -447.231 time_iter: wall: 0.0737931s cpu: 0.0615733s time_optim: wall: 2.16683s cpu: 1.87175s
25 -4.4723112e+02 0.00e+00 1.71e-02 -11.0 6.07e-03 - 1.00e+00 5.00e-01f 2
[2020-06-24 17:41:35] [INF] [-1:140425699804928/] [o0i26] iter: 26 cost: -447.231 time_iter: wall: 0.0784649s cpu: 0.0655171s time_optim: wall: 2.2453s cpu: 1.93727s
26 -4.4723130e+02 0.00e+00 1.31e-02 -11.0 2.84e-03 - 1.00e+00 2.50e-01f 3
[2020-06-24 17:41:35] [INF] [-1:140425699804928/] [o0i27] iter: 27 cost: -447.232 time_iter: wall: 0.0659078s cpu: 0.0578224s time_optim: wall: 2.3112s cpu: 1.99509s
27 -4.4723151e+02 0.00e+00 1.05e-02 -11.0 1.01e-03 - 1.00e+00 1.00e+00f 1
[2020-06-24 17:41:35] [INF] [-1:140425699804928/] [o0i28] iter: 28 cost: -447.232 time_iter: wall: 0.0834543s cpu: 0.0689585s time_optim: wall: 2.39466s cpu: 2.06405s
28 -4.4723162e+02 0.00e+00 1.13e-02 -11.0 2.20e-03 - 1.00e+00 2.50e-01f 3
[2020-06-24 17:41:35] [INF] [-1:140425699804928/] [o0i29] iter: 29 cost: -447.232 time_iter: wall: 0.0683976s cpu: 0.0602698s time_optim: wall: 2.46306s cpu: 2.12432s
29 -4.4723185e+02 0.00e+00 5.13e-03 -11.0 1.09e-03 - 1.00e+00 1.00e+00f 1
[2020-06-24 17:41:35] [INF] [-1:140425699804928/] [o0i30] iter: 30 cost: -447.232 time_iter: wall: 0.0851599s cpu: 0.0702836s time_optim: wall: 2.54822s cpu: 2.1946s
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
30 -4.4723198e+02 0.00e+00 1.25e-02 -11.0 1.23e-02 - 1.00e+00 2.50e-01f 3
Number of Iterations....: 30
(scaled) (unscaled)
Objective...............: -1.0027481219080936e+01 -4.4723198109367854e+02
Dual infeasibility......: 1.2481077281248806e-02 5.5666391157677142e-01
Constraint violation....: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 1.0053736651784596e-11 4.4840298993687491e-10
Overall NLP error.......: 1.2481077281248806e-02 5.5666391157677142e-01
Number of objective function evaluations = 130
Number of objective gradient evaluations = 31
Number of equality constraint evaluations = 0
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 0
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 0
Total CPU secs in IPOPT (w/o function evaluations) = 0.556
Total CPU secs in NLP function evaluations = 2.283
EXIT: Maximum Number of Iterations Exceeded.
[2020-06-24 17:41:35] [INF] [-1:140425699804928/] [o0i31] Optimizer status 1, final llh: -4.472320e+02, time: wall: 2.548704 cpu: 2.194602.
[2020-06-24 17:41:37] [INF] [-1:140425994618816/] Walltime on master: 4.008655s, CPU time of all processes: 3.462642s
Analyze results¶
A good start for checking the results is a look at optimizer trajectories. This can be easily done using the parPE Python package:
[35]:
filename = 'deleteme/_rank00000.h5'
trajectories_ipopt = parpe.getCostTrajectories(filename)
#print(repr(trajectories))
parpe.plotting.plotCostTrajectory(trajectories_ipopt, log=False);
Since this example uses artificial data based on model simulations with known parameters, we can compare them to the optimization results:
[36]:
parpe.compare_optimization_results_to_true_parameters('deleteme/_rank00000.h5')
# __Exp____ __Act______ __Err______ __RelErr___ __ID_______
0: 1.00000 0.30485 -0.69515 -0.69515 p1
1: 0.50000 0.31305 -0.18695 -0.37391 p2
2: 0.40000 0.16030 -0.23970 -0.59925 p3
3: 2.00000 1.81174 -0.18826 -0.09413 p4
4: 0.10000 0.05128 -0.04872 -0.48718 p5
5: 2.00000 0.16231 -1.83769 -0.91885 scaling_x1_common
6: 3.00000 2.99955 -0.00045 -0.00015 offset_x2_batch_0
7: 0.20000 0.13729 -0.06271 -0.31357 x1withsigma_sigma
8: 4.00000 4.00132 0.00132 0.00033 offset_x2_batch_1
Status: 1
Cost: -447.231981 (expected: -0.000000)
The parameters don’t match that greatly. This is not completely unexpected due to the artificial noise introduced. To get a closer look at the optimization result, we can compare the training data to the model output with the optimized parameters.
The model outputs are by default not saved during optimization, because this can lead to much I/O overhead and large files. However, there is an executable to quickly rerun simulation with the optimal parameters:
[37]:
# Simulate with optimal parameters, save results
!rm -f sim.h5 # remove files from previous run
!{example_binary_dir}/example_steadystate_multi_simulator deleteme/_rank00000.h5 /inputData deleteme/_rank00000.h5 /inputData sim.h5 / --at-optimum --nompi --nocompute-inner
Running --at-optimum for
conditions from deleteme/_rank00000.h5:/inputData and
parameters from deleteme/_rank00000.h5:/inputData
> sim.h5:/
Running for start 0
Starting simulation. Number of conditions: 4
[38]:
# Load simulated outputs
(measured, simulated, timepoints, llh) = parpe.readSimulationsFromFile('sim.h5')
start_idx = '0'
[39]:
# Plot correlation of measurements (training data) and model simulation with optimized parameters
parpe.plotting.plotCorrelation(measured[start_idx], simulated[start_idx])
[39]:
<matplotlib.axes._subplots.AxesSubplot at 0x7fc10fbead60>
[40]:
# Plot measurement trajectories (training data) and compare to model simulation with optimized parameters
parpe.plotting.plotTrajectoryFits(measured[start_idx], simulated[start_idx], timepoints[start_idx])
Changing optimizers - Ceres¶
Once parPE has been built with support for different optimizers, selecting a different optimizer is quite easy.
(This part of the example requires a parPE build with PARPE_ENABLE_CERES=ON)
[41]:
# copy input file from above example
example_data_ceres = f'{example_data_dir}/example_data_ceres.h5'
!cp {example_data_dir}/example_data.h5 {example_data_ceres}
# Change optimizer to CERES
# NOTE: For this moment, optimizers are inconveniently selected based on numeric values, 0 is Ipopt, 1 is Ceres.
!{optimization_options_py} {example_data_ceres} -s optimizer 1
# Run optimization
!PARPE_NO_DEBUG=1 {mpiexec} {example_binary_dir}/example_steadystate_multi -o deletemeceres/ {example_data_ceres} --mpi
[2020-06-24 17:41:41] [INF] [0:139880673687488/dweindl-ThinkPad-L480] Running with 4 MPI processes.
[2020-06-24 17:41:41] [INF] [0:139880673687488/dweindl-ThinkPad-L480] Reading random initial theta 0 from /optimizationOptions/randomStarts
callbacks.cc:105 0: f: 5.323027e+02 d: 0.00e+00 g: 4.46e+03 h: 0.00e+00 s: 0.00e+00 e: 0 it: 4.13e-02 tt: 4.13e-02
[2020-06-24 17:41:41] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i0] iter: 0 cost: 532.303 time_iter: wall: 0.0415566s cpu: 0.0809107s time_optim: wall: 0.0415569s cpu: 0.0809107s
callbacks.cc:105 1: f:-3.344605e+02 d: 8.67e+02 g: 1.67e+02 h: 1.13e+00 s: 2.24e-04 e: 1 it: 3.72e-02 tt: 7.95e-02
[2020-06-24 17:41:41] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i1] iter: 1 cost: -334.461 time_iter: wall: 0.0382083s cpu: 0.0764133s time_optim: wall: 0.0797655s cpu: 0.157324s
callbacks.cc:105 2: f:-3.788412e+02 d: 4.44e+01 g: 3.85e+02 h: 3.29e-01 s: 1.28e-03 e: 5 it: 1.56e-01 tt: 2.36e-01
[2020-06-24 17:41:41] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i2] iter: 2 cost: -378.841 time_iter: wall: 0.156987s cpu: 0.293226s time_optim: wall: 0.236753s cpu: 0.45055s
callbacks.cc:105 3: f:-4.183630e+02 d: 3.95e+01 g: 2.30e+02 h: 3.95e-01 s: 4.06e-04 e: 1 it: 3.77e-02 tt: 2.75e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i3] iter: 3 cost: -418.363 time_iter: wall: 0.0381825s cpu: 0.0691572s time_optim: wall: 0.274936s cpu: 0.519708s
callbacks.cc:105 4: f:-4.189047e+02 d: 5.42e-01 g: 2.85e+02 h: 4.76e-02 s: 5.58e-04 e: 2 it: 8.96e-02 tt: 3.65e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i4] iter: 4 cost: -418.905 time_iter: wall: 0.0901106s cpu: 0.161033s time_optim: wall: 0.365047s cpu: 0.68074s
callbacks.cc:105 5: f:-4.197841e+02 d: 8.79e-01 g: 2.78e+02 h: 2.46e-02 s: 3.88e-04 e: 1 it: 3.98e-02 tt: 4.05e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i5] iter: 5 cost: -419.784 time_iter: wall: 0.0402574s cpu: 0.0745627s time_optim: wall: 0.405304s cpu: 0.755303s
callbacks.cc:105 6: f:-4.207404e+02 d: 9.56e-01 g: 2.96e+02 h: 6.32e-02 s: 1.52e-03 e: 1 it: 3.93e-02 tt: 4.45e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i6] iter: 6 cost: -420.74 time_iter: wall: 0.0398202s cpu: 0.0781893s time_optim: wall: 0.445125s cpu: 0.833492s
callbacks.cc:105 7: f:-4.223504e+02 d: 1.61e+00 g: 2.93e+02 h: 8.02e-02 s: 1.09e-03 e: 1 it: 3.71e-02 tt: 4.82e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i7] iter: 7 cost: -422.35 time_iter: wall: 0.0375706s cpu: 0.0742174s time_optim: wall: 0.482696s cpu: 0.907709s
callbacks.cc:105 8: f:-4.252214e+02 d: 2.87e+00 g: 2.84e+02 h: 1.55e-01 s: 2.42e-03 e: 1 it: 3.77e-02 tt: 5.21e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i8] iter: 8 cost: -425.221 time_iter: wall: 0.0381947s cpu: 0.0754364s time_optim: wall: 0.520891s cpu: 0.983146s
callbacks.cc:105 9: f:-4.291242e+02 d: 3.90e+00 g: 2.72e+02 h: 4.47e-01 s: 5.38e-02 e: 1 it: 3.75e-02 tt: 5.59e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i9] iter: 9 cost: -429.124 time_iter: wall: 0.0379482s cpu: 0.0749299s time_optim: wall: 0.558839s cpu: 1.05808s
callbacks.cc:105 10: f:-4.358720e+02 d: 6.75e+00 g: 2.09e+02 h: 5.84e-02 s: 1.20e-01 e: 1 it: 3.65e-02 tt: 5.96e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i10] iter: 10 cost: -435.872 time_iter: wall: 0.036973s cpu: 0.0729143s time_optim: wall: 0.595813s cpu: 1.13099s
callbacks.cc:105 11: f:-4.441651e+02 d: 8.29e+00 g: 3.97e+01 h: 2.26e-01 s: 7.51e-01 e: 1 it: 3.93e-02 tt: 6.35e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i11] iter: 11 cost: -444.165 time_iter: wall: 0.0397685s cpu: 0.0773617s time_optim: wall: 0.635581s cpu: 1.20835s
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i12] iter: 12 cost: -445.062 time_iter: wall: 0.0374097s cpu: 0.0724785s time_optim: wall: 0.672991s cpu: 1.28083s
callbacks.cc:105 12: f:-4.450617e+02 d: 8.97e-01 g: 1.17e+01 h: 6.36e-02 s: 1.00e+00 e: 1 it: 3.65e-02 tt: 6.73e-01
callbacks.cc:105 13: f:-4.451359e+02 d: 7.42e-02 g: 1.17e+01 h: 5.40e-02 s: 1.00e+00 e: 1 it: 4.10e-02 tt: 7.14e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i13] iter: 13 cost: -445.136 time_iter: wall: 0.0415508s cpu: 0.0775626s time_optim: wall: 0.714542s cpu: 1.35839s
callbacks.cc:105 14: f:-4.452398e+02 d: 1.04e-01 g: 1.16e+01 h: 5.48e-02 s: 1.00e+00 e: 1 it: 3.74e-02 tt: 7.52e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i14] iter: 14 cost: -445.24 time_iter: wall: 0.0379656s cpu: 0.0741554s time_optim: wall: 0.752508s cpu: 1.43255s
callbacks.cc:105 15: f:-4.454254e+02 d: 1.86e-01 g: 1.15e+01 h: 8.01e-02 s: 6.39e-01 e: 1 it: 4.32e-02 tt: 7.96e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i15] iter: 15 cost: -445.425 time_iter: wall: 0.0437119s cpu: 0.0795556s time_optim: wall: 0.79622s cpu: 1.5121s
callbacks.cc:105 16: f:-4.457760e+02 d: 3.51e-01 g: 1.08e+01 h: 1.41e-01 s: 2.84e-01 e: 1 it: 3.65e-02 tt: 8.33e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i16] iter: 16 cost: -445.776 time_iter: wall: 0.036956s cpu: 0.0727817s time_optim: wall: 0.833176s cpu: 1.58489s
callbacks.cc:105 17: f:-4.460990e+02 d: 3.23e-01 g: 1.73e+01 h: 2.69e-01 s: 1.62e-01 e: 1 it: 3.91e-02 tt: 8.72e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i17] iter: 17 cost: -446.099 time_iter: wall: 0.0395317s cpu: 0.0750284s time_optim: wall: 0.872708s cpu: 1.65991s
callbacks.cc:105 18: f:-4.465246e+02 d: 4.26e-01 g: 9.07e+00 h: 6.18e-02 s: 8.06e-01 e: 1 it: 3.75e-02 tt: 9.10e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i18] iter: 18 cost: -446.525 time_iter: wall: 0.0380117s cpu: 0.0768193s time_optim: wall: 0.91072s cpu: 1.73673s
callbacks.cc:105 19: f:-4.469159e+02 d: 3.91e-01 g: 8.47e+00 h: 1.57e-01 s: 1.00e+00 e: 1 it: 3.74e-02 tt: 9.48e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i19] iter: 19 cost: -446.916 time_iter: wall: 0.0378456s cpu: 0.0734315s time_optim: wall: 0.948566s cpu: 1.81016s
callbacks.cc:105 20: f:-4.470190e+02 d: 1.03e-01 g: 7.25e+00 h: 3.44e-02 s: 1.00e+00 e: 1 it: 3.77e-02 tt: 9.86e-01
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i20] iter: 20 cost: -447.019 time_iter: wall: 0.0381489s cpu: 0.0755738s time_optim: wall: 0.986715s cpu: 1.88574s
callbacks.cc:105 21: f:-4.470725e+02 d: 5.35e-02 g: 3.81e+00 h: 4.45e-02 s: 1.00e+00 e: 1 it: 3.64e-02 tt: 1.02e+00
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i21] iter: 21 cost: -447.072 time_iter: wall: 0.0368396s cpu: 0.0732056s time_optim: wall: 1.02356s cpu: 1.95894s
callbacks.cc:105 22: f:-4.471107e+02 d: 3.82e-02 g: 5.08e+00 h: 7.65e-02 s: 4.64e-02 e: 1 it: 3.71e-02 tt: 1.06e+00
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i22] iter: 22 cost: -447.111 time_iter: wall: 0.0375187s cpu: 0.0742591s time_optim: wall: 1.06107s cpu: 2.0332s
callbacks.cc:105 23: f:-4.471110e+02 d: 3.08e-04 g: 4.69e+00 h: 6.83e-04 s: 1.81e-03 e: 2 it: 7.50e-02 tt: 1.14e+00
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i23] iter: 23 cost: -447.111 time_iter: wall: 0.0754316s cpu: 0.152713s time_optim: wall: 1.13651s cpu: 2.18592s
callbacks.cc:105 24: f:-4.471154e+02 d: 4.41e-03 g: 6.50e+00 h: 5.26e-03 s: 9.69e-03 e: 2 it: 7.74e-02 tt: 1.21e+00
[2020-06-24 17:41:42] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i24] iter: 24 cost: -447.115 time_iter: wall: 0.0778265s cpu: 0.153936s time_optim: wall: 1.21433s cpu: 2.33985s
callbacks.cc:105 25: f:-4.471214e+02 d: 5.97e-03 g: 6.20e+00 h: 8.19e-03 s: 5.28e-04 e: 1 it: 3.64e-02 tt: 1.25e+00
[2020-06-24 17:41:43] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i25] iter: 25 cost: -447.121 time_iter: wall: 0.0368165s cpu: 0.0730412s time_optim: wall: 1.25115s cpu: 2.41289s
callbacks.cc:105 26: f:-4.471818e+02 d: 6.04e-02 g: 6.25e+00 h: 9.16e-02 s: 4.15e-03 e: 2 it: 7.55e-02 tt: 1.33e+00
[2020-06-24 17:41:43] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i26] iter: 26 cost: -447.182 time_iter: wall: 0.0760229s cpu: 0.14886s time_optim: wall: 1.32717s cpu: 2.56175s
callbacks.cc:105 27: f:-4.471928e+02 d: 1.10e-02 g: 6.28e+00 h: 1.63e-02 s: 1.47e-03 e: 2 it: 7.39e-02 tt: 1.40e+00
[2020-06-24 17:41:43] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i27] iter: 27 cost: -447.193 time_iter: wall: 0.0743093s cpu: 0.149165s time_optim: wall: 1.40148s cpu: 2.71092s
callbacks.cc:105 28: f:-4.471946e+02 d: 1.84e-03 g: 5.48e+00 h: 7.66e-03 s: 2.21e-02 e: 2 it: 7.66e-02 tt: 1.48e+00
[2020-06-24 17:41:43] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i28] iter: 28 cost: -447.195 time_iter: wall: 0.076984s cpu: 0.15148s time_optim: wall: 1.47847s cpu: 2.8624s
callbacks.cc:105 29: f:-4.472208e+02 d: 2.61e-02 g: 2.36e+00 h: 1.22e-02 s: 2.82e-01 e: 2 it: 7.30e-02 tt: 1.55e+00
[2020-06-24 17:41:43] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i29] iter: 29 cost: -447.221 time_iter: wall: 0.0734252s cpu: 0.146759s time_optim: wall: 1.55189s cpu: 3.00916s
callbacks.cc:105 30: f:-4.472269e+02 d: 6.11e-03 g: 2.56e+00 h: 3.82e-02 s: 1.00e+00 e: 1 it: 3.69e-02 tt: 1.59e+00
[2020-06-24 17:41:43] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i30] iter: 30 cost: -447.227 time_iter: wall: 0.037355s cpu: 0.0741047s time_optim: wall: 1.58925s cpu: 3.08326s
callbacks.cc:105 31: f:-4.472342e+02 d: 7.31e-03 g: 1.12e+00 h: 1.67e-02 s: 7.05e-01 e: 1 it: 3.68e-02 tt: 1.63e+00
[2020-06-24 17:41:43] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i31] iter: 31 cost: -447.234 time_iter: wall: 0.0372581s cpu: 0.0736081s time_optim: wall: 1.62651s cpu: 3.15687s
callbacks.cc:105 32: f:-4.472355e+02 d: 1.29e-03 g: 1.60e-01 h: 6.13e-03 s: 1.00e+00 e: 1 it: 3.84e-02 tt: 1.67e+00
[2020-06-24 17:41:43] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i32] iter: 32 cost: -447.235 time_iter: wall: 0.0388177s cpu: 0.0753357s time_optim: wall: 1.66532s cpu: 3.23221s
callbacks.cc:105 33: f:-4.472360e+02 d: 4.63e-04 g: 1.61e-01 h: 1.32e-02 s: 1.00e+00 e: 1 it: 3.70e-02 tt: 1.70e+00
[2020-06-24 17:41:43] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i33] iter: 33 cost: -447.236 time_iter: wall: 0.0374512s cpu: 0.0755949s time_optim: wall: 1.70277s cpu: 3.3078s
callbacks.cc:105 34: f:-4.472361e+02 d: 1.07e-04 g: 1.54e-02 h: 6.50e-03 s: 1.00e+00 e: 1 it: 3.63e-02 tt: 1.74e+00
[2020-06-24 17:41:43] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i34] iter: 34 cost: -447.236 time_iter: wall: 0.036703s cpu: 0.0725629s time_optim: wall: 1.73948s cpu: 3.38036s
callbacks.cc:105 35: f:-4.472361e+02 d: 1.71e-06 g: 4.67e-03 h: 8.97e-04 s: 1.00e+00 e: 1 it: 3.81e-02 tt: 1.78e+00
[2020-06-24 17:41:43] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i35] iter: 35 cost: -447.236 time_iter: wall: 0.0385312s cpu: 0.076953s time_optim: wall: 1.77801s cpu: 3.45732s
line_search.cc:758 Line search failed: Wolfe zoom bracket width: 4.68275e-06 too small with descent_direction_max_norm: 8.19905e-05.
line_search_minimizer.cc:413 Terminating: Parameter tolerance reached. Relative step_norm: 0.000000e+00 <= 1.000000e-08.
[2020-06-24 17:41:43] [INF] [0:139880252290816/dweindl-ThinkPad-L480] [o0i36] Optimizer status 0, final llh: -4.472361e+02, time: wall: 1.970559 cpu: 3.852414.
[2020-06-24 17:41:44] [INF] [0:139880673687488/dweindl-ThinkPad-L480] Walltime on master: 3.286791s, CPU time of all processes: 13.255544s
[2020-06-24 17:41:44] [INF] [0:139880673687488/dweindl-ThinkPad-L480] Sent termination signal to workers.
[42]:
ceres_optimization_result_filename = 'deletemeceres/_rank00000.h5'
trajectories_ceres = parpe.getCostTrajectories(ceres_optimization_result_filename)
#print(repr(trajectories))
ax = parpe.plotting.plotCostTrajectory(trajectories_ipopt, log=False);
parpe.plotting.plotCostTrajectory(trajectories_ceres, log=False, ax=ax);
ax.autoscale(True)
ax.legend(['Ipopt', 'Ceres'])
ax.set_title('Convergence Ipopt vs. Ceres');
[43]:
parpe.compare_optimization_results_to_true_parameters(ceres_optimization_result_filename)
# __Exp____ __Act______ __Err______ __RelErr___ __ID_______
0: 1.00000 0.30548 -0.69452 -0.69452 p1
1: 0.50000 0.30052 -0.19948 -0.39895 p2
2: 0.40000 0.16337 -0.23663 -0.59158 p3
3: 2.00000 1.81043 -0.18957 -0.09478 p4
4: 0.10000 0.04597 -0.05403 -0.54034 p5
5: 2.00000 0.16233 -1.83767 -0.91883 scaling_x1_common
6: 3.00000 2.99965 -0.00035 -0.00012 offset_x2_batch_0
7: 0.20000 0.13703 -0.06297 -0.31484 x1withsigma_sigma
8: 4.00000 4.00120 0.00120 0.00030 offset_x2_batch_1
Status: 0
Cost: -447.236062 (expected: -0.000000)
[43]:
