def trainPolicy(self, policy, env, numIterations):
"""Evaluate `numIterations` updating iterations on the given policy for
the given environment."""
returns = np.zeros([numIterations * self.populationSize])
# Define the objective.
i = 0
def objective(p):
"""Update the policy with given parameters, evalute and return the reward."""
weights = p["Parameters"]
overwriteNetworkParams(policy.layers, weights)
meanReward = 0
for ep in range(env.numEpisodesPerEvaluation
): # Each new episode starts here.
states, actions, policyEvaluations, rewards = env.performOneEpisode(
policy)
meanReward += sum(rewards)
meanReward /= env.numEpisodesPerEvaluation
p["Evaluation"] = meanReward
returns[i] = meanReward
i += 1
# Create Korali and problem objects.
k = korali.Engine()
e = korali.Experiment()
# Configure the problem.
e["Problem"]["Type"] = "Direct/Basic" # Use Korali v1.0.1.
e["Problem"]["Objective Function"] = objective
# Define the problem variables.
numParams = getNumNetworkParams(policy.layers)
print("Number of policy parameters =", numParams)
for i in range(numParams):
e["Variables"][i]["Name"] = "X" + str(i)
# Initial distribution of population samples.
e["Variables"][i]["Initial Mean"] = 0.0
e["Variables"][i]["Initial Standard Deviation"] = self.sigma
# Bounds are necessary to avoid pathological cases generated by Gaussians.
e["Variables"][i]["Lower Bound"] = -100.0
e["Variables"][i]["Upper Bound"] = +100.0
# Configure CMA-ES parameters.
e["Solver"]["Type"] = "Optimizer/CMAES"
e["Solver"]["Population Size"] = self.populationSize
# e["Solver"]["Termination Criteria"]["Min Value Difference Threshold"] = 1e-7
e["Solver"]["Termination Criteria"]["Max Generations"] = numIterations
# Run Korali.
k.run(e)
maxR = np.max(returns.reshape(numIterations, self.populationSize),
axis=1)
file_object = open('CMAES.txt', 'a')
for i in range(numIterations):
file_object.write('%e ' % maxR[i])
file_object.write('\n')
file_object.close()
def model(p):
x = p["Parameters"][0]
# Starting Model's Korali Engine
import korali
k = korali.Engine()
# Creating new experiment
e = korali.Experiment()
# Configuring Problem
e["Random Seed"] = 0xC0FEE
e["Problem"]["Type"] = "Optimization"
e["Problem"]["Objective Function"] = lambda sampleData: subModel(
sampleData, x)
# Defining the problem's variables
e["Variables"][0]["Name"] = "Y"
e["Variables"][0]["Lower Bound"] = -10.0
e["Variables"][0]["Upper Bound"] = +10.0
# Configuring CMA-ES parameters
e["Solver"]["Type"] = "Optimizer/CMAES"
e["Solver"]["Population Size"] = 4
e["Solver"]["Termination Criteria"][
"Min Value Difference Threshold"] = 1e-15
e["Solver"]["Termination Criteria"]["Max Generations"] = 100
e["Console Output"]["Verbosity"] = "Silent"
e["File Output"]["Enabled"] = False
# Running Korali
k.run(e)
# Storing the best Y as result of evaluation
p["F(x)"] = e["Results"]["Best Sample"]["F(x)"]
def sampling(phase_1_path, phase_2_path, phase_3_path):
e = korali.Experiment()
theta = korali.Experiment()
psi = korali.Experiment()
print(phase_1_path)
print(phase_2_path)
theta.loadState(phase_1_path)
psi.loadState(phase_2_path)
e["Problem"]["Type"] = "Hierarchical/Theta"
e["Problem"]["Theta Experiment"] = theta
e["Problem"]["Psi Experiment"] = psi
e["Solver"]["Type"] = "Sampler/TMCMC"
e["Solver"]["Population Size"] = 1000
e["Solver"]["Default Burn In"] = 2
e["Solver"]["Max Chain Length"] = 1
e["Solver"]["Target Coefficient Of Variation"] = 0.6
e["Console Output"]["Verbosity"] = "Detailed"
e["File Output"]["Path"] = phase_3_path + '/_korali_samples/'
# Starting Korali's Engine and running experiment
k = korali.Engine()
# k["Conduit"]["Type"] = "Concurrent"
# k["Conduit"]["Concurrent Jobs"] = 12
k.run(e)
def optimize(self, populationSize, maxiter=1000):
self.nSamples = 1
self.e = korali.Experiment()
self.e['Problem']['Type'] = 'Bayesian/Reference'
self.e['Problem']['Likelihood Model'] = self.likelihoodModel
self.e['Problem']['Reference Data'] = list(
map(float, self.data['Model']['y-data']))
self.e['Problem']['Computational Model'] = self.computational_model
self.e["Solver"]["Type"] = "Optimizer/CMAES"
self.e["Solver"]["Population Size"] = populationSize
self.e["Solver"]["Termination Criteria"]["Max Generations"] = maxiter
self.e["Solver"]["Termination Criteria"][
"Min Value Difference Threshold"] = 1e-9
js = self.get_variables_and_distributions()
self.set_variables_and_distributions(js)
self.set_korali_output_files(self.saveInfo['korali samples'], maxiter)
self.e['Console Output']['Verbosity'] = 'Detailed'
if self.silent:
self.e['Console Output']['Verbosity'] = 'Silent'
k = korali.Engine()
k['Conduit']['Type'] = 'Concurrent'
k['Conduit']['Concurrent Jobs'] = self.nThreads
k.run(self.e)
printlog('Copy variables from Korali to Epidemics...')
self.parameters = []
myDatabase = self.e['Results']['Best Sample']['Parameters']
for j in range(self.nParameters):
self.parameters.append({})
self.parameters[j]['Name'] = self.e['Variables'][j]['Name']
self.parameters[j]['Values'] = np.asarray([myDatabase[j]])
self.has_been_called['optimize'] = True
self.has_been_called['propagate'] = False
printlog('Done copying variables.')
names = []
best = []
for j in range(self.nParameters):
best.append(myDatabase[j])
names.append(self.parameters[j]['Name'])
js = {}
js["Value"] = self.e['Results']['Best Sample']['F(x)']
js["Parameter"] = best
js["Names"] = names
save_file(js, self.saveInfo['cmaes'], 'Optimum', fileType='json')
def run_cmaes_with_termination_criterion(criterion, value):
print("[Korali] Prepare CMAES run with Termination Criteria "\
"'{0}'".format(criterion))
e = korali.Experiment()
e["Problem"]["Type"] = "Evaluation/Direct/Basic"
e["Problem"]["Objective"] = "Maximize"
e["Problem"]["Objective Function"] = evaluateModel
e["Variables"][0]["Name"] = "X"
e["Variables"][0]["Lower Bound"] = +1.0
e["Variables"][0]["Upper Bound"] = +10.0
e["Solver"]["Type"] = "Optimizer/CMAES"
e["Solver"]["Population Size"] = 8
e["Solver"]["Termination Criteria"][criterion] = value
e["Random Seed"] = 1337
k = korali.Engine()
k.run(e)
if (criterion == "Max Generations"):
assert_value(e["Internal"]["Current Generation"], value)
elif (criterion == "Max Infeasible Resamplings"):
assert_greatereq(e["Solver"]["Internal"]["Infeasible Sample Count"],
value)
elif (criterion == "Max Condition Covariance Matrix"):
minEw = e["Solver"]["Internal"]["Minimum Covariance Eigenvalue"]
maxEw = e["Solver"]["Internal"]["Maximum Covariance Eigenvalue"]
assert_greatereq(maxEw / minEw, value)
elif (criterion == "Max Value"):
assert_greatereq(e["Solver"]["Internal"]["Best Ever Value"], value)
elif (criterion == "Min Value Difference Threshold"):
previous = e["Solver"]["Internal"]["Previous Best Ever Value"]
current = e["Solver"]["Internal"]["Best Ever Value"]
assert_smallereq(previous - current, value)
elif (criterion == "Min Standard Deviation"):
assert_smallereq(
e["Solver"]["Internal"]["Current Min Standard Deviation"], value)
elif (criterion == "Max Standard Deviation"):
assert_greatereq(
e["Solver"]["Internal"]["Current Max Standard Deviation"], value)
else:
print("Termination Criterion not recognized!")
exit(-1)
def sample(self, nSamples=1000, cov=0.4, maxiter=100):
self.e = korali.Experiment()
self.nSamples = nSamples
self.e['Problem']['Type'] = 'Bayesian/Reference'
self.e['Problem']['Likelihood Model'] = self.likelihoodModel
self.e['Problem']['Reference Data'] = list(
map(float, self.data['Model']['y-data']))
self.e['Problem']['Computational Model'] = self.computational_model
self.e['Solver']['Type'] = "Sampler/TMCMC"
self.e['Solver']['Version'] = self.sampler
self.e['Solver']['Step Size'] = 0.1
self.e['Solver']['Population Size'] = self.nSamples
self.e['Solver']['Target Coefficient Of Variation'] = cov
self.e['Solver']['Termination Criteria']['Max Generations'] = maxiter
js = self.get_variables_and_distributions()
self.set_variables_and_distributions(js)
self.set_korali_output_files(self.saveInfo['korali samples'], maxiter)
self.e['Console Output']['Verbosity'] = 'Detailed'
if (self.silent): self.e['Console Output']['Verbosity'] = 'Silent'
k = korali.Engine()
k['Conduit']['Type'] = 'Concurrent'
k['Conduit']['Concurrent Jobs'] = self.nThreads
k.run(self.e)
js = {}
js['Log Evidence'] = self.e['Solver']['LogEvidence']
printlog(f"Log Evidence = {js['Log Evidence']}")
save_file(js,
self.saveInfo['evidence'],
'Log Evidence',
fileType='json')
printlog('Copy variables from Korali to Epidemics...')
self.parameters = []
myDatabase = self.e['Results']['Sample Database']
for j in range(self.nParameters):
self.parameters.append({})
self.parameters[j]['Name'] = self.e['Variables'][j]['Name']
self.parameters[j]['Values'] = np.asarray(
[myDatabase[k][j] for k in range(self.nSamples)])
self.has_been_called['sample'] = True
self.has_been_called['propagate'] = False
printlog('Done copying variables.')
def propagate_uncertainty(args, jskSamples, jsData):
sir.set_custom_params(reduction=args.reduction,
infer_reduction=args.infer_reduction,
duration=args.duration,
infer_duration=args.infer_duration)
jsOde = sir.getReferenceData(jsData)
Ns = jskSamples['Solver']['Population Size']
Np = len(jskSamples['Samples'][0]['Parameters'])
db = jskSamples['Results']['Sample Database']
p = []
for j in range(Np):
tmp = []
for k in range(Ns):
tmp.append(db[k][j])
p.append(tmp)
# days of prediction = days in the data + future days
T = jsOde['Time'][-1] + args.futureDays
t = np.linspace(0, T, args.nPoints)
jsOde['Time'] = t.tolist()
e = korali.Experiment()
e['Problem']['Type'] = 'Propagation'
e['Problem']['Execution Model'] = \
lambda modelData: sir.model_for_korali_execute(
modelData, jsOde)
for i, var in enumerate(sir.params_to_infer):
e['Variables'][i]['Name'] = var
e['Variables'][i]['Precomputed Values'] = p[i]
e['Solver']['Type'] = 'Executor'
e['File Output'] = tools.fileOutputDefaults(args, '_korali_propagation/')
if (args.silent):
e['Console Output']['Verbosity'] = 'Silent'
e['Store Sample Information'] = True
k = korali.Engine()
k['Conduit']['Type'] = 'Concurrent'
k['Conduit']['Concurrent Jobs'] = args.nThreads
k.run(e)
return e
def trainPolicy(self, policy, env, numIterations):
"""Evaluate `numIterations` updating iterations on the given policy for
the given environment."""
# Define the objective.
def objective(p):
"""Update the policy with given parameters, evalute and return the reward."""
weights = p["Parameters"]
overwriteNetworkParams(policy.network, weights)
meanTotalReward = 0
for ep in range(env.numEpisodesPerEvaluation): # Each new episode starts here.
states, actions, policyEvaluations, rewards = env.performOneEpisode(policy)
meanTotalReward += sum(rewards)
meanTotalReward /= env.numEpisodesPerEvaluation
print("meanTotalReward", meanTotalReward)
p["Evaluation"] = meanTotalReward # Korali v1.0.1.
# p["F(x)"] = meanTotalReward # Korali master branch (?)
# Create Korali and problem objects.
k = korali.Engine()
e = korali.Experiment()
# Configure the problem.
e["Problem"]["Type"] = "Evaluation/Direct/Basic" # Korali v1.0.1.
# e["Problem"]["Type"] = "Optimization/Stochastic" # Korali master branch (?)
e["Problem"]["Objective Function"] = objective
# Define the problem variables.
numParams = getNumNetworkParams(policy.network);
print("Number of policy parameters =", numParams)
for i in range(numParams):
e["Variables"][i]["Name"] = "X" + str(i)
# Initial distribution of population samples.
e["Variables"][i]["Initial Mean"] = 0.0
e["Variables"][i]["Initial Standard Deviation"] = self.sigma
# Bounds are necessary to avoid pathological cases generated by Gaussians.
e["Variables"][i]["Lower Bound"] = -100.0
e["Variables"][i]["Upper Bound"] = +100.0
# Configure CMA-ES parameters.
e["Solver"]["Type"] = "Optimizer/CMAES"
e["Solver"]["Population Size"] = self.populationSize
# e["Solver"]["Termination Criteria"]["Min Value Difference Threshold"] = 1e-7
e["Solver"]["Termination Criteria"]["Max Generations"] = numIterations
# Run Korali.
k.run(e)
def sample_parameters(args, jsData):
sir.set_custom_params(reduction=args.reduction,
infer_reduction=args.infer_reduction,
duration=args.duration,
infer_duration=args.infer_duration)
jsOde = sir.getReferenceData(jsData)
# Creating new experiment
e = korali.Experiment()
# Setting up the reference likelihood for the Bayesian Problem
e['Problem']['Type'] = 'Bayesian/Reference'
e['Problem']['Likelihood Model'] = sir.likelihood
e['Problem']['Reference Data'] = jsOde['Data']
e['Problem'][
'Computational Model'] = lambda sampleData: sir.model_for_korali_sample(
sampleData, jsOde)
# Configuring TMCMC parameters
e['Solver']['Type'] = 'TMCMC'
e['Solver']['Population Size'] = args.nSamples
for i, var in enumerate(sir.params_to_infer):
distname = 'Uniform ' + var
e['Distributions'][i]['Name'] = distname
e['Distributions'][i]['Type'] = 'Univariate/Uniform'
minmax = sir.params_prior[var]
e['Distributions'][i]['Minimum'] = minmax[0]
e['Distributions'][i]['Maximum'] = minmax[1]
e['Variables'][i]['Name'] = var
e['Variables'][i]['Prior Distribution'] = distname
if (args.silent):
e['Console Output']['Verbosity'] = 'Silent'
else:
e['Console Output']['Verbosity'] = 'Detailed'
e['File Output'] = tools.fileOutputDefaults(args, '_korali_samples/')
e['File Output']['Frequency'] = 50
e["Store Sample Information"] = True
k = korali.Engine()
k['Conduit']['Type'] = 'Concurrent'
k['Conduit']['Concurrent Jobs'] = args.nThreads
k.run(e)
return e
def trainPolicy(self, policy, env, numIterations):
"""Evaluate `numIterations` updating iterations on the given policy for
the given environment."""
# Define the objective.
def objective(p):
"""Update the policy with given parameters, evalute and return the reward."""
weights = p["Parameters"]
# TODO: Update the network weights with values given by Korali (see overwriteNetworkParams).
# Run env.numEpisodesPerEvaluation episodes and compute the mean total reward.
#
#
#
#
meanTotalReward = 0
p["Evaluation"] = meanTotalReward # Korali v1.0.1.
# p["F(x)"] = meanTotalReward # Korali master branch (?)
# Create Korali and problem objects.
k = korali.Engine()
e = korali.Experiment()
# Configure the problem.
e["Problem"]["Type"] = "Evaluation/Direct/Basic" # Korali v1.0.1.
# e["Problem"]["Type"] = "Optimization/Stochastic" # Korali master branch (?)
e["Problem"]["Objective Function"] = objective
# TODO: Define the problem variables (see getNumNetworkParams).
#
# Don't forget to set all parameter values: initial mean, variance, lower/upper bound!
#
#
#
#
# TODO: Set up CMA-ES.
#
#
#
#
# Run Korali.
k.run(e)
def run_nested_with_termination_criterion(criterion, value):
print("[Korali] Prepare Nested run with Termination Criteria "\
"'{0}'".format(criterion))
e = korali.Experiment()
e["Problem"]["Type"] = "Bayesian/Custom"
e["Problem"]["Likelihood Model"] = evaluateLogLikelihood
e["Distributions"][0]["Name"] = "Uniform 0"
e["Distributions"][0]["Type"] = "Univariate/Uniform"
e["Distributions"][0]["Minimum"] = -10.0
e["Distributions"][0]["Maximum"] = +10.0
e["Variables"][0]["Name"] = "X"
e["Variables"][0]["Prior Distribution"] = "Uniform 0"
e["Solver"]["Type"] = "Sampler/Nested"
e["Solver"]["Number Live Points"] = 1500
e["Solver"]["Batch Size"] = 1
e["Solver"]["Add Live Points"] = True
e["Solver"]["Resampling Method"] = "Box"
e["Solver"]["Termination Criteria"][criterion] = value
e["File Output"]["Enabled"] = False
e["Random Seed"] = 1337
k = korali.Engine()
k.run(e)
if (criterion == "Max Generations"):
assert_value(e["Current Generation"], value)
elif (criterion == "Target Annealing Exponent"):
assert_greatereq(e["Solver"]["Annealing Exponent"], value)
elif (criterion == "Max Effective Sample Size"):
assert_greatereq(e["Solver"]["Effective Sample Size"], value)
else:
print("Termination Criterion not recognized!")
exit(-1)
def run_dea_with_termination_criterion(criterion, value):
print("[Korali] Prepare DEA run with Termination Criteria "\
"'{0}'".format(criterion))
e = korali.Experiment()
e["Problem"]["Type"] = "Optimization"
e["Problem"]["Objective Function"] = evaluateModel
e["Variables"][0]["Name"] = "X"
e["Variables"][0]["Lower Bound"] = +1.0
e["Variables"][0]["Upper Bound"] = +10.0
e["Solver"]["Type"] = "Optimizer/DEA"
e["Solver"]["Population Size"] = 10
e["Solver"]["Termination Criteria"][criterion] = value
e["File Output"]["Enabled"] = False
e["Random Seed"] = 1337
k = korali.Engine()
k.run(e)
if (criterion == "Max Generations"):
assert_value(e["Current Generation"], value)
elif (criterion == "Max Infeasible Resamplings"):
assert_greatereq(e["Solver"]["Infeasible Sample Count"], value)
elif (criterion == "Max Value"):
assert_greatereq(e["Solver"]["Best Ever Value"], value)
elif (criterion == "Min Value Difference Threshold"):
previous = e["Solver"]["Previous Best Ever Value"]
current = e["Solver"]["Best Ever Value"]
assert_smallereq(previous - current, value)
else:
print("Termination Criterion not recognized!")
exit(-1)
def run_tmcmc_with_termination_criterion(criterion, value):
print("[Korali] Prepare DEA run with Termination Criteria "\
"'{0}'".format(criterion))
e = korali.Experiment()
e["Problem"]["Type"] = "Bayesian/Custom"
e["Problem"]["Likelihood Model"] = evaluateLogLikelihood
e["Distributions"][0]["Name"] = "Uniform 0"
e["Distributions"][0]["Type"] = "Univariate/Uniform"
e["Distributions"][0]["Minimum"] = -10.0
e["Distributions"][0]["Maximum"] = +10.0
e["Variables"][0]["Name"] = "X"
e["Variables"][0]["Prior Distribution"] = "Uniform 0"
e["Solver"]["Type"] = "TMCMC"
e["Solver"]["Population Size"] = 5000
e["Solver"]["Covariance Scaling"] = 0.001
e["Solver"]["Termination Criteria"][criterion] = value
e["Random Seed"] = 1337
k = korali.Engine()
k.run(e)
if (criterion == "Max Generations"):
assert_value(e["Current Generation"], value)
elif (criterion == "Target Annealing Exponent"):
assert_greatereq(e["Solver"]["Annealing Exponent"], value)
else:
print("Termination Criterion not recognized!")
exit(-1)
def run_ccmaes(constraint):
print("[Korali] Prepare CMAES run with Termination Criteria "\
"'{0}'".format(constraint))
e = korali.Experiment()
e["Problem"]["Type"] = "Optimization/Constrained"
e["Problem"]["Objective Function"] = evaluateModel
e["Variables"][0]["Name"] = "X"
e["Variables"][0]["Lower Bound"] = -10.0
e["Variables"][0]["Upper Bound"] = +10.0
e["Variables"][1]["Name"] = "Y"
e["Variables"][1]["Lower Bound"] = -10.0
e["Variables"][1]["Upper Bound"] = +10.0
e["Solver"]["Type"] = "CMAES"
e["Solver"]["Population Size"] = 8
e["Solver"]["Viability Population Size"] = 2
e["Solver"]["Termination Criteria"]["Max Generations"] = 100
e["Solver"]["Is Sigma Bounded"] = 1
e["Console Output"]["Verbosity"] = "Detailed"
e["Random Seed"] = 1337
k = korali.Engine()
if (constraint == "None"):
k.run(e)
assert_greatereq(e["Solver"]["Best Ever Value"],-6*1e-10)
elif (constraint == "Inactive"):
e["Problem"]["Constraints"] = [ inactive1, inactive2 ]
k.run(e)
assert_greatereq(e["Solver"]["Best Ever Value"],-1.8*1e-10)
elif (constraint == "Active at Max 1"):
e["Problem"]["Constraints"] = [ activeMax1, activeMax2 ]
k.run(e)
assert_greatereq(e["Solver"]["Best Ever Value"],-4.826824e+00)
elif (constraint == "Active at Max 2"):
e["Problem"]["Constraints"] = [ activeMax1, activeMax2, activeMax3, activeMax4 ]
k.run(e)
assert_greatereq(e["Solver"]["Best Ever Value"],-9.653645e+00)
elif (constraint == "Inactive at Max 1"):
e["Problem"]["Constraints"] = [ inactiveMax1, inactiveMax2 ]
k.run(e)
assert_greatereq(e["Solver"]["Best Ever Value"],-2.19963e-10)
elif (constraint == "Inactive at Max 2"):
e["Problem"]["Constraints"] = [ inactiveMax1, inactiveMax2, inactiveMax3, inactiveMax4 ]
k.run(e)
assert_greatereq(e["Solver"]["Best Ever Value"],-4.626392e-10)
elif (constraint == "Mixed"):
e["Problem"]["Constraints"] = [ activeMax1, activeMax2, activeMax3, activeMax4, inactiveMax1, inactiveMax2, inactiveMax3, inactiveMax4 ]
k.run(e)
assert_greatereq(e["Solver"]["Best Ever Value"],-7.895685e+01)
elif (constraint == "Stress"):
e["Problem"]["Constraints"] = [ activeMax1, activeMax2, activeMax3, activeMax4, inactiveMax1, inactiveMax2, inactiveMax3, inactiveMax4, stress1, stress2, stress3, stress4, stress5, stress6, stress7, stress8 ]
k.run(e)
assert_greatereq(e["Solver"]["Best Ever Value"],-7.895685e+01)
else:
print("Constraint not recognized!")
exit(-1)
def run_phase_2(phase_1_path, phase_2_path):
# ---------------------------------------------------------------------------- #
# ---------------------------------- Setup ----------------------------------- #
# ---------------------------------------------------------------------------- #
e = korali.Experiment()
e["Problem"]["Type"] = "Hierarchical/Psi"
e["Problem"]["Sub Problems"] = phase_1_path
# ---------------------------------------------------------------------------- #
# ------------------------------- Conditionals ------------------------------- #
# ---------------------------------------------------------------------------- #
# SIR nbin has 3 parameters: beta, gamma, [r]
# Parameters of the conditionnal
e["Variables"][0]["Name"] = "Psi 0" # R0 mean
e["Variables"][1]["Name"] = "Psi 1" # R0 std
e["Variables"][2]["Name"] = "Psi 2" # gamma mean
e["Variables"][3]["Name"] = "Psi 3" # gamma std
e["Variables"][4]["Name"] = "Psi 4" # delta mean
e["Variables"][5]["Name"] = "Psi 5" # delta std
e["Variables"][6]["Name"] = "Psi 6" # td mean
e["Variables"][7]["Name"] = "Psi 7" # td std
e["Variables"][8]["Name"] = "Psi 8" # [r] mean
e["Variables"][9]["Name"] = "Psi 9" # [r] std
e["Variables"][0]["Prior Distribution"] = "Uniform 0" # R0 mean
e["Variables"][1]["Prior Distribution"] = "Uniform 1" # R0 std
e["Variables"][2]["Prior Distribution"] = "Uniform 2" # gamma mean
e["Variables"][3]["Prior Distribution"] = "Uniform 3" # gamma std
e["Variables"][4]["Prior Distribution"] = "Uniform 4" # delta mean
e["Variables"][5]["Prior Distribution"] = "Uniform 5" # delta std
e["Variables"][6]["Prior Distribution"] = "Uniform 6" # td mean
e["Variables"][7]["Prior Distribution"] = "Uniform 7" # td std
e["Variables"][8]["Prior Distribution"] = "Uniform 8" # [r] mean
e["Variables"][9]["Prior Distribution"] = "Uniform 9" # [r] std
# Contidionals
e["Problem"]["Conditional Priors"] = [
"Conditional R0", "Conditional gamma", "Conditional delta",
"Conditional td", "Conditional [r]"
]
e["Distributions"][0]["Name"] = "Conditional R0"
e["Distributions"][0]["Type"] = "Univariate/Normal"
e["Distributions"][0]["Mean"] = "Psi 0"
e["Distributions"][0]["Standard Deviation"] = "Psi 1"
e["Distributions"][1]["Name"] = "Conditional gamma"
e["Distributions"][1]["Type"] = "Univariate/Normal"
e["Distributions"][1]["Mean"] = "Psi 2"
e["Distributions"][1]["Standard Deviation"] = "Psi 3"
e["Distributions"][2]["Name"] = "Conditional delta"
e["Distributions"][2]["Type"] = "Univariate/Normal"
e["Distributions"][2]["Mean"] = "Psi 4"
e["Distributions"][2]["Standard Deviation"] = "Psi 5"
e["Distributions"][3]["Name"] = "Conditional td"
e["Distributions"][3]["Type"] = "Univariate/Normal"
e["Distributions"][3]["Mean"] = "Psi 6"
e["Distributions"][3]["Standard Deviation"] = "Psi 7"
e["Distributions"][4]["Name"] = "Conditional [r]"
e["Distributions"][4]["Type"] = "Univariate/Normal"
e["Distributions"][4]["Mean"] = "Psi 8"
e["Distributions"][4]["Standard Deviation"] = "Psi 9"
# ---------------------------------------------------------------------------- #
# ---------------------------------- Priors ---------------------------------- #
# ---------------------------------------------------------------------------- #
e["Distributions"][5]["Name"] = "Uniform 0" # R0 mean
e["Distributions"][5]["Type"] = "Univariate/Uniform"
e["Distributions"][5]["Minimum"] = 0.5
e["Distributions"][5]["Maximum"] = 1.5
e["Distributions"][6]["Name"] = "Uniform 1" # R0 std
e["Distributions"][6]["Type"] = "Univariate/Uniform"
e["Distributions"][6]["Minimum"] = 0.0
e["Distributions"][6]["Maximum"] = 1
e["Distributions"][7]["Name"] = "Uniform 2" # gamma mean
e["Distributions"][7]["Type"] = "Univariate/Uniform"
e["Distributions"][7]["Minimum"] = 0.0
e["Distributions"][7]["Maximum"] = 0.5
e["Distributions"][8]["Name"] = "Uniform 3" # gamma std
e["Distributions"][8]["Type"] = "Univariate/Uniform"
e["Distributions"][8]["Minimum"] = 0.0
e["Distributions"][8]["Maximum"] = 0.1
e["Distributions"][9]["Name"] = "Uniform 4" # delta mean
e["Distributions"][9]["Type"] = "Univariate/Uniform"
e["Distributions"][9]["Minimum"] = 0.0
e["Distributions"][9]["Maximum"] = 1.0
e["Distributions"][10]["Name"] = "Uniform 5" # delta std
e["Distributions"][10]["Type"] = "Univariate/Uniform"
e["Distributions"][10]["Minimum"] = 0.0
e["Distributions"][10]["Maximum"] = 0.5
e["Distributions"][11]["Name"] = "Uniform 6" # td mean
e["Distributions"][11]["Type"] = "Univariate/Uniform"
e["Distributions"][11]["Minimum"] = 15.
e["Distributions"][11]["Maximum"] = 30.
e["Distributions"][12]["Name"] = "Uniform 7" # td std
e["Distributions"][12]["Type"] = "Univariate/Uniform"
e["Distributions"][12]["Minimum"] = 0.0
e["Distributions"][12]["Maximum"] = 4.0
e["Distributions"][13]["Name"] = "Uniform 8" # [r] mean
e["Distributions"][13]["Type"] = "Univariate/Uniform"
e["Distributions"][13]["Minimum"] = 2.0
e["Distributions"][13]["Maximum"] = 10.0
e["Distributions"][14]["Name"] = "Uniform 9" # [r] std
e["Distributions"][14]["Type"] = "Univariate/Uniform"
e["Distributions"][14]["Minimum"] = 0.0
e["Distributions"][14]["Maximum"] = 5.
# ---------------------------------------------------------------------------- #
# ---------------------------------- Solver ---------------------------------- #
# ---------------------------------------------------------------------------- #
e["Solver"]["Type"] = "TMCMC"
e["Solver"]["Population Size"] = 2000
e["Solver"]["Default Burn In"] = 3
e["Solver"]["Target Coefficient Of Variation"] = 0.6
e["Solver"]["Covariance Scaling"] = 0.01
e["Console Output"]["Verbosity"] = "Detailed"
e["File Output"]["Path"] = phase_2_path
# Starting Korali's Engine and running experiment
k = korali.Engine()
k["Conduit"]["Type"] = "Concurrent"
k["Conduit"]["Concurrent Jobs"] = 12
k.run(e)
def sampleLatent(self, kSample):
# /*
# * probability to sample from:
# * p(d, z | theta) * p(theta) -- that's the (log-)posterior
# * - use a "Sampling" problem, with our log-posterior as "Likelihood Model" , but with the current values for theta inserted.
# */
hyperparameters = kSample["Hyperparameters"]
numberSamples = kSample["Number Samples"]
if (kSample["Number Of Latent Variables"] != self.numberLatent):
raise ValueError("Implementation error, number of latent variables at initialization does not fit to what was passed as variable")
# * Create one sampling experiment to sample all latent variables. After all, the latent vars are correlated /
# have a joint distribution .
k = korali.Engine()
e = korali.Experiment()
def probability_function(s):
latent_vars = s["Parameters"]
hparams = hyperparameters
if (len(latent_vars) != self.numberLatent):
raise ValueError("Implementation error, latent variable vector had wrong size")
if (len(hparams) != self.numberHyperparameters):
raise ValueError("Implementation error, hyperparameter vector had wrong size")
s["Latent Variables"] = latent_vars
s["Hyperparameters"] = hparams
self.S_func(s)
self.zeta_func(s)
self.phi_func(s)
# -> Assume these are set: sample["S"], sample["zeta"] and sample["phi"]
_zetaValue = s["zeta"]
_sValues = s["S"]
_phiValues = s["phi"]
logP_of_x = - _zetaValue + np.inner(_sValues, _phiValues)
s["P(x)"] = logP_of_x
# * * * * * * * * * * * * * * * probability_function end
# * Based on tutorial a2-sampling
e["Problem"]["Type"] = "Sampling"
e["Problem"]["Probability Function"] = lambda s : probability_function(s)
for i in range(self.numberLatent):
# Defining problem's variables
varName = "latent_" + str(i)
e["Variables"][i]["Name"] = varName
e["Variables"][i]["Initial Mean"] = self.previousSampleMeans[i]
e["Variables"][i]["Initial Standard Deviation"] = 2.0
# Configuring the MCMC sampler parameters
e["Solver"]["Type"] = "MCMC"
e["Solver"]["Burn In"] = 400
e["Solver"]["Termination Criteria"]["Max Samples"] = 1000
# Configuring output settings
e["File Output"]["Frequency"] = 0
e["Console Output"]["Frequency"] = 0
e["Console Output"]["Verbosity"] = "Silent"
#k["Conduit"]["Type"] = "Concurrent"
#k["Conduit"]["Concurrent Jobs"] = 2
k.run(e)
db = e["Solver"]["Sample Database"]
samples = db[-numberSamples : ] # take samples from the end
kSample["Samples"] = samples
# set new "previous sample means"
for i in range(self.numberLatent):
self.previousSampleMeans[i] = np.sum(np.array(samples)[:, i]) / float(numberSamples)
def main():
# Initialize the distribution
distrib1 = ExampleDistribution1()
distrib1_S = lambda s: distrib1.S(s)
distrib1_zeta = lambda s: distrib1.zeta(s)
distrib1_phi = lambda s: distrib1.phi(s)
d1_numberLatentVars = distrib1._p.nDimensions
d1_numberHyperparams = 1
initialSigma = 4
d1_initialLatentValues = np.random.normal(0, 0.5, (d1_numberLatentVars, ))
d1_initialHyperparams = np.array([initialSigma])
gaussian_sampler_obj = MCMCLatentSampler(
d1_numberLatentVars, d1_numberHyperparams, d1_initialLatentValues,
d1_initialHyperparams, distrib1_zeta, distrib1_S, distrib1_phi)
k = korali.Engine()
e = korali.Experiment()
e["Problem"]["Type"] = "Bayesian/Latent/ExponentialLatent"
e["Problem"]["S Of Likelihood Model"] = distrib1_S
e["Problem"]["Zeta Of Likelihood Model"] = distrib1_zeta
e["Problem"]["Phi Of Likelihood Model"] = distrib1_phi
e["Problem"]["S Dimension"] = 1
e["Problem"][
"Latent Variable Sampler"] = lambda sample: gaussian_sampler_obj.sampleLatent(
sample)
e["Solver"]["Type"] = "SAEM"
e["Solver"]["Number Samples Per Step"] = 10
e["Solver"]["Termination Criteria"]["Max Generations"] = 40
e["Variables"][0]["Name"] = "sigma"
e["Variables"][0]["Bayesian Type"] = "Hyperparameter"
e["Variables"][0]["Prior Distribution"] = "Uniform 0"
e["Variables"][0]["Initial Value"] = 5.0 # Initial hyperparameter value
e["Variables"][0]["Upper Bound"] = 15
e["Variables"][0]["Lower Bound"] = 0
# define a variable for each coordinate of mu
for i in range(distrib1._p.nDimensions):
e["Variables"][1 + i]["Name"] = "mu" + str(i)
e["Variables"][1 + i]["Bayesian Type"] = "Latent"
e["Variables"][1 + i]["Prior Distribution"] = "Uniform 1"
e["Variables"][1 + i]["Initial Value"] = 0
e["Distributions"][0]["Name"] = "Uniform 0"
e["Distributions"][0]["Type"] = "Univariate/Uniform"
e["Distributions"][0]["Minimum"] = 0
e["Distributions"][0]["Maximum"] = 5
e["Distributions"][1]["Name"] = "Uniform 1"
e["Distributions"][1]["Type"] = "Univariate/Uniform"
e["Distributions"][1]["Minimum"] = -5
e["Distributions"][1]["Maximum"] = 5
# Configuring results path
e["File Output"]["Path"] = '_korali_result_saem'
e["Random Seed"] = 0xC0FFEE
#k["Conduit"]["Type"] = "Concurrent"
#k["Conduit"]["Concurrent Jobs"] = 4
#k["Conduit"]["Type"] = "Distributed"
k.run(e)
def main():
# Initialize the distribution
distrib2 = ExampleDistribution2()
distrib2_S = lambda s: distrib2.S(s)
distrib2_zeta = lambda s: distrib2.zeta(s)
distrib2_phi = lambda s: distrib2.phi(s)
d2_numberLatentVars = distrib2._p.nPoints # one for each datapoint
d2_numberHyperparams = distrib2._p.nDimensions * distrib2._p.nClusters + 1
d2_initialLatentValues = np.random.normal(0.5, 0.5, (d2_numberLatentVars))
d2_initialHyperparams = np.random.normal(0, 1, (d2_numberHyperparams))
gaussian_sampler_obj = MultimodalGaussianSampler(distrib2._p.points,
distrib2._p.nDimensions,
distrib2._p.nClusters)
multimodal_gaussian_sampler = lambda s: gaussian_sampler_obj.sampleLatent(s
)
k = korali.Engine()
e = korali.Experiment()
e["Problem"]["Type"] = "Bayesian/Latent/ExponentialLatent"
e["Problem"]["S Of Likelihood Model"] = distrib2_S
e["Problem"]["Zeta Of Likelihood Model"] = distrib2_zeta
e["Problem"]["Phi Of Likelihood Model"] = distrib2_phi
e["Problem"]["S Dimension"] = distrib2.sufficientStatisticsDimension
e["Problem"]["Latent Variable Sampler"] = multimodal_gaussian_sampler
e["Solver"]["Type"] = "SAEM"
e["Solver"]["Number Samples Per Step"] = 100
e["Solver"]["Termination Criteria"]["Max Generations"] = 50
e["Distributions"][0]["Name"] = "Uniform 0"
e["Distributions"][0]["Type"] = "Univariate/Uniform"
e["Distributions"][0]["Minimum"] = 0
e["Distributions"][0]["Maximum"] = 5
e["Distributions"][1]["Name"] = "Uniform 1"
e["Distributions"][1]["Type"] = "Univariate/Uniform"
e["Distributions"][1]["Minimum"] = -5
e["Distributions"][1]["Maximum"] = 5
e["Distributions"][2]["Name"] = "Multinomial 2"
e["Distributions"][2]["Type"] = "Specific/Multinomial"
# Define which hyperparameters we use (all mu, and sigma)
variable_counter = 0
for cluster_idx in range(distrib2._p.nClusters):
for dim in range(distrib2._p.nDimensions):
e["Variables"][variable_counter]["Name"] = "mu_" + str(
cluster_idx) + "_" + str(dim)
e["Variables"][variable_counter][
"Bayesian Type"] = "Hyperparameter"
e["Variables"][variable_counter][
"Prior Distribution"] = "Uniform 1" # not used (?) but required
e["Variables"][variable_counter][
"Initial Value"] = d2_initialHyperparams[variable_counter]
e["Variables"][variable_counter]["Upper Bound"] = e[
"Distributions"][1]["Maximum"]
e["Variables"][variable_counter]["Lower Bound"] = e[
"Distributions"][1]["Minimum"]
variable_counter += 1
e["Variables"][variable_counter]["Name"] = "sigma"
e["Variables"][variable_counter]["Bayesian Type"] = "Hyperparameter"
e["Variables"][variable_counter]["Prior Distribution"] = "Uniform 0"
e["Variables"][variable_counter]["Initial Value"] = 2.0
e["Variables"][variable_counter]["Upper Bound"] = 5
e["Variables"][variable_counter]["Lower Bound"] = 0
variable_counter += 1
# Latent variables
latent_counter = 0
for cluster_idx in range(distrib2._p.nPoints):
e["Variables"][variable_counter]["Name"] = "cluster_assignment_" + str(
latent_counter)
e["Variables"][variable_counter]["Bayesian Type"] = "Latent"
e["Variables"][variable_counter][
"Prior Distribution"] = "Multinomial 2"
e["Variables"][variable_counter][
"Initial Value"] = d2_initialLatentValues[latent_counter]
variable_counter += 1
latent_counter += 1
# Configuring results path
e["File Output"]["Path"] = '_korali_result_saem-mixture'
e["File Output"]["Frequency"] = 50
e["Console Output"]["Frequency"] = 10
e["Console Output"]["Verbosity"] = "Detailed"
e["Random Seed"] = 0xC0FFEE
#k["Conduit"]["Type"] = "Concurrent"
#k["Conduit"]["Concurrent Jobs"] = 4
k.run(e)
def propagate(self, nPropagate=1000):
if not self.has_been_called['sample'] and not self.has_been_called[
'optimize']:
abort('[Error] Sample or Optimize before propagation')
return
self.e = korali.Experiment()
self.nPropagate = nPropagate
self.e['Problem']['Type'] = 'Propagation'
self.e['Problem'][
'Execution Model'] = self.computational_model_propagate
for k in range(self.nParameters):
self.e['Variables'][k]['Name'] = self.parameters[k]['Name']
self.e['Variables'][k]['Precomputed Values'] = self.parameters[k][
'Values'].tolist()
self.e['Solver']['Type'] = 'Executor'
self.set_korali_output_files(self.saveInfo['korali propagation'])
if (self.silent): self.e['Console Output']['Verbosity'] = 'Silent'
self.e['Store Sample Information'] = True
k = korali.Engine()
k.run(self.e)
propagate_idx = random.sample(range(self.nSamples), nPropagate)
Nv = self.e['Samples'][0]['Saved Results']['Number of Variables']
Nt = self.e['Samples'][0]['Saved Results']['Length of Variables']
varNames = []
for k in range(Nv):
varNames.append(
self.e['Samples'][0]['Saved Results']['Variables'][k]['Name'])
printlog('Copy variables from Korali to Epidemics...')
self.propagatedVariables = {}
for i, x in enumerate(varNames):
self.propagatedVariables[x] = np.zeros((nPropagate, Nt))
for k, idx in enumerate(propagate_idx):
self.propagatedVariables[x][k] = np.asarray(
self.e['Samples'][idx]['Saved Results']['Variables'][i]
['Values'])
varNames = []
if (self.likelihoodModel == 'Normal'
or self.likelihoodModel == 'Positive Normal'):
if self.useInfections:
varNames.append('Standard Deviation Daily Incidence')
if self.useDeaths:
varNames.append('Standard Deviation Daily Deaths')
elif (self.likelihoodModel == 'StudentT'
or self.likelihoodModel == 'Positive StudentT'):
if self.useInfections:
varNames.append('Degrees Of Freedom Daily Incidence')
if self.useDeaths:
varNames.append('Degrees Of Freedom Daily Deaths')
elif (self.likelihoodModel == 'Poisson'):
pass
elif (self.likelihoodModel == 'Geometric'):
pass
elif (self.likelihoodModel == 'Negative Binomial'):
if self.useInfections:
varNames.append('Dispersion Daily Incidence')
if self.useDeaths:
varNames.append('Dispersion Daily Deaths')
else:
abort('Likelihood not found in propagate.')
for varName in varNames:
self.propagatedVariables[varName] = np.zeros((nPropagate, Nt))
for k in range(nPropagate):
self.propagatedVariables[varName][k] = np.asarray(
self.e['Samples'][k]['Saved Results'][varName])
printlog('Done copying variables.')
# TODO clear variable?
self.e = korali.Experiment()
self.has_been_called['propagate'] = True
def sample_knested(self,
nLiveSamples=1500,
freq=1500,
maxiter=1e9,
dlogz=0.1,
batch=1):
self.e = korali.Experiment()
self.e['Problem']['Type'] = 'Bayesian/Reference'
self.e['Problem']['Likelihood Model'] = self.likelihoodModel
self.e['Problem']['Reference Data'] = list(
map(float, self.data['Model']['y-data']))
self.e['Problem']['Computational Model'] = self.computational_model
self.e["Solver"]["Type"] = "Sampler/Nested"
self.e["Solver"]["Resampling Method"] = "Multi Ellipse"
self.e["Solver"]["Number Live Points"] = nLiveSamples
self.e["Solver"]["Proposal Update Frequency"] = freq
self.e["Solver"]["Ellipsoidal Scaling"] = 1.10
self.e["Solver"]["Batch Size"] = batch
self.e["Solver"]["Termination Criteria"]["Max Generations"] = maxiter
self.e["Solver"]["Termination Criteria"][
"Min Log Evidence Delta"] = dlogz
self.e["Solver"]["Termination Criteria"][
"Max Effective Sample Size"] = 25000
js = self.get_variables_and_distributions()
self.set_variables_and_distributions(js)
self.set_korali_output_files(self.saveInfo['korali samples'], maxiter)
self.e['Console Output']['Verbosity'] = 'Detailed'
self.e["Console Output"]["Frequency"] = 100
if (self.silent): self.e['Console Output']['Verbosity'] = 'Silent'
k = korali.Engine()
k['Conduit']['Type'] = 'Concurrent'
k['Conduit']['Concurrent Jobs'] = self.nThreads
k.run(self.e)
js = {}
js['Log Evidence'] = self.e['Solver']['LogEvidence']
js['Error'] = self.e['Solver']['LogEvidence Var']
printlog(f"Log Evidence = {js['Log Evidence']}")
printlog(f"Variance = {js['Error']}")
save_file(js,
self.saveInfo['evidence'],
'Log Evidence',
fileType='json')
printlog('Copy variables from Korali to Epidemics...')
myDatabase = self.e['Results']['Posterior Sample Database']
self.nSamples, _ = np.shape(myDatabase)
self.parameters = []
for j in range(self.nParameters):
self.parameters.append({})
self.parameters[j]['Name'] = self.e['Variables'][j]['Name']
self.parameters[j]['Values'] = np.asarray(
[myDatabase[k][j] for k in range(self.nSamples)])
self.has_been_called['sample'] = True
self.has_been_called['propagate'] = False
printlog('Done copying variables.')
e["Problem"]["Type"] = "Optimization/Stochastic" e["Problem"]["Objective Function"] = model # Creating 10 variables and setting their CMA-ES bounds for i in range(10) : e["Variables"][i]["Name"] = "X" + str(i) e["Variables"][i]["Initial Mean"] = 1.0 e["Variables"][i]["Lower Bound"] = -19.0 e["Variables"][i]["Upper Bound"] = +21.0 # We set some of them as discrete. e["Variables"][0]["Granularity"] = 1.0 e["Variables"][1]["Granularity"] = 1.0 e["Variables"][3]["Granularity"] = 1.0 e["Variables"][6]["Granularity"] = 1.0 # Configuring CMA-ES parameters e["Solver"]["Type"] = "CMAES" e["Solver"]["Population Size"] = 8 e["Solver"]["Termination Criteria"]["Min Value Difference Threshold"] = 1e-9 e["Solver"]["Termination Criteria"]["Max Generations"] = 5000 # Configuring output settings e["File Output"]["Frequency"] = 50 e["Console Output"]["Frequency"] = 50 # Starting Korali's Engine and running experiment k = korali.Engine() k.run(e)
def run_phase_2(phase_1_paths, phase_2_path, variables):
# Problem
e = korali.Experiment()
e["Problem"]["Type"] = "Hierarchical/Psi"
for i in range(len(phase_1_paths)):
print(phase_1_paths[i])
subProblem = korali.Experiment()
subProblem.loadState(phase_1_paths[i])
e["Problem"]["Sub Experiments"][i] = subProblem
# Define conditionals
e["Problem"]["Conditional Priors"] = [
"Conditional " + str(var['name']) for var in variables
]
for i, var in enumerate(variables):
e["Distributions"][i]["Name"] = "Conditional " + str(var['name'])
if var['cond_type'] == 'Normal':
e["Distributions"][i]["Type"] = "Univariate/Normal"
e["Distributions"][i]["Mean"] = var['name'] + ' Mean'
e["Distributions"][i]["Standard Deviation"] = var['name'] + ' Std'
else:
print('not implemented yet')
# Define hyperparameters
distrib_counter = len(variables)
i = 0
for var in variables:
cond_params = [
ele for ele in list(var.keys())
if ele not in ['name', 'cond_type']
]
for cond_param in cond_params:
var_name = var['name'] + ' ' + cond_param
e["Variables"][i]["Name"] = var_name
e["Variables"][i]["Prior Distribution"] = 'Uniform ' + var_name
j = distrib_counter + i # offset to take into account the prior distributions
e["Distributions"][j]["Name"] = 'Uniform ' + var_name
e["Distributions"][j]["Type"] = "Univariate/Uniform"
e["Distributions"][j]["Minimum"] = var[cond_param][0]
e["Distributions"][j]["Maximum"] = var[cond_param][1]
i += 1
#Solver
# e["Solver"]["Type"] = "Sampler/TMCMC"
# e["Solver"]["Population Size"] = 2000
# e["Solver"]["Default Burn In"] = 3;
# e["Solver"]["Target Coefficient Of Variation"] = 0.6
# e["Solver"]["Covariance Scaling"] = 0.01
e["Solver"]["Type"] = "Sampler/Nested"
e["Solver"]["Resampling Method"] = "Multi Ellipse"
e["Solver"]["Number Live Points"] = 1500
e["Solver"]["Proposal Update Frequency"] = 1500
e["Solver"]["Ellipsoidal Scaling"] = 1.10
batch = 12
e["Solver"]["Batch Size"] = batch
e["Solver"]["Termination Criteria"]["Max Generations"] = 1e9
e["Solver"]["Termination Criteria"]["Min Log Evidence Delta"] = 0.1
e["Solver"]["Termination Criteria"]["Max Effective Sample Size"] = 25000
e["Console Output"]["Verbosity"] = "Detailed"
e["File Output"]["Path"] = phase_2_path
e["File Output"]["Frequency"] = 5000
create_folder(phase_2_path)
# Starting Korali's Engine and running experiment
k = korali.Engine()
# k["Conduit"]["Type"] = "Concurrent"
# k["Conduit"]["Concurrent Jobs"] = batch
# print('Launching Korali')
k.run(e)
