from uqpylab import sessions
import scipy.io

# Start the session
mySession = sessions.cloud()
# (Optional) Get a convenient handle to the command line interface
uq = mySession.cli
# Reset the session
mySession.reset()

Processing .

.

 done!

 uqpylab.sessions :: INFO     :: This is UQ[py]Lab, version 1.00, running on https://uqcloud.ethz.ch. 
                                 UQ[py]Lab is free software, published under the open source BSD 3-clause license.
                                 To request special permissions, please contact:
                                  - Stefano Marelli (marelli@ibk.baug.ethz.ch).
                                 A new session (aea9f728d6f544918e1782206413759b) started.

 uqpylab.sessions :: INFO     :: Reset successful.

uq.rng(100, 'twister');

file_location = './Bayesian_Data'
mat = scipy.io.loadmat('{}/{}'.format(file_location,'uq_Example_BayesianHydro.mat'))
Data = mat['Data'].tolist()
ModelSetup = mat['ModelSetup']
# store contents of ModelSetup in non-numpy dictionary
ModelSetup = {name: ModelSetup[name][0,0].tolist() for name in ('E','P','F','MaxT')}

ModelOpts = {'Type': 'Model', 
             'ModelFun':'HYMOD.model',
             'Parameters': ModelSetup
            }
myForwardModel = uq.createModel(ModelOpts)

PriorOpts = {
    'Name': 'Prior distribution on HYMOD parameters',
    'Marginals': [
        {
            'Name': 'cmax', # maximum interception
            'Type': 'Uniform',
            'Parameters': [1, 500] # (mm)
        },
        {
            'Name': 'bexp', # soil water storage capacity
            'Type': 'Uniform',
            'Parameters': [0.1, 2] # (-)
        },
        {
            'Name': 'alpha', # maximum percolation rate
            'Type': 'Uniform',
            'Parameters': [0.1, 0.99] # (-)
        },
        {
            'Name': 'rs', # recession constant slow-flow
            'Type': 'Uniform',
            'Parameters': [0, 0.1] # (-)
        },
        {
            'Name': 'rq', # recession constant fast-flow
            'Type': 'Uniform',
            'Parameters': [0.1, 0.99] # (-)
        }
    ]
}
    
myPriorDist = uq.createInput(PriorOpts)

myData = {
    'y': Data, # (m)
    'Name': 'Leaf river discharge'
}

SigmaOpts = {
    'Marginals': {
        'Name': 'sigma2',
        'Type': 'Uniform',
        'Parameters': [0, 300]
    }
}

mySigmaDist = uq.createInput(SigmaOpts)

DiscrepancyOpts = {
    'Type': 'Gaussian',
    'Prior': mySigmaDist['Name']
}

Solver = {
    'Type': 'MCMC',
    'MCMC': {
        'Sampler': 'AM',
        'NChains': 100,
        'Steps': 200
    }
}

BayesOpts = {
    'Type': 'Inversion',
    'Name': 'Bayesian model',
    'Prior': myPriorDist['Name'],
    'Data': myData,
    'Discrepancy': DiscrepancyOpts,
    'Solver': Solver
}

myBayesianAnalysis = uq.createAnalysis(BayesOpts)

 uqpylab.sessions :: INFO     :: Received intermediate compute request, function: HYMOD.model.

 uqpylab.sessions :: INFO     :: Carrying out local computation...

 uqpylab.sessions :: INFO     :: Local computation complete.

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((100, 731))...

 uqpylab.sessions :: INFO     :: Intermediate compute results sent.

 uqpylab.sessions :: INFO     :: Received intermediate compute request, function: HYMOD.model.

 uqpylab.sessions :: INFO     :: Carrying out local computation...

 uqpylab.sessions :: INFO     :: Local computation complete.

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((70, 731))...

 uqpylab.sessions :: INFO     :: Intermediate compute results sent.

uq.print(myBayesianAnalysis)

%----------------------- Inversion output -----------------------%
   Number of calibrated model parameters:         5
   Number of non-calibrated model parameters:     0

   Number of calibrated discrepancy parameters:   1

%------------------- Data and Discrepancy
%  Data-/Discrepancy group 1:
   Number of independent observations:            1

   Discrepancy:
      Type:                                       Gaussian
      Discrepancy family:                         Scalar
      Discrepancy parameters known:               No

   Associated outputs:
      Model 1: 
         Output dimensions:                       1
                                                  to
                                                  731


%------------------- Solver
   Solution method:                               MCMC

   Algorithm:                                     AM
   Duration (HH:MM:SS):                           00:04:37
   Number of sample points:                       2.00e+04

%------------------- Posterior Marginals
-------------------------------------------------------------------
| Parameter | Mean    | Std   | (0.025-0.97) Quant. | Type        |
-------------------------------------------------------------------
| cmax      | 3.9e+02 | 56    | (2.6e+02 - 4.8e+02) | Model       |
| bexp      | 0.31    | 0.34  | (0.11 - 1.5)        | Model       |
| alpha     | 0.78    | 0.13  | (0.47 - 0.98)       | Model       |
| rs        | 0.053   | 0.031 | (0.00098 - 0.098)   | Model       |
| rq        | 0.47    | 0.026 | (0.41 - 0.52)       | Model       |
| sigma2    | 2.6e+02 | 31    | (1.9e+02 - 3e+02)   | Discrepancy |
-------------------------------------------------------------------

%------------------- Point estimate
----------------------------------------
| Parameter | Mean    | Parameter Type |
----------------------------------------
| cmax      | 3.9e+02 | Model          |
| bexp      | 0.31    | Model          |
| alpha     | 0.78    | Model          |
| rs        | 0.053   | Model          |
| rq        | 0.47    | Model          |
| sigma2    | 2.6e+02 | Discrepancy    |
----------------------------------------

%------------------- Correlation matrix (model parameters)
---------------------------------------------------------
|       |  cmax      bexp     alpha    rs       rq      |
---------------------------------------------------------
| cmax  |  1         0.26     0.26     0.21     -0.072  |
| bexp  |  0.26      1        -0.15    -0.25    -0.35   |
| alpha |  0.26      -0.15    1        -0.22    -0.35   |
| rs    |  0.21      -0.25    -0.22    1        0.19    |
| rq    |  -0.072    -0.35    -0.35    0.19     1       |
---------------------------------------------------------

uq.display(myBayesianAnalysis);

myBayesianAnalysis = uq.postProcessInversion(myBayesianAnalysis, 'burnIn', 0.75)

 uqpylab.sessions :: INFO     :: Received intermediate compute request, function: HYMOD.model.

 uqpylab.sessions :: INFO     :: Carrying out local computation...

 uqpylab.sessions :: INFO     :: Local computation complete.

 uqpylab.sessions :: INFO     :: Starting transmission of intermediate compute results ((1, 731))...

 uqpylab.sessions :: INFO     :: Intermediate compute results sent.

uq.display(myBayesianAnalysis, scatterplot='all');

mySession.quit()

 uqpylab.sessions :: INFO     :: Session aea9f728d6f544918e1782206413759b terminated.

True

INVERSION: HYDROLOGICAL MODEL CALIBRATION¶

Package imports¶

Start a remote UQCloud session¶

Set the random seed for reproducibility¶

Forward model¶

Prior distribution of the model parameters¶

Measurement data¶

Discrepancy model¶

Bayesian analysis¶

Solver options¶

Posterior sample generation¶

Posterior sample post-processing¶

Terminate the remote UQCloud session¶