In [4]:
Mads.plotmadsproblem(md, keyword="all_wells")
Import Mads
import Mads
┌ Info: Precompiling Mads [d6bdc55b-bd94-5012-933c-1f73fc2ee992] └ @ Base loading.jl:1317
Mads: Model Analysis & Decision Support ==== ___ ____ ____ ____ ______ / \ / \ / | | \ / __ \ | \ / | / | | \ / / \__\ | |\ \/ /| | / | | \ | | | | \ / | | / /| | | |\ \ \ \______. | | \__/ | | / / | | | | \ \ \_______ \ | | | | / / | | | | \ \ \ \ | | | | / /===| | | |___\ \ __. | | | | | | / / | | | \ \ \______/ / |__| |__| /__/ |___| |____________\ \__________/ MADS is an integrated high-performance computational framework for data- and model-based analyses. MADS can perform: Sensitivity Analysis, Parameter Estimation, Model Inversion and Calibration, Uncertainty Quantification, Model Selection and Model Averaging, Model Reduction and Surrogate Modeling, Machine Learning, Decision Analysis and Support.
WARNING: Method definition getparamsmin(Base.AbstractDict{K, V} where V where K) in module Mads at /Users/vvv/.julia/dev/Mads/src/MadsParameters.jl:148 overwritten at /Users/vvv/.julia/dev/Mads/src/MadsParameters.jl:170.
** incremental compilation may be fatally broken for this module **
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Change the working directory
cd(joinpath(Mads.madsdir, "examples", "contamination"))
Load Mads input file
md = Mads.loadmadsfile("w01.mads")
Dict{String, Any} with 7 entries:
"Grid" => Dict{Any, Any}("zmax"=>50, "time"=>50, "xcount"=>33, "zcoun…
"Sources" => Dict{Any, Any}[Dict("box"=>Dict{Any, Any}("dz"=>Dict{Any, A…
"Parameters" => OrderedCollections.OrderedDict{String, OrderedCollections.O…
"Wells" => OrderedCollections.OrderedDict{String, Any}("w1a"=>Dict{Any…
"Time" => Dict{Any, Any}("step"=>1, "start"=>1, "end"=>50)
"Observations" => OrderedCollections.OrderedDict{Any, Any}("w1a_1"=>OrderedCo…
"Filename" => "w01.mads"
Generate a plot of the loaded problem showing the well locations and the location of the contaminant source:
Mads.plotmadsproblem(md, keyword="all_wells")
There are 20 monitoring wells.
Each well has 2 measurement ports: shallow (3 m below the water table labeled a) and deep (33 m below the water table labeled b).
Contaminant concentrations are observed for 50 years at each well.
The contaminant transport is solved using the Anasol package in Mads.
Analysis of the data from only 2 monitoring locations: w13a and w20a.
Mads.allwellsoff!(md) # turn off all wells
Mads.wellon!(md, "w13a") # use well w13a
Mads.wellon!(md, "w20a") # use well w20a
OrderedCollections.OrderedDict{Any, Any} with 100 entries:
"w13a_1" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_2" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_3" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_4" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_5" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_6" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_7" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_8" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_9" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_10" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_11" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_12" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_13" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_14" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_15" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_16" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_17" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_18" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_19" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_20" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_21" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_22" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_23" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_24" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
"w13a_25" => OrderedCollections.OrderedDict{Any, Any}("well"=>"w13a", "time"=…
⋮ => ⋮
Generate a plot of the updated problem showing the 2 well locations applied in the analyses as well as the location of the contaminant source:
Mads.plotmadsproblem(md; keyword="w13a_w20a")
Plot initial estimates of the contamiant concentrations at the 2 monitoring wells based on the initial model parameters:
Mads.plotmatches(md, "w13a"; display=true)
Mads.plotmatches(md, "w20a"; display=true)
Execute model calibration based on the concentrations observed in the two monitoring wells:
calib_param, calib_results = Mads.calibrate(md)
(OrderedCollections.OrderedDict("n" => 0.1, "rf" => 1.0, "lambda" => 0.0, "theta" => 0.0, "vx" => 31.059669248076222, "vy" => 0.0, "vz" => 0.0, "ax" => 70.0, "ay" => 15.0, "az" => 0.3…), OptimBase.MultivariateOptimizationResults{LsqFit.LevenbergMarquardt, Float64, 1}(LsqFit.LevenbergMarquardt(), [0.740931532960472, -0.20135792079033074, -0.44291104407363896], [0.6737086338839451, 0.007322888567510982, -0.34261232076929443], 41650.46179056277, 13, false, true, 0.0001, 0.0, false, 0.001, 0.0, false, 1.0e-6, 0.0, false, Iter Function value Gradient norm
------ -------------- --------------
, 170, 13, 0))
Compute forward model predictions based on the calibrated model parameters:
calib_predictions = Mads.forward(md, calib_param)
OrderedCollections.OrderedDict{Any, Float64} with 100 entries:
"w13a_1" => 0.0
"w13a_2" => 0.0
"w13a_3" => 0.0
"w13a_4" => 0.0
"w13a_5" => 0.0
"w13a_6" => 4.79956e-11
"w13a_7" => 0.000284228
"w13a_8" => 0.0590933
"w13a_9" => 0.92868
"w13a_10" => 5.08796
"w13a_11" => 16.2469
"w13a_12" => 37.7882
"w13a_13" => 71.6886
"w13a_14" => 118.275
"w13a_15" => 176.509
"w13a_16" => 244.465
"w13a_17" => 319.785
"w13a_18" => 400.036
"w13a_19" => 482.934
"w13a_20" => 566.28
"w13a_21" => 647.03
"w13a_22" => 720.732
"w13a_23" => 782.658
"w13a_24" => 829.249
"w13a_25" => 858.781
⋮ => ⋮
Plot the predicted estimates of the contamiant concentrations at the 2 monitoring wells based on the estimated model parameters based on the performed model calibration:
Mads.plotmatches(md, calib_predictions, "w13a")
Mads.plotmatches(md, calib_predictions, "w20a")
Initial values of the optimized model parameters are:
Mads.showparameters(md)
Pore x velocity [L/T] : vx = 40 log-transformed min = 0.01 max = 200.0 Start Time [T] : source1_t0 = 4 min = 0.0 max = 10.0 End Time [T] : source1_t1 = 15 min = 5.0 max = 40.0 Number of optimizable parameters: 3
Estimated values of the optimized model parameters are:
Mads.showparameterestimates(md, calib_param)
3-element Vector{Pair{String, Float64}}:
"vx" => 31.059669248076222
"source1_t0" => 5.036614115598699
"source1_t1" => 16.62089724181972