02enKF_1DinverseHeatTransfer.H

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#ifndef EnKF_1DinverseHeatTransfer_H
#define EnKF_1DinverseHeatTransfer_H
#include "simpleControl.H"
#include "fvOptions.H"
 
 
class EnKF_1DinverseHeatTransfer: public laplacianProblem
{
    public:
        explicit EnKF_1DinverseHeatTransfer(int argc, char* argv[], int Nseeds_)
            :
            laplacianProblem(argc, argv)
        {
            fvMesh& mesh = _mesh();
            _simple = autoPtr<simpleControl>
                      (
                          new simpleControl
                          (
                              mesh
                          )
                      );
            simpleControl& simple = _simple();
            Time& runTime = _runTime();
#include "createFvOptions.H"
            left_ind = mesh.boundaryMesh().findPatchID("left");
            Nseeds = Nseeds_;
            Tensemble = PtrList<volScalarField>(Nseeds);
            volScalarField& T(_T());
            stateSize = T.size();
            priorSamples = Eigen::MatrixXd::Zero(stateSize, Nseeds);
            posteriorSamples = priorSamples;
            startTime = runTime.startTime().value();
            deltaTime = runTime.deltaTValue();
            endTime = runTime.endTime().value();
            Ntimes = (endTime - startTime) / deltaTime;
            Info << "startTime = " << startTime << endl;
            Info << "endTime = " << endTime << endl;
            Info << "deltaTime = " << deltaTime << endl;
            Info << "Ntimes = " << Ntimes << endl;
            timeVector.resize(Ntimes);
            probe_mean.resize(Nprobes, Ntimes);
            probe_true = probe_mean;
            probe_MaxConfidence = probe_mean;
            probe_minConfidence = probe_mean;
        }
 
        autoPtr<simpleControl> _simple;
        autoPtr<fv::options> _fvOptions;
        double k;
        double rho;
        double Cp;
        label left_ind;
        Eigen::MatrixXd measurements;
        int NtimeStepsBetweenSamps = 3;
        int Nseeds;
 
        PtrList<volScalarField> Tensemble;
        PtrList<volScalarField> Tmean;
        int stateSize;
 
        std::shared_ptr<muq::Modeling::Gaussian> priorDensity;
        std::shared_ptr<muq::Modeling::Gaussian> modelErrorDensity;
        std::shared_ptr<muq::Modeling::Gaussian> measNoiseDensity;
        double meas_cov;
 
        Eigen::MatrixXd priorSamples;
        Eigen::MatrixXd posteriorSamples;
 
        double startTime;
        double deltaTime;
        double endTime;
        int Ntimes;
 
        Eigen::VectorXd timeVector;
        int Nprobes = 1;
        Foam::vector probePosition = Foam::vector(0.5, 0.1, 0.005);
        Eigen::MatrixXd probe_true;
        Eigen::MatrixXd probe_mean;
        Eigen::MatrixXd probe_MaxConfidence;
        Eigen::MatrixXd probe_minConfidence;
 
        int samplingTimeI = 0;
        int sampleI = 0;
        int sampleFlag = 0;
 
        double updateBC(bool reconstruction = 0)
        {
            Time& runTime = _runTime();
            scalar time = runTime.value();
            double BC = time * 5 + 2;
 
            if (reconstruction)
            {
                BC = time * 5 + 0;
            }
 
            return BC;
        }
 
        void resetSamplingCounters()
        {
            samplingTimeI = 0;
            sampleI = 0;
            sampleFlag = 0;
        }
 
        Eigen::VectorXd observe(volScalarField field)
        {
            fvMesh& mesh = _mesh();
            Time& runTime = _runTime();
            IOdictionary measurementsDict
            (
                IOobject
                (
                    "measurementsDict",
                    runTime.constant(),
                    mesh,
                    IOobject::MUST_READ,
                    IOobject::NO_WRITE
                )
            );
            List<vector> measurementPoints(measurementsDict.lookup("positions"));
            Eigen::VectorXd measures(measurementPoints.size());
            forAll(measurementPoints, pntI)
            {
                //TODO
                //add check if I put two measurements on the same cell
                measures(pntI) = field[mesh.findCell(measurementPoints[pntI])];
            }
            return measures;
        }
 
        Eigen::MatrixXd solve(volScalarField& T, word outputFolder,
                              word outputFieldName, bool reconstruction = 0)
        {
            Eigen::MatrixXd obsMat;
            fvMesh& mesh = _mesh();
            Foam::Time& runTime = _runTime();
            simpleControl& simple = _simple();
            fv::options& fvOptions(_fvOptions());
            dimensionedScalar diffusivity("diffusivity", dimensionSet(0, 2, -1, 0, 0, 0, 0),
                                          k / (rho * Cp));
            Info << "Thermal diffusivity = " << diffusivity << " m2/s" << endl;
            int timeI = 0;
 
            while (runTime.loop())
            {
                scalar time = runTime.value();
 
                if (!reconstruction)
                {
                    sampleFlag++;
                    timeVector(timeI) = time;
                    timeI++;
                }
 
                // Update BC
                ITHACAutilities::assignBC(T, mesh.boundaryMesh().findPatchID("left"),
                                          updateBC(reconstruction));
 
                // Solve
                while (simple.correctNonOrthogonal())
                {
                    fvScalarMatrix TEqn
                    (
                        fvm::ddt(T) - fvm::laplacian(diffusivity, T)
                    );
                    fvOptions.constrain(TEqn);
                    TEqn.solve();
                    fvOptions.correct(T);
                }
 
                if (reconstruction)
                {
                    //Adding model error
                    forAll(T.internalField(), cellI)
                    {
                        T.ref()[cellI] += modelErrorDensity->Sample()(cellI);
                    }
                }
                else
                {
                    probe_true.col(timeI - 1) = sampleField(T, probePosition);
                }
 
                ITHACAstream::exportSolution(T, runTime.timeName(),
                                             outputFolder,
                                             outputFieldName);
 
                if (sampleFlag == NtimeStepsBetweenSamps)
                {
                    Info << "Sampling at time = " << runTime.timeName() << nl << endl;
                    obsMat.conservativeResize(observe(T).size(), obsMat.cols() + 1);
                    obsMat.col(sampleI) = observe(T);
 
                    if (!reconstruction)
                    {
                        sampleFlag = 0;
                        sampleI++;
                    }
                }
 
                runTime.write();
            }
 
            if (!reconstruction)
            {
                ITHACAstream::exportMatrix(timeVector, "timeVector", "eigen", outputFolder);
                ITHACAstream::exportMatrix(probe_true, "probe_true", "eigen", outputFolder);
            }
 
            return obsMat;
        }
 
        void solveDirect()
        {
            Info << "\n****************************************\n" << endl;
            Info << "\nPerforming true solution\n" << endl;
            word outputFolder = "./ITHACAoutput/direct/";
            restart();
            volScalarField& T(_T());
            measurements = solve(T, outputFolder, "Tdirect");
            ITHACAstream::exportMatrix(measurements, "trueMeasurements", "eigen",
                                       outputFolder);
            std::cout << "Number of samples in time = " << measurements.cols() << std::endl;
            std::cout << "Number of sample in space = " << measurements.rows() << std::endl;
            resetSamplingCounters();
            Info << "\nEND true solution\n" << endl;
            Info << "\n****************************************\n" << endl;
        }
 
 
        void reconstruct()
        {
            restart();
            Time& runTime = _runTime();
            resetSamplingCounters();
            std::vector<Eigen::MatrixXd> observationTensor;
            word outputFolder = "ITHACAoutput/reconstuction";
            Tmean.resize(Ntimes);
            Info << "\n****************************************\n" << endl;
            Info << "\nStarting reconstruction\n" << endl;
            int samplesCounter = 0;
            // Read true field
            PtrList<volScalarField> Ttrue;
            ITHACAstream::read_fields(Ttrue, "Tdirect",
                                      "ITHACAoutput/direct/");
 
            for (int timeI = 0; timeI < Ntimes; timeI++)
            {
                double initialTime = timeI * deltaTime + startTime;
                Info << "\n\nTime " << initialTime + deltaTime << endl;
                Eigen::MatrixXd forecastOutput = forecastStep(initialTime, timeI,
                                                 initialTime + deltaTime);
 
                if (forecastOutput.cols() > 0)
                {
                    // This is a sampling step
                    samplesCounter++;
                    observationTensor.push_back(forecastOutput);
                    sampleFlag = 0;
                    Eigen::VectorXd meas = measurements.col(samplesCounter - 1);
                    // Kalman filter
                    posteriorSamples = ITHACAmuq::muq2ithaca::EnsembleKalmanFilter(Tensemble, meas,
                                       Eigen::MatrixXd::Identity(meas.size(), meas.size()) * meas_cov, forecastOutput);
 
                    for (int i = 0; i < Nseeds; i++)
                    {
                        restart();
                        volScalarField& T = _T();
                        Eigen::VectorXd internalField = posteriorSamples.col(i);
                        assignIF(T, internalField);
                        Tensemble.Foam::PtrList<volScalarField>::set(i, T.clone());
                    }
                }
                else
                {
                    Info << "debug : NOT a sampling step" << endl;
                }
 
                // Fill the mean value field
                Eigen::VectorXd internalField = Foam2Eigen::PtrList2Eigen(
                                                    Tensemble).rowwise().mean();
                volScalarField& Tmean = _T();
                assignIF(Tmean, internalField);
                ITHACAstream::exportSolution(Tmean, std::to_string(initialTime + deltaTime),
                                             outputFolder, "Tmean");
                ITHACAstream::exportSolution(Ttrue[timeI],
                                             std::to_string(initialTime + deltaTime),
                                             outputFolder, "Ttrue");
                // Save values at measurements points
                Eigen::MatrixXd ensambleProbe(Nprobes, Nseeds);
 
                for (int i = 0; i < Nseeds; i++)
                {
                    ensambleProbe.col(i) = sampleField(Tensemble[i], probePosition);
                }
 
                probe_mean.col(timeI) = ensambleProbe.rowwise().mean();
                probe_MaxConfidence.col(timeI) = ITHACAmuq::muq2ithaca::quantile(ensambleProbe,
                                                 0.95);
                probe_minConfidence.col(timeI) = ITHACAmuq::muq2ithaca::quantile(ensambleProbe,
                                                 0.05);
            }
 
            ITHACAstream::exportMatrix(probe_mean, "probe_mean", "eigen", outputFolder);
            ITHACAstream::exportMatrix(probe_MaxConfidence, "probe_MaxConfidence", "eigen",
                                       outputFolder);
            ITHACAstream::exportMatrix(probe_minConfidence, "probe_minConfidence", "eigen",
                                       outputFolder);
            Info << "\n****************************************\n" << endl;
        }
 
 
        Eigen::MatrixXd forecastStep(double startTime_, int startIndex_,
                                     double endTime_)
        {
            word outputFolder = "ITHACAoutput/forwardSamples";
            bool reconstructionFlag = 1;
            Eigen::MatrixXd observationMat;
            sampleFlag++;
 
            for (int i = 0; i < Nseeds; i++)
            {
                word fieldName = "Tsample" + std::to_string(i);
                volScalarField T(_T());
 
                if (startIndex_ == 0)
                {
                    restart();
                    T = _T();
                    Eigen::VectorXd internalField = priorSamples.col(i);
                    assignIF(T, internalField);
                }
                else
                {
                    T = Tensemble.set(i, nullptr)();
                }
 
                resetRunTime(startTime_, startIndex_, endTime_);
 
                if (observationMat.cols() == 0)
                {
                    observationMat = solve(T, outputFolder, fieldName, reconstructionFlag);
                }
                else
                {
                    observationMat.conservativeResize(observationMat.rows(),
                                                      observationMat.cols() + 1);
                    Eigen::MatrixXd observationForCheck = solve(T, outputFolder, fieldName,
                                                          reconstructionFlag);
                    M_Assert(observationForCheck.cols() == 1,
                             "The forecast step passed trough more than a sampling step");
                    observationMat.col(i) = observationForCheck;
                }
 
                Tensemble.set(i, T.clone());
            }
 
            return observationMat;
        }
 
        void assignIF(volScalarField& field_, Eigen::VectorXd internalField_)
        {
            for (int i = 0; i < internalField_.size(); i++)
            {
                field_.ref()[i] = internalField_(i);
            }
        }
 
        Eigen::VectorXd sampleField(volScalarField field_, Foam::vector probeLocation_)
        {
            Foam::fvMesh& mesh = _mesh();
            Eigen::VectorXd output(1);
            output(0) = field_[mesh.findCell(probeLocation_)];
            return output;
        }
 
        void restart()
        {
            Time& runTime = _runTime();
            instantList Times = runTime.times();
            runTime.setTime(Times[1], 0);
            _simple.clear();
            _T.clear();
            Foam::fvMesh& mesh = _mesh();
            _simple = autoPtr<simpleControl>
                      (
                          new simpleControl
                          (
                              mesh
                          )
                      );
            _T = autoPtr<volScalarField>
                 (
                     new volScalarField
                     (
                         IOobject
                         (
                             "T",
                             runTime.timeName(),
                             mesh,
                             IOobject::MUST_READ,
                             IOobject::AUTO_WRITE
                         ),
                         mesh
                     )
                 );
        }
 
        void resetRunTime(double startTime_, int startIndex_, double endTime_)
        {
            Time& runTime = _runTime();
            instantList Times = runTime.times();
            runTime.setTime(startTime_, startIndex_);
            runTime.setEndTime(endTime_);
            _simple.clear();
            Foam::fvMesh& mesh = _mesh();
            _simple = autoPtr<simpleControl>
                      (
                          new simpleControl
                          (
                              mesh
                          )
                      );
        }
 
        void priorSetup(double mean, double cov)
        {
            volScalarField& T(_T());
            int stateSize = T.size();
            Eigen::VectorXd prior_mu = Eigen::MatrixXd::Ones(stateSize, 1) * mean;
            Eigen::MatrixXd prior_cov = Eigen::MatrixXd::Identity(stateSize,
                                        stateSize) * cov;
            priorDensity = std::make_shared<muq::Modeling::Gaussian>(prior_mu, prior_cov);
        }
 
        void priorSampling()
        {
            for (int i = 0; i < Nseeds; i++)
            {
                priorSamples.col(i) = priorDensity->Sample();
            }
 
            posteriorSamples = priorSamples;
        }
 
        void modelErrorSetup(double mean, double cov)
        {
            volScalarField& T(_T());
            int stateSize = T.size();
            Eigen::VectorXd modelError_mu = Eigen::MatrixXd::Ones(stateSize, 1) * mean;
            Eigen::MatrixXd modelError_cov = Eigen::MatrixXd::Identity(stateSize,
                                             stateSize) * cov;
            modelErrorDensity = std::make_shared<muq::Modeling::Gaussian>(modelError_mu,
                                modelError_cov);
        }
 
        void measNoiseSetup(double mean, double cov)
        {
            meas_cov = cov;
            int obsSize = measurements.rows();
            M_Assert(obsSize > 0, "Read measurements before setting up the noise");
            Eigen::VectorXd measNoise_mu = Eigen::MatrixXd::Ones(obsSize, 1) * mean;
            Eigen::MatrixXd measNoise_cov = Eigen::MatrixXd::Identity(obsSize,
                                            obsSize) * cov;
            measNoiseDensity = std::make_shared<muq::Modeling::Gaussian>(measNoise_mu,
                               measNoise_cov);
        }
};
 
#endif