Added functionality to load a initial wavefunction if necessary to bias the solver, modified the conjugate gradient descent algorithm.
This commit is contained in:
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@ -20,7 +20,7 @@ OptionsStruct.UseApproximationForLHY = true;
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OptionsStruct.IncludeDDICutOff = true;
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OptionsStruct.CutoffType = 'Cylindrical';
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OptionsStruct.SimulationMode = 'EnergyMinimization'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution' | 'EnergyMinimization'
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OptionsStruct.GradientDescentMethod = 'HeavyBall'; % 'HeavyBall' | 'NonLinearCGD'
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OptionsStruct.GradientDescentMethod = 'NonLinearCGD'; % 'HeavyBall' | 'NonLinearCGD'
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OptionsStruct.MaxIterationsForGD = 2E5;
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OptionsStruct.TimeStepSize = 1E-4; % in s
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OptionsStruct.MinimumTimeStepSize = 2E-10; % in s
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@ -50,35 +50,6 @@ sim.Potential = pot.trap(); % + pot.repulsive_chopstick(
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Plotter.visualizeTrapPotential(sim.Potential,Params,Transf)
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%% - Plot initial wavefunction
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Plotter.visualizeWavefunction(psi,Params,Transf)
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%% - Plot GS wavefunction
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% SaveDirectory = './Results/Data_3D/CompleteLHY/AspectRatio2_8';
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% SaveDirectory = './Results/Data_3D/CompleteLHY/AspectRatio3_7';
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SaveDirectory = './Results/Data_3D/CompleteLHY/AspectRatio3_8';
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JobNumber = 0;
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Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
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%%
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% SaveDirectory = './Results/Data_3D/CompleteLHY/BeyondSSD_SSD';
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% SaveDirectory = './Results/Data_3D/CompleteLHY/BeyondSSD_Labyrinth';
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SaveDirectory = './Results/Data_3D/CompleteLHY/BeyondSSD_Honeycomb';
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JobNumber = 0;
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Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
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%% - Plot GS wavefunction
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SaveDirectory = './Results/Data_3D/ApproximateLHY/AspectRatio2_8';
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% SaveDirectory = './Results/Data_3D/ApproximateLHY/AspectRatio3_7';
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% SaveDirectory = './Results/Data_3D/ApproximateLHY/AspectRatio3_8';
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% SaveDirectory = './Results/Data_3D/ApproximateLHY/AspectRatio3_9';
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JobNumber = 3;
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Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
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%%
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% SaveDirectory = './Results/Data_3D/ApproximateLHY/BeyondSSD_SSD';
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% SaveDirectory = './Results/Data_3D/ApproximateLHY/BeyondSSD_Labyrinth';
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SaveDirectory = './Results/Data_3D/ApproximateLHY/BeyondSSD_Honeycomb';
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JobNumber = 0;
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Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
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%%
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SaveDirectory = './Results/Data_3D/GradientDescent';
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JobNumber = 0;
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Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
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%%
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% To reproduce results from the Blair Blakie paper:
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@ -438,4 +409,40 @@ JobNumber = 2; % 82
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% JobNumber = 3; % 83
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Plotter.visualizeGSWavefunction2D(SaveDirectory, JobNumber)
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[contrast, period_X, period_Y] = Scripts.analyzeGSWavefunction_in_plane_trap(SaveDirectory, JobNumber);
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%% - Plot GS wavefunction
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% SaveDirectory = './Results/Data_3D/CompleteLHY/AspectRatio2_8';
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% SaveDirectory = './Results/Data_3D/CompleteLHY/AspectRatio3_7';
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SaveDirectory = './Results/Data_3D/CompleteLHY/AspectRatio3_8';
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JobNumber = 0;
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Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
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%%
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% SaveDirectory = './Results/Data_3D/CompleteLHY/BeyondSSD_SSD';
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% SaveDirectory = './Results/Data_3D/CompleteLHY/BeyondSSD_Labyrinth';
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SaveDirectory = './Results/Data_3D/CompleteLHY/BeyondSSD_Honeycomb';
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JobNumber = 0;
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Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
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%% - Plot GS wavefunction
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SaveDirectory = './Results/Data_3D/ApproximateLHY/AspectRatio2_8';
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% SaveDirectory = './Results/Data_3D/ApproximateLHY/AspectRatio3_7';
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% SaveDirectory = './Results/Data_3D/ApproximateLHY/AspectRatio3_8';
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% SaveDirectory = './Results/Data_3D/ApproximateLHY/AspectRatio3_9';
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JobNumber = 3;
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Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
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%%
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% SaveDirectory = './Results/Data_3D/ApproximateLHY/BeyondSSD_SSD';
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% SaveDirectory = './Results/Data_3D/ApproximateLHY/BeyondSSD_Labyrinth';
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SaveDirectory = './Results/Data_3D/ApproximateLHY/BeyondSSD_Honeycomb';
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JobNumber = 0;
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Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
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%%
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SaveDirectory = './Results/Data_3D/TiltedDipoles15';
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JobNumber = 0;
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Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
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%%
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SaveDirectory = './Results/Data_3D/TiltedDipoles30';
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JobNumber = 0;
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Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
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%%
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SaveDirectory = './Results/Data_3D/TiltedDipoles45';
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JobNumber = 1;
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Plotter.visualizeGSWavefunction(SaveDirectory, JobNumber)
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@ -1,18 +1,20 @@
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%% Scaled parameters
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theta = 0;
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phi = 0;
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ScalingFactor = (4/5)^2;
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% - SSD: N = 1E5, as = 86ao
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OptionsStruct = struct;
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OptionsStruct.NumberOfAtoms = sqrt(ScalingFactor) * 5E5;
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OptionsStruct.DipolarPolarAngle = deg2rad(0);
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OptionsStruct.DipolarAzimuthAngle = 0;
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OptionsStruct.ScatteringLength = 75;
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OptionsStruct.NumberOfAtoms = 1E5;
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OptionsStruct.DipolarPolarAngle = deg2rad(theta);
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OptionsStruct.DipolarAzimuthAngle = deg2rad(phi);
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OptionsStruct.ScatteringLength = 86;
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AspectRatio = 2.8;
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HorizontalTrapFrequency = 125/ScalingFactor;
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VerticalTrapFrequency = AspectRatio * HorizontalTrapFrequency;
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OptionsStruct.TrapFrequencies = [HorizontalTrapFrequency, HorizontalTrapFrequency, VerticalTrapFrequency];
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% AspectRatio = 2.0;
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% HorizontalTrapFrequency = 125;
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% VerticalTrapFrequency = AspectRatio * HorizontalTrapFrequency;
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% OptionsStruct.TrapFrequencies = [HorizontalTrapFrequency, HorizontalTrapFrequency, VerticalTrapFrequency];
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OptionsStruct.TrapFrequencies = [150, 150, 300];
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OptionsStruct.TrapPotentialType = 'Harmonic';
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OptionsStruct.NumberOfGridPoints = [128, 128, 64];
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@ -21,18 +23,18 @@ OptionsStruct.UseApproximationForLHY = true;
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OptionsStruct.IncludeDDICutOff = true;
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OptionsStruct.CutoffType = 'Cylindrical';
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OptionsStruct.SimulationMode = 'ImaginaryTimeEvolution'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution'
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OptionsStruct.TimeStepSize = 1E-4; % in s
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OptionsStruct.MinimumTimeStepSize = 2E-6; % in s
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OptionsStruct.TimeStepSize = 1E-3; % in s
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OptionsStruct.MinimumTimeStepSize = 2E-6; % in s
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OptionsStruct.TimeCutOff = 2E6; % in s
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OptionsStruct.EnergyTolerance = 5E-10;
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OptionsStruct.ResidualTolerance = 1E-08;
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OptionsStruct.NoiseScaleFactor = 0.01;
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OptionsStruct.PlotLive = false;
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OptionsStruct.JobNumber = 2;
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OptionsStruct.RunOnGPU = true;
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OptionsStruct.PlotLive = true;
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OptionsStruct.JobNumber = 0;
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OptionsStruct.RunOnGPU = false;
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OptionsStruct.SaveData = true;
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OptionsStruct.SaveDirectory = sprintf('./Results/Data_3D/ApproximateLHY/AspectRatio%s', strrep(num2str(AspectRatio), '.', '_'));
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OptionsStruct.SaveDirectory = './Results/Data_3D/TiltedDipoles0';
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options = Helper.convertstruct2cell(OptionsStruct);
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clear OptionsStruct
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@ -43,46 +45,3 @@ sim.Potential = pot.trap();
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%-% Run Simulation %-%
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[Params, Transf, psi, V, VDk] = sim.run();
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%{
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%% - Gradient Descent Test
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OptionsStruct = struct;
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OptionsStruct.NumberOfAtoms = 8E4;
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OptionsStruct.DipolarPolarAngle = deg2rad(0);
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OptionsStruct.DipolarAzimuthAngle = 0;
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OptionsStruct.ScatteringLength = 95;
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OptionsStruct.TrapFrequencies = [30, 60, 90];
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OptionsStruct.TrapPotentialType = 'Harmonic';
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OptionsStruct.NumberOfGridPoints = [256, 128, 128];
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OptionsStruct.Dimensions = [30, 20, 20];
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OptionsStruct.UseApproximationForLHY = true;
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OptionsStruct.IncludeDDICutOff = true;
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OptionsStruct.CutoffType = 'Cylindrical';
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OptionsStruct.SimulationMode = 'EnergyMinimization'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution' | 'EnergyMinimization'
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OptionsStruct.MaxIterationsForGD = 2E4;
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% OptionsStruct.TimeStepSize = 1E-4; % in s
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% OptionsStruct.MinimumTimeStepSize = 2E-10; % in s
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% OptionsStruct.TimeCutOff = 2E6; % in s
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% OptionsStruct.EnergyTolerance = 5E-10;
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% OptionsStruct.ResidualTolerance = 1E-08;
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OptionsStruct.NoiseScaleFactor = 0.01;
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OptionsStruct.PlotLive = true;
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OptionsStruct.JobNumber = 0;
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OptionsStruct.RunOnGPU = false;
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OptionsStruct.SaveData = true;
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OptionsStruct.SaveDirectory = './Results/Data_3D/GradientDescent';
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options = Helper.convertstruct2cell(OptionsStruct);
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clear OptionsStruct
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sim = Simulator.DipolarGas(options{:});
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pot = Simulator.Potentials(options{:});
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sim.Potential = pot.trap(); % + pot.repulsive_chopstick();
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%-% Run Simulation %-%
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[Params, Transf, psi, V, VDk] = sim.run();
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%}
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@ -41,8 +41,19 @@ function [psi,V,VDk] = initialize(this,Params,Transf,TransfRad)
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end
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% == Setting up the initial wavefunction == %
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psi = this.setupWavefunction(Params,Transf);
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WavefunctionFile = fullfile(this.SaveDirectory, 'psi_init.mat');
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if isfile(WavefunctionFile)
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loadedData = load(WavefunctionFile);
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if isgpuarray(loadedData.psi)
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psi = gather(loadedData.psi);
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else
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psi = loadedData.psi;
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end
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else
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psi = this.setupWavefunction(Params,Transf);
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end
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if this.RunOnGPU
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psi = gpuArray(psi);
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end
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@ -12,6 +12,7 @@ function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
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Observ.res = 1;
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psi_old = psi; % Previous psi value (for heavy-ball method)
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% Live Plotter
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if this.PlotLive
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Plotter.plotLive(psi,Params,Transf,Observ)
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drawnow
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@ -24,7 +25,6 @@ function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
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J = compute_gradient(psi, Params, Transf, VDk, V);
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% Calculate chemical potential and norm
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% Can also be calculated as --> muchem = this.Calculator.calculateChemicalPotential(psi,Params,Transf,VDk,V);
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muchem = sum(real(conj(psi(:)) .* J(:))) / sum(abs(psi(:)).^2);
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% Calculate residual and check convergence
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@ -83,12 +83,11 @@ function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
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disp('Saving data...');
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save(sprintf(strcat(this.SaveDirectory, '/Run_%03i/psi_gs.mat'),Params.njob),'psi','muchem','Observ','Transf','Params','VDk','V');
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disp('Save complete!');
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case 'NonLinearCGD'
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% Define the function handle
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f = @(X) this.Calculator.calculateTotalEnergy(X, Params, Transf, VDk, V)/Params.N;
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case 'NonLinearCGD'
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% Convergence Criteria:
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Epsilon = 1E-5;
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epsilon = 1E-13;
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% Iteration Counter:
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i = 1;
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@ -98,65 +97,80 @@ function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
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% Initialize the PrematureExitFlag to false
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PrematureExitFlag = false;
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% Live plotter
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if this.PlotLive
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Plotter.plotLive(psi,Params,Transf,Observ)
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drawnow
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end
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% Minimization Loop
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while true
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% Compute gradient
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J = compute_gradient(psi, Params, Transf, VDk, V);
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% Check stopping criterion (Gradient norm)
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if norm(J(:)) < Epsilon
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disp('Tolerance reached: Gradient norm is below the specified epsilon.');
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J = compute_gradient(psi, Params, Transf, VDk, V);
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% Calculate chemical potential
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muchem = real(conj(psi(:))' * J(:)) / norm(psi(:))^2;
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% Calculate residual
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residual = J - (muchem * psi);
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% Compute energy difference between the last two saved energy values
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if i == 1
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energydifference = NaN;
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elseif mod(i,100) == 0 && length(Observ.EVec) > 1
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energydifference = abs(Observ.EVec(end) - Observ.EVec(end-1));
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end
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% Convergence check - if energy difference is below set tolerance, then exit
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if energydifference <= epsilon
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disp('Tolerance reached: Energy difference is below the specified epsilon.');
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PrematureExitFlag = true; % Set flag to indicate premature exit
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break;
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elseif i >= this.MaxIterationsForCGD
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elseif i >= this.MaxIterationsForGD % If set maximum number of iterations reached, then exit
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disp('Maximum number of iterations for CGD reached.');
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PrematureExitFlag = true; % Set flag to indicate premature exit
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break;
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end
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% Initialize search direction if first iteration
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if i == 1
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S = -J;
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else
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% Update search direction
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S = update_search_direction(S, J, J_old);
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d = -residual;
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else % Compute beta via Polak-Ribiere and create new direction
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residual_new = residual;
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beta = compute_beta(residual_new, residual_old);
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d = -residual_new + beta * p_old;
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end
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% Step Size Optimization (Line Search)
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alpha = optimize_step_size(f, psi, S, Params, Transf, VDk, V);
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residual_old = residual;
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p = d - (real(conj(d(:))' * psi(:)) .* psi);
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p_old = p;
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% Compute optimal theta to generate psi in the direction of minimum in the energy landscape
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theta = compute_optimal_theta(p, muchem, psi, Params, Transf, VDk, V);
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% Update solution
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psi = psi + alpha * S;
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psi = (cos(theta).*psi) + (sin(theta).*(p / norm(p(:))));
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% Normalize psi
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Norm = sum(abs(psi(:)).^2) * Transf.dx * Transf.dy * Transf.dz;
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psi = sqrt(Params.N) * psi / sqrt(Norm);
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% Store old gradient
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J_old = J;
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i = i + 1;
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muchem = this.Calculator.calculateChemicalPotential(psi,Params,Transf,VDk,V);
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if mod(i,500) == 0
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Norm = sum(abs(psi(:)).^2) * Transf.dx * Transf.dy * Transf.dz;
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psi = sqrt(Params.N) * psi / sqrt(Norm);
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i = i + 1;
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% Calculate chemical potential with new psi
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muchem = real(conj(psi(:))' * J(:)) / norm(psi(:))^2;
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if mod(i,100) == 0
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% Change in Energy
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% Collect Energy value
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E = this.Calculator.calculateTotalEnergy(psi,Params,Transf,VDk,V);
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E = E/Norm;
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Observ.EVec = [Observ.EVec E];
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% Chemical potential
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% Collect Chemical potential value
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Observ.mucVec = [Observ.mucVec muchem];
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% Normalized residuals
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% Collect Normalized residuals
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res = this.Calculator.calculateNormalizedResiduals(psi,Params,Transf,VDk,V,muchem);
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Observ.residual = [Observ.residual res];
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Observ.res_idx = Observ.res_idx + 1;
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% Live plotter
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if this.PlotLive
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Plotter.plotLive(psi,Params,Transf,Observ)
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drawnow
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@ -185,7 +199,7 @@ function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
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end
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%% Modules
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% Numerical Gradient Calculation using the finite differences method
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function J = compute_gradient(psi, Params, Transf, VDk, V)
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% Operators
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@ -210,44 +224,48 @@ function J = compute_gradient(psi, Params, Transf, VDk, V)
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H = @(w) HKin(w) + HV(w) + Hint(w) + Hddi(w) + Hqf(w);
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J = H(psi);
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J = H(psi);
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end
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% Backtracking Line Search (Step Size Optimization)
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function alpha = optimize_step_size(f, X, S, Params, Transf, VDk, V)
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alpha = 1; % Initial step size
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rho = 0.5; % Step size reduction factor
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c = 1E-4; % Armijo condition constant
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max_iter = 100; % Max iterations for backtracking
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tol = 1E-4; % Tolerance for stopping
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function g = compute_g(psi, p, Params, VDk)
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rho = real(psi.*conj(p));
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grad = compute_gradient(X, Params, Transf, VDk, V); % Compute gradient once
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f_X = f(X); % Evaluate f(X) once
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% Contact interactions
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C = Params.gs*Params.N;
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gint = @(w)(C.*rho).*w;
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% DDIs
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D = Params.gdd*Params.N;
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rhotilde = fftn(rho);
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Phi = real(ifftn(rhotilde.*VDk));
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gaddi = @(w)(D.*Phi).*w;
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for k = 1:max_iter
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% Evaluate Armijo condition with precomputed f(X) and grad
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if f(X + alpha * S) <= f_X + c * alpha * (S(:)' * grad(:))
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break;
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else
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alpha = rho * alpha; % Reduce the step size
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end
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% Early stopping if step size becomes too small
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if alpha < tol
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break;
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end
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end
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% Quantum fluctuations
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eps_dd = Params.add/Params.as;
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Q = (4/(3*pi^2)) * (C^(5/2)/Params.N) * (1 + ((3*eps_dd^2)/2));
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gqf = @(w)(((3/2)*Q).*abs(psi).*rho).*w;
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gop = @(w) gint(w) + gaddi(w) + gqf(w);
|
||||
|
||||
g = gop(psi);
|
||||
|
||||
end
|
||||
|
||||
% Update Search Direction
|
||||
function S_new = update_search_direction(S, J_new, J_old)
|
||||
% (Fletcher-Reeves method)
|
||||
% beta = (norm(J_new(:))^2) / (norm(J_old(:))^2);
|
||||
% S_new = -J_new + beta * S;
|
||||
% Optimal direction via line search
|
||||
function theta = compute_optimal_theta(p, muchem, psi, Params, Transf, VDk, V)
|
||||
|
||||
Hpsi = compute_gradient(psi, Params, Transf, VDk, V);
|
||||
Hp = compute_gradient(p, Params, Transf, VDk, V);
|
||||
g = compute_g(psi, p, Params, VDk);
|
||||
numerator = real(conj(p(:))' * Hpsi(:))/norm(p(:));
|
||||
denominator = muchem - ((conj(p(:))' * Hp(:)) + real(conj(g(:))' * p(:)))/norm(p(:))^2;
|
||||
|
||||
% (Polak-Ribiere method)
|
||||
beta = max(0, (J_new(:)' * (J_new(:) - J_old(:))) / (norm(J_old(:))^2));
|
||||
S_new = -J_new + beta * S;
|
||||
theta = numerator / denominator;
|
||||
end
|
||||
|
||||
% Optimal step size via Polak-Ribiere
|
||||
function beta = compute_beta(residual_new, residual_old)
|
||||
beta = max(0, (residual_new(:)' * (residual_new(:) - residual_old(:))) / (norm(residual_old(:))^2));
|
||||
end
|
||||
Loading…
x
Reference in New Issue
Block a user