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Possible fully functional gradient descent code for further modification, testing.

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Karthik 2025-04-29 17:18:26 +02:00
parent f88ebc298d
commit 7e5aa3df23
1 changed files with 50 additions and 42 deletions
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92
Dipolar-Gas-Simulator/+Simulator/@DipolarGas/runGradientDescent.m
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@ -8,9 +8,9 @@ function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
switch this.GradientDescentMethod
case 'HeavyBall'
% Convergence Criteria:
epsilon = 1E-6;
alpha = 1E-3;
alpha = 1E-6;
beta = 0.9;
epsilon = 1E-8;
Observ.residual = 1;
Observ.res = 1;
@ -46,7 +46,7 @@ function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
% Normalize psi
Norm = inner_product(psi_new, psi_new, Transf);
psi = sqrt(Params.N) * psi_new / sqrt(Norm);
psi = psi_new / sqrt(Norm);
% Write output at specified intervals
if mod(idx,100) == 0
@ -156,7 +156,7 @@ function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
% Normalize psi
Norm = abs(inner_product(psi, psi, Transf));
psi = sqrt(Params.N) * psi / sqrt(Norm);
psi = psi / sqrt(Norm);
i = i + 1;
% Calculate chemical potential with new psi
@ -208,59 +208,67 @@ end
%% Modules
function J = compute_gradient(psi, Params, Transf, VDk, V)
% === Precompute quantities ===
absPsi2 = abs(psi).^2; % Density |ψ|^2
absPsi3 = abs(psi).^3; % |ψ|^3
N = Params.N;
% Operators
% Kinetic energy
KEop = 0.5 * (Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
HKin = @(w) ifft(KEop.*fft(w));
% === Kinetic energy operator: -∇²/2 ===
KEop = 0.5 * (Transf.KX.^2 + Transf.KY.^2 + Transf.KZ.^2);
HKin = @(w) ifftn(KEop .* fftn(w));
% Trap Potential
HV = @(w) V.*w;
% === External potential (already scaled by ℏω₀) ===
HV = @(w) V .* w;
% Contact interactions
Hint = @(w) (Params.gs*abs(psi).^2).*w;
% DDIs
frho = fftn(abs(psi).^2);
Phi = ifftn(frho.*VDk);
Hddi = @(w) (Params.gdd*Phi).*w;
% === Contact interaction: C|ψ|² ===
C = Params.gs * N;
Hint = @(w) (C * absPsi2) .* w;
% Quantum fluctuations
Hqf = @(w) (Params.gammaQF*abs(psi).^3).*w;
H = @(w) HKin(w) + HV(w) + Hint(w) + Hddi(w) + Hqf(w);
% === Dipole-dipole interaction: D U_dd * |ψ|² ===
frho = fftn(absPsi2);
Phi_dd = ifftn(frho .* VDk);
D = Params.gdd * N;
Hddi = @(w) (D * Phi_dd) .* w;
J = H(psi);
% === Quantum fluctuations: Q|ψ|³ ===
Q = Params.gammaQF * N^(3/2);
Hqf = @(w) (Q * absPsi3) .* w;
% === Total Hamiltonian operator ===
H = @(w) HKin(w) + HV(w) + Hint(w) + Hddi(w) + Hqf(w);
% === Compute gradient ===
J = H(psi);
end
function g = compute_g(psi, p, Params, VDk)
rho = real(psi.*conj(p));
% === Precompute necessary quantities ===
rho = real(psi .* conj(p)); % Mixed density
absPsi = abs(psi); % Magnitude of wavefunction
N = Params.N;
% Contact interactions
C = Params.gs*Params.N;
gint = @(w)(C.*rho).*w;
% DDIs
D = Params.gdd*Params.N;
rhotilde = fftn(rho);
Phi = ifftn(rhotilde.*VDk);
gaddi = @(w)(D.*Phi).*w;
% === Contact interaction term ===
C = Params.gs * N;
g_contact = @(w) (C * rho) .* w;
% Quantum fluctuations
eps_dd = Params.add/Params.as;
Q = (4/(3*pi^2)) * (C^(5/2)/Params.N) * (1 + ((3*eps_dd^2)/2));
gqf = @(w)(((3/2)*Q).*abs(psi).*rho).*w;
gop = @(w) gint(w) + gaddi(w) + gqf(w);
% === Dipole-dipole interaction term ===
rhotilde = fftn(rho);
Phi_dd = ifftn(rhotilde .* VDk); % Convolution with DDI kernel
D = Params.gdd * N;
g_ddi = @(w) (D * Phi_dd) .* w;
g = gop(psi);
% === Quantum fluctuation (LHY) correction ===
Q = Params.gammaQF * N^(3/2); % LHY prefactor
g_qf = @(w) ((3/2) * Q * absPsi .* rho) .* w;
% === Total effective operator applied to psi ===
g_total = @(w) g_contact(w) + g_ddi(w) + g_qf(w);
% === Multiply by factor of 2, as per gradient expression ===
g = 2 * g_total(psi);
end
% Optimal direction via line search
% Optimal direction
function theta = compute_optimal_theta(p, muchem, psi, Params, Transf, VDk, V)
Hpsi = compute_gradient(psi, Params, Transf, VDk, V);