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Usage Of DACE Toolbox

Usage Of DACE Toolbox. Lien-Chi Lai , Optimization Lab 2009/10/09. Download DACE Toolbox (1/2). DACE website: http://www2.imm.dtu.dk/~hbn/dace/. Download DACE Toolbox (2/2). Command and Parameter (1/5). Command >> [ dmodel,perf ] = dacefit (S,Y,regr,corr,theta0)

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Usage Of DACE Toolbox

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  1. Usage Of DACE Toolbox Lien-Chi Lai, Optimization Lab2009/10/09

  2. Download DACE Toolbox (1/2) • DACE website: http://www2.imm.dtu.dk/~hbn/dace/ Usage of DACE Toolbox

  3. Download DACE Toolbox (2/2) Usage of DACE Toolbox

  4. Command and Parameter (1/5) • Command • >> [dmodel,perf] = dacefit(S,Y,regr,corr,theta0) • >> pred = predictor(x, dmodel) • Parameter • S experimental points (m-by-n) • Y responses at S(m-by-1) • regrregression function • corrcorrelation function • theta0 parameter of correlation function (1-by-1 if all dimensions are identical, or n-by-1) • x ptrial points with n dimensions (p-by-n) • predpredicted responses (p-by-1) Usage of DACE Toolbox

  5. Command and Parameter (2/5) • Command • >> [dmodel,perf] = ... dacefit(S,Y,regr,corr,theta0,lob,upb) • >> pred = predictor(x, dmodel) • Parameter • lob,upboptional parameter, if present, then should be vectors of the same length astheta0 dim. should be same as the one of theta0 Usage of DACE Toolbox

  6. Command and Parameter (3/5) • Command • >> [dmodel,perf] = ... dacefit(S,Y,regr,corr,theta0,lob,upb) • >> pred = predictor(x, dmodel) • Parameter • dmodelDACE model, struct with regr, corr, theta, beta … • perfinformation about the optimization, struct with nv,… Usage of DACE Toolbox

  7. Command and Parameter (4/5) • Regression Models • regpoly0 Zero order polynomial • regpoly1 First order polynomial • regpoly2 Second order polynomial • Correlation Models • correxp Exponential • correxpg Generalized exponential • corrgauss Gaussian • corrlin Linear • corrspherical Spherical • corrspline Cubic spline Usage of DACE Toolbox

  8. Command and Parameter (5/5) • Command • >> x = gridsamp([1 1;3 3], 3) x = 1 1 1 2 1 3 2 1 2 2 2 3 3 1 3 2 3 3 Usage of DACE Toolbox

  9. Example • >> [dmodel, perf] = dacefit(S, Y, @regpoly0, ... @corrgauss, 10); • >> [dmodel, perf] = dacefit(S, Y, @regpoly0, ... @corrgauss, 10, 0.1, 20); • >> [dmodel, perf] = dacefit(S, Y, @regpoly0, ... @corrgauss, [10 10], ... [0.1 0.1], [20 20]); • >> pred = predictor(x, dmodel); Usage of DACE Toolbox

  10. Example • Complete code for Branin function Usage of DACE Toolbox

  11. Appendix – Complete Code (1/2) % S = lhsamp(25,2); load S.mat S = [S(:,1)*15-5, S(:,2)*15]; Y = ft_branin(S(:,1), S(:,2)); x = gridsamp([-5 0;10 15], 25); theta = [10 10]; lob = [1e-1 1e-1]; upb = [20 20]; [dmodel, perf] = dacefit(S, Y, @regpoly0, ... @corrgauss, theta, lob, upb); % [dmodel, perf] = dacefit(S, Y, @regpoly0, ... @corrgauss, 1); pred = predictor(x, dmodel); Usage of DACE Toolbox

  12. Appendix – Complete Code (1/2) [x_grid, y_grid] = meshgrid(-5:15/24:10, 0:15/24:15); surf(x_grid, y_grid, reshape(pred, 25, 25)); view(2); xlabel('x'); ylabel('y'); title('Surrogate Surface'); % final_theta = dmodel.theta; % function z = ft_branin(x, y) % z = (y - 5.1*x.^2/(4*pi*pi) + 5*x/pi -6).^2 + ... 10*(1-1/(8*pi))*cos(x) + 10; Usage of DACE Toolbox

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