aPC

MATLAB code for arbitrary polynomial chaos (aPC), scalar surrogate modeling, uncertainty quantification, and Sobol sensitivity analysis.

Supports moment-based and Stieltjes polynomial bases, sparse regression, dimension reduction, and model selection by leave-one-out (LOO) error.

Requirements

MATLAB. Optional dependencies:

• Statistics and Machine Learning Toolbox: PLS, PCA, Ridge cross-validation, and Lasso.
• Parallel Computing Toolbox: parallel searches.
• Manopt: MCP dimension reduction.

Quick start

From the repository root in MATLAB:

addpath('core');
aPC;
rng(1);

data.X_train = 2 * rand(100, 2) - 1;
data.Y_train = data.X_train(:, 1).^2 + data.X_train(:, 2);

opts.Order = 2;
opts.qnorm = 1;
opts.aPC_Method = 'stieltjes';
opts.RegressionMethod = 'ols';
opts.Parallel = false;

[model, opts, data, reduction] = aPC_Train(data, opts);
Xtest = 2 * rand(20, 2) - 1;
Ypred = aPC_Predict(Xtest, model, opts, reduction);

Inputs use one sample per row: X_train is N x D and Y_train is N x 1.

Options

Order sets the polynomial degree; qnorm controls hyperbolic truncation. Use vectors to compare candidate values. Set ReductionMethod and red_dim to enable dimension reduction, or Parallel = true for parallel searches.

aPC_Method accepts '2012', '2018', or 'stieltjes'. RegressionMethod accepts 'ols', 'lars', 'omp', 'ridge', or 'lasso'.

Use aPC_ComputeUQ(model, data) for statistics and aPC_ComputeSensitivity(model, opts) for Sobol indices.