gPCE_model

A Python package implementing generalized Polynomial Chaos Expansion (gPCE) for uncertainty quantification and surrogate modeling. The software is built on Elmar Zander's sglib approach. Website: https://buildchain.ilab.sztaki.hu/ Source code: https://github.com/TRACE-Structures/gPCE_model Bug reports: https://github.com/TRACE-Structures/gPCE_model/issues Overview The gPCE_model package provides a complete framework for building and using generalized Polynomial Chaos Expansion (gPCE) surrogate models. These models efficiently approximate computational expensive simulations while quantifying uncertainty in the outputs. The implementation supports various polynomial systems, multi-index generation, and comprehensive uncertainty analysis including Sobol sensitivity indices. Installation pip install gPCE-model Features Generalized Polynomial Chaos Expansion: Build surrogate models using orthogonal polynomial bases Multiple Training Methods: Regression-based coefficient computation Projection-based coefficient computation Multi-index Management: Flexible basis construction with total degree or full tensor product Uncertainty Quantification: Mean and variance computation Sobol sensitivity indices (partial variances) SHAP value integration for interpretability Orthogonal Polynomial Support: Works with various polynomial systems (Hermite, Legendre, Jacobi, etc.) Model Export: JSON-LD metadata export for interoperability Core Components GpcModel Class The main class for generalized polynomial chaos expansion models. Key Attributes: basis: GpcBasis object containing basis functions Q: VariableSet defining probabilistic input variables u_alpha_i: Coefficients of the gPCE expansion p: Maximum polynomial degree Key Methods: compute_coeffs_by_regression(q_k_j, u_k_i): Train using least squares regression compute_coeffs_by_projection(q_k_j, u_k_i, w_k): Train using quadrature projection predict(q_k_j): Predict output at new input points mean(): Compute mean of the gPCE model variance(): Compute variance of the gPCE model compute_partial_vars(model_obj, max_index=1): Compute Sobol sensitivity indices GpcBasis Class Manages the polynomial basis functions for gPCE. Key Attributes: m: Number of random variables syschars: System characters defining polynomial types p: Maximum polynomial degree I: Multi-index set defining basis functions Key Methods: evaluate(xi, dual=False): Evaluate basis functions at given points norm(do_sqrt=True): Compute norm of basis functions size(): Get size of the multi-index set Multi-index Functions Functions for generating and managing multi-index sets. multiindex(m, p, full_tensor=False): Generate multi-index set for m variables and degree p np_sortrows(M, columns=None): Sort rows of 2D array by specified columns Authors and acknowledgment The code is developed by András Urbanics, Bence Popovics, Emese Vastag, Elmar Zander and Noémi Friedman in the TRACE-Structures group. This work has been funded by the European Commission Horizon Europe Innovation Action project 101092052 BUILDCHAIN License This project is licensed under the GNU General Public License v3.0 (GPL-3.0-only). See the LICENSE file for details. Related Projects uncertain_variables: Probabilistic variable management digital_twinning: Digital Twinning Support For questions or issues, please refer to the project repository or contact the development team.