gPCE-model 0.1.0

Implementing generalized Polynomial Chaos Expansion (gPCE) for uncertainty quantification and surrogate modeling

gPCE_model

A Python package implementing generalized Polynomial Chaos Expansion (gPCE) for uncertainty quantification and surrogate modeling.

• 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.

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. The softwer is built on Elmar Zander's sglib approach.

The research and the development is founded by the Eurpean Union as part of the BUILDCHAIN project.

License

This project is licensed under the GNU General Public License v3.0 (GPL-3.0-only). See the LICENSE file for details.

Support

For questions or issues, please refer to the project repository or contact the development team.