name: polynomial-chaos-expansion description: Polynomial chaos for uncertainty propagation allowed-tools:

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• Grep metadata: specialization: mathematics domain: science category: uncertainty-quantification phase: 6

Polynomial Chaos Expansion

Purpose

Provides polynomial chaos expansion methods for efficient uncertainty propagation in computational models.

Capabilities

• Generalized polynomial chaos bases
• Sparse PCE construction
• Adaptive basis selection
• PCE-based sensitivity indices
• Low-rank tensor approximation
• Stochastic Galerkin projection

Usage Guidelines

1. Basis Selection: Match basis to input distributions
2. Truncation: Choose appropriate polynomial order
3. Sparsity: Exploit sparsity for high dimensions
4. Sensitivity: Extract Sobol indices from PCE coefficients

Tools/Libraries

• Chaospy
• UQLab
• OpenTURNS