polynomial-chaos-expansion

---
name: polynomial-chaos-expansion
description: Polynomial chaos for uncertainty propagation
allowed-tools:
  - Bash
  - Read
  - Write
  - Edit
  - Glob
  - 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