Polynomial chaos for uncertainty propagation
Scanned 9/2/2026
Install to Claude Code
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---
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
graph:
domains: [domain:mathematics]
specializations: [specialization:computational-mathematics]
skillAreas: [skill-area:statistical-analysis, skill-area:mathematical-reasoning, skill-area:data-analysis]
workflows: [workflow:experiment-design]
roles: [role:research-scientist, role:data-scientist]
---
# 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
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