TSEUQLib: Taylor Series Expansion Uncertainty Quantification Library

Construct Taylor series expansions for surrogate modelling. Compute UQ and sensitivity analysis metrics of the Taylor series expansion.

Features

Function	Description	Symbol
tse	n-th-order Taylor Series	$T_{n}(\boldsymbol{x})$
expectation	Expected Value	$E\left[T_{n}(\boldsymbol{x})\right]$
central_moment	Central Moment	$\mu_{k}\left[T_{n}(\boldsymbol{x})\right]$
sobol_indices	Partial Variances	$V_{ij\ldots}\left[T_{n}(\boldsymbol{x})\right]$
sobol_indices	Sobol’ Indices	$S_{ij\ldots}\left[T_{n}(\boldsymbol{x})\right]$
total_sobol_indices	Total Sobol’ Indices	$S_{i}^{T}\left[T_{n}(\boldsymbol{x})\right]$
shapley_values	Shapley effects	$\phi_{i}\left[T_{n}(\boldsymbol{x})\right]$
remainder	Error of $\xi\left[T_{n}(\boldsymbol{x})\right]$	$\varepsilon\left[\xi\left[T_{n}(\boldsymbol{x})\right]\right]$
—	Sensitivities, $\frac{\partial \xi[T_n(\boldsymbol{x})]}{\partial \theta_i}$	$S^{\xi}_{\theta_i}$

Prerequisites

Install OTILib from https://github.com/mauriaristi/otilib. This will create a new conda environment with OTILib installed.

Activate the otilib conda environment, for example:

conda activate pyoti

Add the TSEUQLib dependencies in one of two ways (TESTING IN PROGRESS).

1. Update the pyoti environment with:

conda env update -f environment.yml

Or, 2) Update the pyoti environment with:

conda install line_profiler sympy scipy pandas

Usage

Run the examples in examples/ with python. For example, run the ishigami example by:

cd TSEUQLib/examples/
python ishigami.py

Copyright

LANL O5031

© 2025. Triad National Security, LLC. All rights reserved.

This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. Department of Energy/National Nuclear Security Administration. All rights in the program are reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear Security Administration. The Government is granted for itself and others acting on its behalf a nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare. derivative works, distribute copies to the public, perform publicly and display publicly, and to permit others to do so.