In Owen et al. (2017), the Exp-Tanh function is used to test metamodeling approaches, namely polynomial chaos expansions and Gaussian process modeling.

## Description

The Exp-Tanh function is defined as:

where \mathbf{x} = \{x_1, x_2\} are the input variables.

Figure 1 and 2 show the surface and contour plots of the Exp-Tanh function, respectively.

**Figure 1**: Surface plot of the Exp-Tanh function.

**Figure 2**: Contour plot of the Exp-Tanh function.

## Inputs

For computer experiment purposes, the inputs x_1, x_2 are modeled as two independent uniform random variables.

No | Variable | Distribution | Parameters |
---|---|---|---|

1 | x_1 | Uniform | x_{1,\min} = -1, x_{1,\max} = 1 |

2 | x_2 | Uniform | x_{2,\min} = -1, x_{2,\max} = 1 |

## Resources

The vectorized implementation of the Exp-Tanh function in MATLAB as well as the script file with the model and probabilistic inputs definitions for the function in UQLAB can be downloaded below:

uq_expTanh.zip (2.1 KB)

The contents of the file are:

Filename | Description |
---|---|

`uq_expTanh.m` |
vectorized implementation of the Exp-Tanh function |

`uq_Example_expTanh.m` |
definitions for the model and probabilistic inputs in UQLab |

`LICENSE` |
license for the function (BSD 3-Clause) |

## References

- N. E. Owen, P. Challenor, P. P. Menon, and S. Bennani, â€śComparison of surrogate-based uncertainty quantification methods for computationally expensive simulators,â€ť
*SIAM/ASA Journal on Uncertainty Quantification*, vol. 5, no. 1, pp. 403â€“435, 2017. DOI:10.1137/15M1046812