# Tritium Diffusion Posterior¶

## Overview¶

In this benchmark, we use Achlys to model the macroscopic transport of tritium through fusion reactor materials using the Foster-McNabb equations. Achlys is built on top of the MOOSE Finite Element Framework. The aim of this benchmark is to compute the (unnormalised) posterior density of the input parameters given the experimental data of Ogorodnikova et al. (2003).

## Run¶

docker run -it -p 4243:4243 linusseelinger/benchmark-achlys:latest


## Properties¶

Model

Description

posterior

Posterior density

forward

Forward model

### posterior¶

Mapping

Dimensions

Description

input

[5]

E1, E2, E3: The detrapping energy of the traps. n1, n2: The density of the intrinsic traps.

output

[1]

Log posterior density

### forward¶

Mapping

Dimensions

Description

input

[5]

E1, E2, E3: The detrapping energy of the traps. n1, n2: The density of the intrinsic traps.

output

[500]

Flux of tritium across the boundary as a function of time in atomic fraction.

Feature

Supported

Evaluate

True

False

ApplyJacobian

False

ApplyHessian

False

Config

Type

Default

Description

None

Mount directory

Purpose

None

Model sources

## Description¶

1. The prior distributions of input parameters $$\theta = E_1, E_2, E_3, n_1, n_2$$ are all uniform:

• $$E_1 \sim \mathcal U(0.7, 1.0)$$

• $$E_2 \sim \mathcal U(0.9, 1.3)$$

• $$E_3 \sim \mathcal U(1.1, 1.75)$$

• $$n_1 \sim \mathcal U(5 \cdot 10^{-4}, 5 \cdot 10^{-3})$$

• $$n_2 \sim \mathcal U(10^{-4}, 10^{-3})$$

2. The following parameter to data map is assumed:

• $$d = \mathcal F(\theta) + \varepsilon$$ with $$\varepsilon \sim \mathcal N(0, \sigma^2)$$.

Accordingly, the likelihood of the data given the input parameters is modelled as a Gaussian.

3. The log-posterior is returned as the sum of the log-prior density and the log-likelihood.