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 |
Gradient |
False |
ApplyJacobian |
False |
ApplyHessian |
False |
Config |
Type |
Default |
Description |
---|---|---|---|
None |
Mount directories#
Mount directory |
Purpose |
---|---|
None |
Source code#
Description#
The prior distributions of input parameters \(\theta = E_1, E_2, E_3, n_1, n_2\) are all uniform:
\(E_1 \sim \mathcal U(0.7, 1.0)\)
\(E_2 \sim \mathcal U(0.9, 1.3)\)
\(E_3 \sim \mathcal U(1.1, 1.75)\)
\(n_1 \sim \mathcal U(5 \cdot 10^{-4}, 5 \cdot 10^{-3})\)
\(n_2 \sim \mathcal U(10^{-4}, 10^{-3})\)
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.
The log-posterior is returned as the sum of the log-prior density and the log-likelihood.