Speaker
Description
A set of Python tools useful for benchmarking, benchmark selection, nuclear data validation, and nuclear data evaluation support called Faust is currently under development at Los Alamos National Laboratory. The goals and objectives for Faust are to:
- Provide input and output processing for different calculation codes
- Allow for exchanging results between different applications and codes
- Run benchmarks and process the results
- Automate and simplify plotting and report generation
- Provide a basis for developing applications useful for nuclear data evaluators
Faust now includes tools to assess similarities (or similarity coefficients) between benchmarks using precalculated sensitivity profiles. This new features is the subject of the present contribution.
Sensitivity profiles indicate by how much a given observable (or response) will change following a change in a specific parameter. These sensitivity profiles are used in various applications. They are for instance used as input in error propagation of nuclear data for application by folding them with covariance matrices using the Sandwich rule [A]. Another use of these sensitivities is to calculate the impact of a nuclear data change on the values of the associated observables - as long as that change is small enough so that linear perturbation theory still applies [B]. In this paper, we will explore the use of sensitivity profiles for assessing the similarity of benchmarks in benchmark selection.
When performing nuclear data validation and testing during evaluation work, we prefer to work with a small set of benchmarks. The benchmarks in this set should be the most diverse (or dissimilar) ones we can find. They should also represent the highest sensitivity to the nuclide or nuclides being considered in the evaluation work.
Similarity between two benchmarks can be assessed in many different ways, depending on how similarity is defined. For instance, one can argue that two criticality benchmarks are similar to one another when they have roughly the same neutron spectrum. In this case, the similarity is assessed based on the average system behavior defined by the neutron spectrum.
Sensitivity profiles offer another way of assessing a similarity between benchmarks. Sensitivity profiles tell us what the impact is of a given change in a nuclear data parameter (such as a cross section in a specific energy region) on the observable (such as an effective multiplication factor). When the shape of a sensitivity profile for two different benchmark is the same, then the impact of a change in the associated parameter will be the same as well. This feature can be used to define a similarity coefficient.
One way to assess this is by looking at the sensitivity profiles as if they are vectors in an n-dimensional space. A normalized inner product between such vectors will tell us how well aligned they are with one another, and thus provide a measure of similarity between two benchmarks. This can be calculated for a single profile, or for a previously selected set of profiles for different nuclides and/or reactions. In this last case, the profiles need to be sorted by nuclide and reaction first.
In this contribution we investigate the possibility of using sensitivity profiles for a series of very similar criticality benchmarks to obtain a more detailed and more precise insight in the differences between transport calculations of effective multiplication factors for these benchmarks. We’ll show that under certain conditions such information can be obtained without performing actual transport calculations. For example, the two benchmarks, MIX-MET-FAST-007-01 and MIX-MET-FAST-007-02, with similarity coefficient of 0.9975, MCNP calculates respectively 102 and 562 pcm above measured values. The difference between the two biases is thus 460 pcm. A very simple algebraic formula operating on the integrated sensitivities yields 455 pcm (i.e., agrees within ~1% with the MCNP calculations). This 455 pcm is partitioned into individual contributions from all materials/reactions to which the benchmarks are sensitive.
Such similarity analysis offers a number of advantages:
- Ascertain which of the nuclear reactions might be responsible for the bias in the calculation
- Point to potential problems with the benchmark if difference in the benchmark biases cannot be reproduced with reasonable changes in the nuclear data
- Wisely designed series of experiments may provide stringent constraints on selected nuclear reactions
- Precision of the above-mentioned constraints may be considerably higher than the precision of the benchmarks themselves because by operating on the relative differences most of the sources of systematic uncertainties are eliminated leaving only uncertainties related to the change of configuration.