The full representation of a d-variate function requires exponentially storage size as a function of dimension d and high computational cost. In order to reduce these complexities, function approximation methods (called reconstruction in our context) are proposed, such as: interpolation, approximation, etc. The traditional interpolation model like the multilinear one, has this dimensionality problem. To deal with this problem, we propose a new model based on the Tucker format-a low-rank tensor approximation method, called here the Tucker decomposition. The Tucker decomposition is built as a tensor product of one-dimensional spaces where their one-variate basis functions are constructed by an extension of the Karhunen-Loève decomposition into high-dimensional space. Using this technique, we can acquire, direction by direction, the most important information of the function and convert it into a small number of basis functions. Hence, the approximation for a given function needs less data than that of the multilinear model. Results of a test case on the neutron crosssection reconstruction demonstrate that the Tucker decomposition achieves a better accuracy while using less data than the multilinear interpolation.

LLNL's Computational Nuclear Physics Group and Nuclear Theory and Modeling Group have collaborated to produce the next iteration of LLNL's evaluated nuclear database ENDL2009. ENDL2009 is the second in a series of major ENDL library releases designed to support LLNL's current and future nuclear data needs. This library contains many new evaluations for radiochemical diagnostics, structural materials, and thermonuclear reactions. We have striven to keep ENDL2009 at the leading edge of nuclear data library development by reviewing and incorporating new evaluations as they are made available to the nuclear data community. In addition, ENDL2009 support new features such as energy dependent Q values from fission and unresolved resonances. Furthermore, this is the first ENDL library release to be released in the TDF format. Finally, this release is our most highly tested release as we have strengthened our already rigorous testing regime by adding tests against LANL Activation Ratio Measurements and many more new critical assemblies. Our testing is now being incorporated into our development process and is serving to guide library improvements. Contents

The neutron cross-sections are inputs for nuclear reactor core simulations, they depend on various physical parameters. Because of industrial constraint (e.g. calculation time), the cross-sections can not be calculated on the fly due to the huge number of them. Hence, a reconstruction (or interpolation) process is used in order to evaluate the cross-sections at every point required, from (as few as possible) pre-calculated points. With most classical methods (for example: multilinear interpolation which is used in the core code COCAGNE of EDF (Électricité De France)), high accuracy for the reconstruction often requires a lot of pre-calculated points. We propose to use the Tucker decomposition, a low-rank tensor approximation method, to deal with this problem. The Tucker decomposition allows us to capture the most important information (one parameter at a time) to reconstruct the cross-sections. This information is stored as basis functions (called tensor directional basis functions) and the coefficients of the decomposition instead of pre-calculated points. Full reconstruction is done at the core code level using these decompositions. In this paper, a simplified multivariate analysis technique (based on statistical analysis) is also proposed in order to demonstrate that we can improve the quality of the acquired information as well as the accuracy of our approach. Using the Tucker decomposition, we will show in proposed use cases that we can reduce significantly the number of pre-calculated points and the storage size (compared to the multilinear interpolations) while achieving high accuracy for the reconstruction, even on a larger domain of parameters.