A first sketch: Construction of model defect priors inspired by dynamic time warping

Abstract

Model defects are known to cause biased nuclear data evaluations if they are not taken into account in the evaluation procedure. We suggest a method to construct prior distributions for model defects for reaction models using neighboring isotopes of $^{56}$Fe as an example. A model defect is usually a function of energy and describes the difference between the model prediction and the truth. Of course, neither the truth nor the model defect are accessible. A Gaussian process (GP) enables to define a probability distribution on possible shapes of a model defect by referring to intuitively understandable concepts such as smoothness and the expected magnitude of the defect. Standard specifications of GPs impose a typical length-scale and amplitude valid for the whole energy range, which is often not justified, e.g., when the model covers both the resonance and statistical range. In this contribution, we show how a GP with energy-dependent length-scales and amplitudes can be constructed from available experimental data. The proposed construction is inspired by a technique called dynamic time warping used, e.g., for speech recognition. We demonstrate the feasibility of the data-driven determination of model defects by inferring a model defect of the nuclear models code TALYS for (n,p) reactions of isotopes with charge number between 20 and 30. The newly introduced GP parametrization besides its potential to improve evaluations for reactor relevant isotopes, such as $^{56}$Fe, may also help to better understand the performance of nuclear models in the future.