Constitutive model discovery refers to the task of identifying an appropriate model structure, usually from a predefined model library, while simultaneously inferring its material parameters. The data used to discover constitutive models are usually measured in mechanical tests and thus inevitably corrupted by noise, which, in turn, induces uncertainties. Previously proposed methods for uncertainty quantification in model discovery either require the selection of a prior probability distribution for the material parameters, are restricted to the linear coefficients of the model library or are limited in the expressivity of the inferred parameter probability distribution. However, the selection of a suitable prior probability distribution for Bayesian model discovery is complicated by the large number of material parameters and the fact that the relevance of the material parameters is unknown a priori. We therefore propose a four-step partially Bayesian framework for uncertainty quantification in model discovery [1] that does not require prior selection for the material parameters, also allows for the discovery of constitutive models with inner-non-linear parameters, and is very expressive in modeling the joint probability distribution of the material parameters. First, we augment the available stress-deformation data with a Gaussian process. Second, we approximate the parameter distribution by a normalizing flow [2], which enables us to model complex joint distributions. Third, we distill the parameter distribution by minimizing the Wasserstein-1 distance between the distribution of stress-deformation functions induced by the material parameters and the Gaussian process posterior. Fourth, we perform a Sobol’ sensitivity analysis to obtain a sparse and interpretable model. We demonstrate the capability of the proposed framework for the isotropic Treloar dataset and an anisotropic dataset of human cardiac tissue [3]. References: [1] Anton et al., Uncertainty quantification in model discovery by distilling interpretable material constitutive models from Gaussian process posteriors, arXiv Preprint, arXiv:2510.22345 [cs.LG], 2025. [2] Tabak et al., A Family of Nonparametric Density Estimation Algorithms, Communications on Pure and Applied Mathematics, 66, pp. 145-164, 2013. [3] Sommer et al., Biomechanical properties and microstructure of human ventricular myocardium, Acta Biomaterialia, 24, pp. 172-192, 2015.