Constitutive model discovery seeks to identify both the structure and parameters of constitutive models from experimental or monitoring data. In practice, this goal is challenged by the nature of the available data: stresses can be measured only under specific experimental conditions, and kinematic observations can be sparse, noisy, and incomplete. Under these conditions, model discovery frameworks built on the VFM become unreliable, as the VFM requires access to dense full-field kinematics to enable stable inference. An example for VFM-based model discovery is EUCLID approach [1]. In its original formulation, EUCLID enforces parsimony via l1-regularization, yielding sparse models but offering only limited insight into how and why individual candidate terms enter the model during the discovery process. In this contribution, we present a workflow that addresses two core limitations of existing model discovery frameworks: (i) its reliance on dense, low-noise full-field kinematics and (ii) the limited traceability of the constitutive model construction. To address (i), we couple EUCLID with statFEM, using statFEM as a Bayesian data-assimilation layer to reconstruct full-field kinematics with quantified uncertainty from sparse and noisy measurements. The resulting framework is denoted as statFEM–EUCLID [2]. To tackle (ii), we move beyond shrinkage-only selection approaches. While l1-regularization via LASSO yields sparse constitutive models, it provides limited insight into how individual model terms are selected. We therefore employ forward-stepwise sparse optimization algorithms, in particular, LARS and OMP, which construct the constitutive models incrementally and produce an explicit, rank-ordered selection path [3]. This traceable construction exposes how the discovered model structure depends on the information content of the assimilated kinematics and the imposed deformation modes, and highlights which model terms are supported by the available experiments. The approach is demonstrated for isotropic and anisotropic hyperelastic materials. [1] Flaschel et al., “Unsupervised discovery of interpretable hyperelastic constitutive laws,” CMAME, 381, 113852, 2021. [2] Knauf Narouie et al., “Unsupervised constitutive model discovery from sparse and noisy data,” CMAME, 452, 118722, 2026. [3] Urrea-Quintero et al., “Automated constitutive model discovery by pairing sparse regression algorithms with model selection criteria,” CMAME, 449, 118551, 2026.