We consider a high-dimension nonlinear computational model (CM) of a dynamical system, parameterized by a vector-valued control parameter (CP), in presence of uncertainties represented by a vector-valued random uncontrolled parameter (UCP). The stochastic response (SR) of the stochastic computational model (SCM) is a vector-valued timediscretized stochastic process in high-dimension, which depends on CP. It is assumed that the numerical cost of a single evaluation of the deterministic CM is large. The predictions, which are performed with the time-discretized SCM, are relative to a CP-dependent vector-valued random observation that is a non-injective nonlinear mapping O of the CP-dependent SR. For the probabilistic updating, we consider a subset of the components of the random observation, called the random identification observation (IO) for which a small target dataset is given. Therefore, the target dataset is associated with a partial observability, which thus corresponds to an incomplete data case. For a given prior probability model of the random CP and UCP, a training dataset is constructed, whose points are realizations of the random triplet made up of the SR, the random IO, and the random CP. Since the numerical cost of a single evaluation of the deterministic CM is assumed large, the training dataset is also of small size. The objective is to construct a predictive statistical surrogate model defined as the family of the updated random observation as a function of CP. The main difficulties of this problem are due (i) to the high dimension, (ii) to a partial observability inducing incomplete data for the target dataset of the IO, (iii) to the non-injectivity of the nonlinear mapping that allows the IO to be computed from the computational stochastic responses, (iv) to the fact that only a small training dataset is available. For these reasons, we propose a methodology [1] based on statistical methods for the necessary construction of reduced representations, on a direct probabilistic learning under constraints based on PLoM constrained by the target dataset [2, 3] and on the use of a weak formulation of the Fourier transform of probability measures [4], and on statistical conditioning exploring the learned dataset. The predictive statistical surrogate model that is constructed can be implemented in the context of online computation. The proposed approach is applied to a problem of nonlinear stochastic dynamics in high dimension within the framework of the mechanics of deformable solids. References [1] C. Soize, R. Ghanem, Surrogate constrained probabilistic learning for under-observed nonlinear computational models, Submitted (2023). [2] C. Soize, R. Ghanem, Data-driven probability concentration and sampling on manifold, Journal of Computational Physics 321 (2016) 242–258. doi:10.1016/j.jcp.2016.05.044. [3] C. Soize, R. Ghanem, Physics-constrained non-Gaussian probabilistic learning on manifolds, International Journal for Numerical Methods in Engineering 121 (1) (2020) 110–145. doi:10.1002/nme.6202. [4] C. Soize, Probabilistic learning constrained by realizations using a weak formulation of fourier transform of probability measures, doi:10.1007/s00180-022-01300-w, published online 23 December 2022.