## Abstract

The nonparametric probabilistic method (NPM) for modeling and quantifying model-form uncertainties is a physics-based, computationally tractable, machine learning method for performing uncertainty quantification and model updating. It extracts from data information not captured by a deterministic, high-dimensional model (HDM) of dimension N and infuses it into a counterpart stochastic, hyperreduced, projection-based reduced-order model (SHPROM) of dimension n ≪ N. Here, the robustness and performance of NPM are improved using a two-pronged approach. First, the sensitivities of its stochastic loss function with respect to the hyperparameters are computed analytically, by tracking the complex web of operations underlying the construction of that function. Next, the theoretical number of hyperparameters is reduced from $O(n2)$ to $O(n)$, by developing a network of autoencoders that provides a nonlinear approximation of the dependence of the SHPROM on the hyperparameters. The robustness and performance of the enhanced NPM are demonstrated using two nonlinear, realistic, structural dynamics applications.

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