Acceleration of a PhysicsBased Machine Learning Approach for Modeling and Quantifying ModelForm Uncertainties and Performing Model Updating

Abstract

The nonparametric probabilistic method (NPM) for modeling and quantifying modelform uncertainties is a physicsbased, computationally tractable, machine learning method for performing uncertainty quantification and model updating. It extracts from data information not captured by a deterministic, highdimensional model (HDM) of dimension N and infuses it into a counterpart stochastic, hyperreduced, projectionbased reducedorder model (SHPROM) of dimension n ≪ N. Here, the robustness and performance of NPM are improved using a twopronged 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.