Multimodal Data-Assimilation using the Nonparametric Probabilistic Method for Model-Form Uncertainty Quantification, Stochastic Model Updating, and Digital Twinning

The nonparametric probabilistic method (NPM) introduced in [1] is a physics-based machine learning method for performing model-form (MF) uncertainty quantiőcation (UQ), model updating, and digital twinning. It extracts from experimental, test, operational, or even high-dimensional numerical but sparse data ś collectively referred to here as łreferencež data ś information not captured by a deterministic, low-dimensional, real-time computational model; and infuses it into a łhyperparameterizedž, stochastic version of the real-time model. NPM performs the aforementioned infusion by solving an inverse statistical problem formulated in terms of the hyperparameters and designed such that the mean value and statistical ŕuctuations of some quantities of interest (QoIs) predicted using the real-time stochastic model match target values obtained from the reference data. The performance of NPM hinges upon the efficient minimization of the loss function underlying the formulation of the inverse problem. Because this function is stochastic and nonconvex, it is prone to getting trapped in suboptimal local minima. This scenario is exacerbated when the reference data is scarce, as this compromises the well-posedness of the inverse problem. The present paper addresses these issues by adopting the squared quadratic Wasserstein distance as the measure of dissimilarity between two different sets of data due to its attractive convexity properties, and adapting it to the context of NPM; and by reformulating NPM's inverse statistical problem as a multimodal data-assimilation problem that leverages other available information besides the reference data. The potential of the resulting enhanced NPM for MF-UQ, model updating, and digital twinning is demonstrated using numerical simulations relevant to various structural dynamics applications, including structural health monitoring.