This tutorial provides a broad introduction to uncertainty quantification (UQ) for computational models, spanning both classical physics-based simulations and modern neural network models. The first part reviews the standard framework for forward and inverse UQ: casting model inputs and outputs as random variables, Polynomial Chaos (PC) expansions as the primary functional representation for forward uncertainty propagation and global sensitivity analysis, and Bayesian inference via Markov chain Monte Carlo (MCMC) and related scalable alternatives (variational inference, transport maps, amortized inference) for inverse UQ, parameter estimation and model calibration. Embedded and structural model error representations are discussed as a means of accounting for the residual discrepancy between models and data, along with high-dimensionality challenges common to both forward and inverse settings. The second part turns to UQ for neural networks, covering MCMC, variational inference, Laplace approximation and ensembling approaches for casting standard PyTorch modules as probabilistic models – implemented in the QUiNN library (github.com/sandialabs/quinn) – and discusses outstanding challenges specific to the neural-network setting, such as the role of the loss landscape, the interplay between priors/regularization and initialization, and the lack of standard benchmarks and diagnostics. The tutorial closes with an overview of relevant software tools and literature for both physics-model and neural-network UQ.
PDF link may fail to capture animations. Alternatively, download the underlying Mac Keynote file of the presentation uq_tutorial_sargsyan.key.