Tractable Inverse Uncertainty Quantification via Probabilistic Circuits for Applied Mechanics

Inverse uncertainty quantification is essential in applied mechanics, particularly for characterizing the uncertainty in model parameters based on uncertain observations of a model's output. Approaches via Bayesian inference often struggle with the intractability of the likelihood due to the complexities of real-world simulators and experiments. This paper addresses these challenges by proposing a novel approach to tractable inverse uncertainty quantification using probabilistic circuits. The method circumvents the need for an explicit likelihood by directly learning the joint distribution of system inputs and observations through density estimation. Additionally, this approach allows for various probabilistic queries, including marginals, posterior distributions, and sensitivity analysis on a single model, while ensuring computational tractability. Through numerical experiments on representative problems in applied mechanics, we demonstrate the effectiveness and flexibility of our method to real-world problems.