Bayesian model calibration for wetting processes via simulation-based inference and measure transport

The controlled and precise wetting of drops and films on solid surfaces is fundamental for many energy, health, and manufacturing applications. Often, measuring states and parameters, like velocity fields inside a spreading drop or contact angles on complex surfaces, is difficult or even impossible. Recently, detailed simulations have proven to be a vital tool for learning about the underlying mechanisms as well as for the design of industrial processes. Because we rely more and more on model-based predictions, it is increasingly important to ensure the reliability of these simulations. Therefore, careful model calibration from experimental data is necessary to produce reliable predictions and designs. Here, we use a Bayesian probabilistic approach and describe the uncertainty in model parameters with probability distributions. Our likelihood function includes the costly simulation model of the wetting process. To make the Bayesian model calibration problem tractable, we adopt the measure transport approach to simulation-free inference and construct a probabilistic surrogate for our likelihood function. We demonstrate the applicability of our approach by calibrating the complex Cahn-Hilliard-Navier-Stokes equations with simulated, noisy data of spreading drops.