Abstract

Taking the ubiquitous multiphysical nature of technical systems or physical, chemical and biological processes, respectively, into account when simulating such problems is inevitable in most of the cases for truly reflecting their real-world features. For this purpose, it is typically both mandatory and challenging to consider all (nonlinear) effects of the individual fields as well as their mutual interactions. Only this way, it is ensured that one obtains reliable simulation results eventually. This is particularly true as soon as one approaches, for instance, the threshold range for dimensioning technical systems. Another important topic for enabling truly predictive multiphysics simulations is that the real-world variabilities and uncertainties, such as unknown physical conditions and parameters, are taken into account by way of an adequate uncertainty quantification approach. Particularly challenging problem configurations in this context arise as soon as their stochastic dimensions are rather high, for instance, when uncertainties vary in space. For such scenarios, standard uncertainty quantification methods are typically not capable of providing a reasonable solution. In this presentation, we will propose an advanced computational method for predictive simulation and uncertainty quantification capable of accurately and efficiently solving challenging large-scale multiphysics problems with high stochastic dimensions. Our approach for quantifying the uncertainties in the case of high stochastic dimensions is based on the so-called Bayesian Multi-Fidelity Monte-Carlo (BMFMC) method. We support the BMFMC method by a physics-informed machine learning approach in that powerful data-oriented machine learning techniques are beneficially combined with actual first principles of physics, such that the application of the proposed computational method is ensured to yield solutions fulfilling the respective physical laws. Results obtained for various multiphysics applications will be presented, such as the simulation and UQ of fluid-structure interaction (FSI; two-field interaction of flow and structure), all-solid-state batteries (ASSB; two- or three-field interaction of electrochemistry, i.e., mass and charge conservation, structure and potentially temperature), and thermal elastohydrodynamic lubrication (TEHL; four-field interaction of lubrication, structure as well as temperature in both lubrication and structure domain).