Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference

Simulations of complex phenomena are crucial in the natural sciences and engineering for different scenarios, e.g., for gaining system understanding, prediction of future scenarios, risk assessment, or system design. However, often they are based on complex ordinary differential equations or partial differential equations which may not have closed-form solutions and may have to be solved using expensive numerical methods. To overcome computational overhead, the field of surrogate models (Zhu and Zabaras, 2018; Gramacy, 2020; Lavin et al., 2021) has emerged which provide fast approximations of computationally expensive simulation. Examples are polynomial chaos expansion (Wiener, 1938; Sudret, 2008; Oladyshkin and Nowak, 2012; Bürkner et al., 2023), Gaussian processes (Rasmussen and Williams, 2005) or neural networks (Goodfellow et al., 2016). Recently there has been a great interest in applying surrogate models in relevant areas, for example in hydrology (Mohammadi et al., 2018; Tarakanov and Elsheikh, 2019; Zhang et al., 2020), in fluid dynamics (Meyer et al., 2021), in climate prediction (Kuehnert et al., 2022), or in systems biology (Renardy et al., 2018; Alden et al., 2020).