“…Another challenge in hierarchical Bayesian inversion is to invert high‐dimensional large spatial fields. We often perform dimension reduction techniques before the actual inversion to make those problems more tractable: principal component analysis (Fouedjio et al., 2021; Grana et al., 2019; Kitanidis & Lee, 2014; Lee & Kitanidis, 2014; Scheidt et al., 2018; Sun & Durlofsky, 2017; Yin et al., 2020), kernel principal component analysis (Sarma et al., 2007, 2008; Scheidt & Caers, 2009), optimized‐based principal component analysis (Vo & Durlofsky, 2015), convolutional autoencoder (Liu & Grana, 2020) and convolutional variational autoencoder (Canchumuni et al., 2019). These dimension reduction techniques are mostly bijective or we can use approximations (Scheidt & Caers, 2009) to project back to high‐dimensional spatial fields.…”