Enhancing model parameterization with linearly constrained deep generative network for ensemble-based history matching

Ensemble-based data assimilation methods have been widely used for history matching in subsurface reservoir modeling, but struggle to handle the complex nonlinear and non-Gaussian behaviors prevalent in real field applications. To address these limitations, this paper introduces a deep generative model-based parameterization that effectively reduces dimensionality, preserves non-Gaussian patterns, and enhances linearity with observational data. We propose a regularized variational autoencoder (RVAE) comprising three integrated components: (1) an encoder that projects high-dimensional reservoir model parameters into a low-dimensional latent space, capturing complex non-Gaussian distributions; (2) a decoder that maps latent variables back to the original model space, ensuring accurate and geologically consistent reconstruction; and (3) a lightweight linear subnetwork that imposes additional regularization on the latent space, enforcing a linear relationship with observational data. This RVAE framework strengthens ensemble-based methods by aligning the parameterization more closely with their linear-Gaussian assumptions, thereby enhancing compatibility and improving history matching accuracy. Given the high computational cost and time typically required for forward reservoir simulations, we adopt a semi-supervised learning approach, utilizing a dataset where only a small subset of the generated model realizations is paired with production data derived from these simulations. For the network design, the core architecture of the RVAE is based on a convolutional DenseNet, integrated with an attention mechanism to optimize feature representation. Experimental results demonstrate that the proposed approach effectively captures non-Gaussian patterns in permeability fields and significantly improves the assimilation of highly nonlinear production data. • A deep generative parameterization framework is introduced to overcome nonlinear and non-Gaussian challenges in ensemble-based data assimilation. • Improved latent representations are achieved via a regularized variational autoencoder with linear data constraint under semi-supervised learning. • Results demonstrate the framework’s effectiveness in enhancing history matching efficiency and accuracy.