Behnam Jafarpour

University of Southern California

Subsurface Flow Data Assimilation in Deep Learning–Based Low-Dimensional Latent Spaces

Subsurface flow data assimilation is challenged by complex geologic heterogeneity, high-dimensional and nonlinear models, and limited, noisy observations. Traditional methods often rely on linear-Gaussian update forms, which constrain their ability to capture the complexity of real-world systems. To address these limitations, we propose Latent Space Data Assimilation (LSDA), a deep learning–based framework that performs data assimilation in adaptively learned, low-dimensional latent spaces. LSDA employs convolutional neural networks to jointly encode model parameters and observations into a shared latent space, where the statistical properties are more amenable to simplified (e.g., Gaussian) descriptions. In this space, the original high-dimensional, nonlinear forward simulation model is approximated by a fast, neural network–based low-dimensional mapping. These characteristics enable more effective updates and significantly improve computational efficiency by avoiding repeated PDE solves. We demonstrate the performance of LSDA in the context of geologic CO₂ storage, showing that it produces more consistent parameter estimates while reducing the computational cost of data assimilation.