Latent Data Assimilation for Efficient and Accurate Groundwater Modeling

Abstract Groundwater model predictions are often inaccurate due to uncertainties in model structure, heterogeneous parameters, and initial conditions, leading to error accumulation during simulations. Traditional data assimilation (DA) faces severe computational challenges in high‐dimensional systems due to the costly inversion of large covariance matrices. In addition, the inaccurate estimation of background and observation error statistics introduces further biases. To address these challenges, we develop and evaluate an integrated framework that couples a computationally efficient deep learning surrogate model for rapid prediction with Latent Data Assimilation (LDA) to accurately correct simulations. The framework employs dimensionality reduction, specifically Proper Orthogonal Decomposition (POD), to project the high‐dimensional physical state into a low‐dimensional latent space. Data assimilation is then performed in this reduced space using the Ensemble Kalman Filter (EnKF). Results demonstrate that POD provides a robust representation of simulated concentration fields and interpolated observations for dimensionality reduction. The EnKF operating in the latent space effectively reduces prediction errors. Key advantages of the LDA framework include: enabling sparse observations to effectively inform global state updates through the low‐dimensional latent variables, achieving higher accuracy comparable to traditional physical‐space DA while requiring significantly fewer observations, and inherently filtering high‐frequency noise from the initial condition during the dimensionality reduction process. Collectively, these features establish LDA as a powerful and computationally efficient methodology for enhancing predictive accuracy and managing uncertainty in complex and high‐dimensional groundwater systems.