TorchDA: A Python package for performing data assimilation with deep learning forward and transformation functions

Data assimilation techniques are often confronted with challenges handling complex high dimensional physical systems, because high precision simulation in complex high dimensional physical systems is computationally expensive and the exact observation functions that can be applied in these systems are difficult to obtain. It prompts growing interest in integrating deep learning models within data assimilation workflows, but current software packages for data assimilation cannot handle deep learning models inside. This study presents a novel Python package seamlessly combining data assimilation with deep neural networks to serve as models for state transition and observation functions. The package, named TorchDA, implements Kalman Filter, Ensemble Kalman Filter (EnKF), 3D Variational (3DVar), and 4D Variational (4DVar) algorithms, allowing flexible algorithm selection based on application requirements. Comprehensive experiments conducted on the Lorenz 63 and a two-dimensional shallow water system demonstrate significantly enhanced performance over standalone model predictions without assimilation. The shallow water analysis validates data assimilation capabilities mapping between different physical quantity spaces in either full space or reduced order space. Overall, this innovative software package enables flexible integration of deep learning representations within data assimilation, conferring a versatile tool to tackle complex high dimensional dynamical systems across scientific domains.