Latent assimilation with implicit neural representations for unknown dynamics

Data assimilation is crucial in a wide range of applications, but it often faces challenges such as high computational costs due to data dimensionality and incomplete understanding of underlying mechanisms. To address these challenges, this study presents a novel assimilation framework, termed Latent Assimilation with Implicit Neural Representations (LAINR). By introducing Spherical Implicit Neural Representations (SINR) along with a data -driven uncertainty estimator of the trained neural networks, LAINR enhances efficiency in the assimilation process. Experimental results indicate that LAINR holds a certain advantage over existing methods based on AutoEncoders, both in terms of accuracy and efficiency.