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 assimilation process. Experimental results indicate that LAINR holds certain advantage over existing methods based on AutoEncoders, both in terms of accuracy and efficiency.

翻译：数据同化在众多应用中至关重要，但常面临数据维度高导致的计算成本高以及对底层机制理解不完整等挑战。为解决这些问题，本研究提出了一种新型同化框架，称为隐式神经表征下的潜在同化（LAINR）。通过引入球形隐式神经表征（SINR）以及训练神经网络的数据驱动不确定性估计器，LAINR提升了同化过程的效率。实验结果表明，与基于自编码器的现有方法相比，LAINR在精度和效率方面均具有一定优势。