Numerical simulation for climate modeling resolving all important scales is a computationally taxing process. Therefore, to circumvent this issue a low resolution simulation is performed, which is subsequently corrected for bias using reanalyzed data (ERA5), known as nudging correction. The existing implementation for nudging correction uses a relaxation based method for the algebraic difference between low resolution and ERA5 data. In this study, we replace the bias correction process with a surrogate model based on the Deep Operator Network (DeepONet). DeepONet (Deep Operator Neural Network) learns the mapping from the state before nudging (a functional) to the nudging tendency (another functional). The nudging tendency is a very high dimensional data albeit having many low energy modes. Therefore, the DeepoNet is combined with a convolution based auto-encoder-decoder (AED) architecture in order to learn the nudging tendency in a lower dimensional latent space efficiently. The accuracy of the DeepONet model is tested against the nudging tendency obtained from the E3SMv2 (Energy Exascale Earth System Model) and shows good agreement. The overarching goal of this work is to deploy the DeepONet model in an online setting and replace the nudging module in the E3SM loop for better efficiency and accuracy.

翻译：用于气候建模的数值模拟需要解析所有重要尺度，这是一个计算成本高昂的过程。因此，为了规避这一问题，通常采用低分辨率模拟，随后利用再分析数据（ERA5）进行偏差校正，这被称为松弛逼近校正。现有的松弛逼近校正实现基于松弛方法处理低分辨率数据与ERA5数据之间的代数差异。在本研究中，我们采用基于深度算子网络（DeepONet）的代理模型替代偏差校正过程。DeepONet（深度算子神经网络）学习从松弛逼近前的状态（一个泛函）到松弛逼近趋势（另一个泛函）的映射。松弛逼近趋势虽然包含许多低能模态，但属于极高维数据。因此，我们将DeepONet与基于卷积的自编码-解码器（AED）架构相结合，以在低维潜在空间中高效学习松弛逼近趋势。通过对比E3SMv2（能源百亿亿次地球系统模型）获得的松弛逼近趋势，验证了DeepONet模型的准确性，结果显示两者具有良好的一致性。本研究的总体目标是实现DeepONet模型的在线部署，并在E3SM循环中替代松弛逼近模块，以提高效率和精度。