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Predicting sea surface temperature (SST) within the El Ni\~no-Southern Oscillation (ENSO) region has been extensively studied due to its significant influence on global temperature and precipitation patterns. Statistical models such as linear inverse model (LIM), analog forecasting (AF), and recurrent neural network (RNN) have been widely used for ENSO prediction, offering flexibility and relatively low computational expense compared to large dynamic models. However, these models have limitations in capturing spatial patterns in SST variability or relying on linear dynamics. Here we present a modified Convolutional Gated Recurrent Unit (ConvGRU) network for the ENSO region spatio-temporal sequence prediction problem, along with the Ni\~no 3.4 index prediction as a down stream task. The proposed ConvGRU network, with an encoder-decoder sequence-to-sequence structure, takes historical SST maps of the Pacific region as input and generates future SST maps for subsequent months within the ENSO region. To evaluate the performance of the ConvGRU network, we trained and tested it using data from multiple large climate models. The results demonstrate that the ConvGRU network significantly improves the predictability of the Ni\~no 3.4 index compared to LIM, AF, and RNN. This improvement is evidenced by extended useful prediction range, higher Pearson correlation, and lower root-mean-square error. The proposed model holds promise for improving our understanding and predicting capabilities of the ENSO phenomenon and can be broadly applicable to other weather and climate prediction scenarios with spatial patterns and teleconnections., Comment: 13 pages, 7 figures

In a seminal 2007 paper, Andrews introduced a class of combinatorial objects that generalize partitions called $k$-marked Durfee symbols. Multivariate rank generating functions for these objects have been shown by many to have interesting modularity properties at certain vectors of roots of unity. Motivated by recent studies of rank generating functions for strongly unimodal sequences, we apply methods of Andrews to define an analogous class of combinatorial objects called $k$-marked strongly unimodal symbols that generalize strongly unimodal sequences. We establish a multivariate rank generating function for these objects, which we study combinatorially. We conclude by discussing potential quantum modularity properties for this rank generating function at certain vectors of roots of unity., Comment: 10 pages