While large climate model ensembles are invaluable tools for physically consistent climate prediction, they also present a large burden in terms of computational resources and storage requirements. A complementary approach to large initial-condition ensembles is to train a stochastic generator on fewer runs. While simulations from a statistical model cannot capture the complexity of climate model runs, they can address some specific scientific questions of interest, such as sampling the variability of regional trends. We demonstrate this potential by comparing simulations from a large ensemble and a stochastic generator trained with only four runs, and show that the variability of regional temperature trends is almost indistinguishable. Training stochastic generators on fewer runs might prove especially useful in the context of large climate model intercomparison projects where creating large ensembles for each model is not possible.

In this work, we propose to train a graph neural network via resampling from a graphon estimate obtained from the underlying network data. More specifically, the graphon or the link probability matrix of the underlying network is first obtained from which a new network will be resampled and used during the training process at each layer. Due to the uncertainty induced from the resampling, it helps mitigate the well-known issue of over-smoothing in a graph neural network (GNN) model. Our framework is general, computationally efficient, and conceptually simple. Another appealing feature of our method is that it requires minimal additional tuning during the training process. Extensive numerical results show that our approach is competitive with and in many cases outperform the other over-smoothing reducing GNN training methods.

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