Recently, a lot of research has been done on the development of Neural Operators. The aim is to map infinite-dimensional functions to infinite-dimensional functions with neural networks. One approach is the Fourier Neural Operator [1]. We use this model to estimate the annual temperature based on the global land-sea-ice distribution. The input of the neural network is the earth’s geography, the output is the global temperature over one year. The training and testing data set is generated with the simulation framework “Klimakoffer” (for more information see Snapshot: Numerical simulations of earth’s climate and [2]).

The best results are achieved when using 4 Fourier integral operator layers, 16 Fourier modes, and a network width of 20. The model thus has 52 433 557 trainable parameters. The remaining specifications are as chosen by Li et al. [1]. It took 4 hours and 26 minutes to train the model on an NVIDIA GeForce RTX 3090 GPU and 0.77 seconds to evaluate it for one given example on a CPU. A relative L2 loss of approximately 0.0025 was achieved during training.

The first video shows one exemplary output. The second animation visualizes the difference between the temperature calculated by the FNO model and the “true” temperature determined by the framework “Klimakoffer”.

References:
[1] Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., Anandkumar, A. (2020). “Fourier Neural Operator for Parametric Partial Differential Equations”, arXiv, https://arxiv.org/abs/2010.08895
[2] Zhuang, K., North, G.R., Stevens, Mark J. (2017). “A NetCDF version of the two-dimensional energy balance model based on the full multigrid algorithm”, SoftwareX