Exploring Randomly Wired Neural Networks for Climate Model Emulation

TL;DR

This work assesses randomly wired neural networks (RandDense) as efficient climate model emulators, comparing them to standard dense architectures (MLP, CNN, CNN-LSTM) on ClimateBench data. RandDense often yields measurable performance gains, notably in simpler models and precipitation tasks, with up to 30.4% improvement in 1M-parameter MLPs and 14 significant improvements across 24 combinations, while prediction speed remains on par with traditional networks. The paper analyzes node operations and shows that random wiring can impact how inputs are processed, not just training, and that certain configurations (e.g., ReLU placement) can affect performance. Overall, RandDense networks emerge as viable direct replacements for dense layers in climate emulation, offering a practical path to cheaper yet effective data-driven Earth system components.

Abstract

Exploring the climate impacts of various anthropogenic emissions scenarios is key to making informed decisions for climate change mitigation and adaptation. State-of-the-art Earth system models can provide detailed insight into these impacts, but have a large associated computational cost on a per-scenario basis. This large computational burden has driven recent interest in developing cheap machine learning models for the task of climate model emulation. In this manuscript, we explore the efficacy of randomly wired neural networks for this task. We describe how they can be constructed and compare them to their standard feedforward counterparts using the ClimateBench dataset. Specifically, we replace the serially connected dense layers in multilayer perceptrons, convolutional neural networks, and convolutional long short-term memory networks with randomly wired dense layers and assess the impact on model performance for models with 1 million and 10 million parameters. We find that models with less complex architectures see the greatest performance improvement with the addition of random wiring (up to 30.4% for multilayer perceptrons). Furthermore, out of 24 different model architecture, parameter count, and prediction task combinations, only one saw a statistically significant performance deficit in randomly wired networks compared to their standard counterparts, with 14 cases showing statistically significant improvement. We also find no significant difference in prediction speed between networks with standard feedforward dense layers and those with randomly wired layers. These findings indicate that randomly wired neural networks may be suitable direct replacements for traditional dense layers in many standard models.

Figures (10)

• Figure 1: Graph representations of a six layer MLP (left) and six layer RandDense network (right) shown side-by-side with their respective node operations in the insets. White circles represent hidden dense layers and their activation functions. Brown circles represent the output layer discussed in Section \ref{['sec: rand nn']}. Lastly, the upper rectangular block represents neural network layers preceding the dense layers. In this case, it is a simple input layer which performs no operation, but other choices such as a convolutional block are possible (see Section \ref{['sec: exp setup']}). For the RandDense network, aggregation from three previous input nodes is done via weighted sum with weights $w_0$, $w_1$, and $w_2$. The summation is followed by ReLU activation and the dense layer. Lastly, two identical copies of the output are sent to two separate nodes downstream.
• Figure 2: Graph representations of the six layer MLP (left) and six layer RandDense network (right) from Figure \ref{['fig: dense and rand dense']} shown side-by-side with their respective adjacency matrices.
• Figure 3: Each of the three baseline models with six MLP dense layers shown next to an example RandDense variation.
• Figure 4: Mean total RMSE of 50 MLP models vs. mean RMSE of 50 RandDense models for both TAS and DTR. The color heatmaps to the right indicate the number of hidden layers. Errorbars show $\pm$ standard error of the mean.
• Figure 5: Mean total RMSE of 50 CNN models vs. mean RMSE of 50 CNN RandDense models for both TAS and DTR. The color heatmaps to the right indicate the number of hidden layers. Errorbars show $\pm$ standard error of the mean.