A nudge to the truth: atom conservation as a hard constraint in models of atmospheric composition using an uncertainty-weighted correction

Computational models of atmospheric composition are not always physically consistent. For example, not all models respect fundamental conservation laws such as conservation of atoms in an interconnected chemical system. In well performing models, these nonphysical deviations are often ignored because they are frequently minor, and thus only need a small nudge to perfectly conserve mass. Here we introduce a method that anchors a prediction from any numerical model to physically consistent hard constraints, nudging concentrations to the nearest solution that respects the conservation laws. This closed-form model-agnostic correction uses a single matrix operation to minimally perturb the predicted concentrations to ensure that atoms are conserved to machine precision. To demonstrate this approach, we train a gradient boosting decision tree ensemble to emulate a small reference model of ozone photochemistry and test the effect of the correction on accurate but non-conservative predictions. The nudging approach minimally perturbs the already well-predicted results for most species, but decreases the accuracy of important oxidants, including radicals. We develop a weighted extension of this nudging approach that considers the uncertainty and magnitude of each species in the correction. This species-level weighting approach is essential to accurately predict important low concentration species such as radicals. We find that applying the uncertainty-weighted correction to the nonphysical predictions slightly improves overall accuracy, by nudging the predictions to a more likely mass-conserving solution.

Enforcing Equity in Neural Climate Emulators

Neural network emulators have become an invaluable tool for a wide variety of climate and weather prediction tasks. While showing incredibly promising results, these networks do not have an inherent ability to produce equitable predictions. That is, they are not guaranteed to provide a uniform quality of prediction along any particular class or group of people. This potential for inequitable predictions motivates the need for explicit representations of fairness in these neural networks. To that end, we draw on methods for enforcing analytical physical constraints in neural networks to bias networks towards more equitable predictions. We demonstrate the promise of this methodology using the task of climate model emulation. Specifically, we propose a custom loss function which punishes emulators with unequal quality of predictions across any prespecified regions or category, here defined using human development index (HDI). This loss function weighs a standard loss metric such as mean squared error against another metric which captures inequity along the equity category (HDI), allowing us to adjust the priority of each term before training. Importantly, the loss function does not specify a particular definition of equity to bias the neural network towards, opening the door for custom fairness metrics. Our results show that neural climate emulators trained with our loss function provide more equitable predictions and that the equity metric improves with greater weighting in the loss function. We empirically demonstrate that while there is a tradeoff between accuracy and equity when prioritizing the latter during training, an appropriate selection of the equity priority hyperparameter can minimize loss of performance.

Exploring Randomly Wired Neural Networks for Climate Model Emulation

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 average performance improvements of 4.2% across model complexities and prediction tasks, with substantial performance improvements of up to 16.4% in some cases. Furthermore, we 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.