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The trustworthiness of neural networks is often challenged because they lack the ability to express uncertainty and explain their skill. This can be problematic given the increasing use of neural networks in high stakes decision‐making such as in climate change applications. We address both issues by successfully implementing a Bayesian Neural Network (BNN), where parameters are distributions rather than deterministic, and applying novel implementations of explainable AI (XAI) techniques. The uncertainty analysis from the BNN provides a comprehensive overview of the prediction more suited to practitioners' needs than predictions from a classical neural network. Using a BNN means we can calculate the entropy (i.e., uncertainty) of the predictions and determine if the probability of an outcome is statistically significant. To enhance trustworthiness, we also spatially apply the two XAI techniques of Layer‐wise Relevance Propagation (LRP) and SHapley Additive exPlanation (SHAP) values. These XAI methods reveal the extent to which the BNN is suitable and/or trustworthy. Using two techniques gives a more holistic view of BNN skill and its uncertainty, as LRP considers neural network parameters, whereas SHAP considers changes to outputs. We verify these techniques using comparison with intuition from physical theory. The differences in explanation identify potential areas where new physical theory guided studies are needed. Plain Language Summary: Understanding ocean dynamics and how they are affected by global heating is crucial for understanding climate change impacts. Neural networks are ideally suited to this problem, but do not explain how they make predictions nor express how certain they are of the predictions' accuracy, which considerably limits their trustworthiness for ocean science problems. Here, we address both issues by using a "Bayesian Neural Network" (BNN), which directly expresses prediction uncertainty, and applying explainable AI (XAI) techniques to explain how the BNN arrives at its prediction. The BNN provides a comprehensive overview more suited to addressing the core problem than that provided by classical neural networks. We also apply two XAI techniques (SHAP and LRP) to the BNN and evaluate their trustworthiness by comparing the similarities and differences between their explanations with intuition from physical theory. Any differences offer an opportunity to develop physical theory guided by what the BNN considers important. Key Points: Novel use of a Bayesian Neural Network (BNN) to quantify uncertainty in ocean dynamical regime classifications, giving a holistic predictionExplaining the skill of a BNN using two techniques originating from two different classes of explainable AI: SHapley Additive exPlanation (SHAP) and Layer‐wise Relevance Propagation (LRP)Trustworthiness is evaluated by comparing similarities and differences between SHAP and LRP explanations with intuition from physical theory [ABSTRACT FROM AUTHOR]

The success of deep learning techniques over the last decades has opened up a new avenue of research for weather forecasting. Here, we take the novel approach of using a neural network to predict full probability density functions at each point in space and time rather than a single output value, thus producing a probabilistic weather forecast. This enables the calculation of both uncertainty and skill metrics for the neural network predictions, and overcomes the common difficulty of inferring uncertainty from these predictions. This approach is data-driven and the neural network is trained on theWeatherBench dataset (processed ERA5 data) to forecast geopotential and temperature 3 and 5 days ahead. Data exploration leads to the identification of the most important input variables. In order to increase computational efficiency, several neural networks are trained on small subsets of these variables. The outputs are then combined through a stacked neural network, the first time such a technique has been applied to weather data. Our approach is found to be more accurate than some coarse numerical weather prediction models and as accurate as more complex alternative neural networks, with the added benefit of providing key probabilistic information necessary for making informed weather forecasts. [ABSTRACT FROM AUTHOR]

Wind farm modelling is an area of rapidly increasing interest with numerous analytical and computational-based approaches developed to extend the margins of wind farm efficiency and maximise power production. In this work, we present the novel ML framework WakeNet, which reproduces generalised 2D turbine wake velocity fields at hub-height, with a mean accuracy of 99.8% compared to the solution calculated by the state-of-the-art wind farm modelling software FLORIS. As the generation of sufficient high-fidelity data for network training purposes can be cost-prohibitive, the utility of multi-fidelity transfer learning has also been investigated. Specifically, a network pre-trained on the low-fidelity Gaussian wake model is fine-tuned in order to obtain accurate wake results for the mid-fidelity Curl wake model. The overall performance of WakeNet is validated on various wake steering control and layout optimisation scenarios, obtaining at least 90% of the power gained by the FLORIS optimiser. Moreover, the Curl-based WakeNet provides similar power gains to FLORIS, two orders of magnitude faster. These promising results show that generalised wake modelling with ML tools can be accurate enough to contribute towards robust real-time active yaw and layout optimisation under uncertainty, while producing realistic optimised configurations at a fraction of the computational cost. • WakeNet produces generalised wakes 2 orders of magnitude faster than the Curl model. • The local turbulence and generated power can be approximated from 2D flow predictions. • Multi-fidelity transfer learning reduces the mid-fidelity data required for training. • WakeNet performs yaw and layout optimisation 2 orders of magnitude faster than FLORIS. • Deep Learning can produce fast realistic optimised wind farm configurations. [ABSTRACT FROM AUTHOR]