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Accurate and computationally-viable representations of clouds and turbulence are a long-standing challenge for climate model development. Traditional parameterizations that crudely but efficiently approximate these processes are a leading source of uncertainty in long-term projected warming and precipitation patterns. Machine Learning (ML)-based parameterizations have long been hailed as a promising alternative with the potential to yield higher accuracy at a fraction of the cost of more explicit simulations. However, these ML variants are often unpredictably unstable and inaccurate in \textit{coupled} testing (i.e. in a downstream hybrid simulation task where they are dynamically interacting with the large-scale climate model). These issues are exacerbated in out-of-distribution climates. Certain design decisions such as ``climate-invariant" feature transformation for moisture inputs, input vector expansion, and temporal history incorporation have been shown to improve coupled performance, but they may be insufficient for coupled out-of-distribution generalization. If feature selection and transformations can inoculate hybrid physics-ML climate models from non-physical, out-of-distribution extrapolation in a changing climate, there is far greater potential in extrapolating from observational data. Otherwise, training on multiple simulated climates becomes an inevitable necessity. While our results show generalization benefits from these design decisions, the obtained improvment does not sufficiently preclude the necessity of using multi-climate simulated training data. 

We present Q-functionals, an alternative architecture for continuous control deep reinforcement learning. Instead of returning a single value for a state-action pair, our network transforms a state into a function that can be rapidly evaluated in parallel for many actions, allowing us to efficiently choose high-value actions through sampling. This contrasts with the typical architecture of off-policy continuous control, where a policy network is trained for the sole purpose of selecting actions from the Q-function. We represent our action-dependent Q-function as a weighted sum of basis functions (Fourier, Polynomial, etc) over the action space, where the weights are state-dependent and output by the Q-functional network. Fast sampling makes practical a variety of techniques that require Monte-Carlo integration over Q-functions, and enables action-selection strategies besides simple value-maximization. We characterize our framework, describe various implementations of Q-functionals, and demonstrate strong performance on a suite of continuous control tasks.