  Machine-learning-based parameterizations (i.e. representation of sub-grid
processes) of global climate models or turbulent simulations have recently been
proposed as a powerful alternative to physical, but empirical, representations,
offering a lower computational cost and higher accuracy. Yet, those approaches
still suffer from a lack of generalization and extrapolation beyond the
training data, which is however critical to projecting climate change or
unobserved regimes of turbulence. Here we show that a multi-fidelity approach,
which integrates datasets of different accuracy and abundance, can provide the
best of both worlds: the capacity to extrapolate leveraging the
physically-based parameterization and a higher accuracy using the
machine-learning-based parameterizations. In an application to climate
modeling, the multi-fidelity framework yields more accurate climate projections
without requiring major increase in computational resources. Our multi-fidelity
randomized prior networks (MF-RPNs) combine physical parameterization data as
low-fidelity and storm-resolving historical run's data as high-fidelity. To
extrapolate beyond the training data, the MF-RPNs are tested on high-fidelity
warming scenarios, $+4K$, data. We show the MF-RPN's capacity to return much
more skillful predictions compared to either low- or high-fidelity (historical
data) simulations trained only on one regime while providing trustworthy
uncertainty quantification across a wide range of scenarios. Our approach paves
the way for the use of machine-learning based methods that can optimally
leverage historical observations or high-fidelity simulations and extrapolate
to unseen regimes such as climate change.
