Coupled online learning as a way to tackle instabilities and biases in neural network parameterizations: general algorithms and Lorenz 96 case study (v1.0)

Abstract

Abstract. Over the last couple of years, machine learning parameterizations have emerged as a potential way to improve the representation of subgrid processes in Earth system models (ESMs). So far, all studies were based on the same three-step approach: first a training dataset was created from a high-resolution simulation, then a machine learning algorithm was fitted to this dataset, before the trained algorithm was implemented in the ESM. The resulting online simulations were frequently plagued by instabilities and biases. Here, coupled online learning is proposed as a way to combat these issues. Coupled learning can be seen as a second training stage in which the pretrained machine learning parameterization, specifically a neural network, is run in parallel with a high-resolution simulation. The high-resolution simulation is kept in sync with the neural network-driven ESM through constant nudging. This enables the neural network to learn from the tendencies that the high-resolution simulation would produce if it experienced the states the neural network creates. The concept is illustrated using the Lorenz 96 model, where coupled learning is able to recover the “true” parameterizations. Further, detailed algorithms for the implementation of coupled learning in 3D cloud-resolving models and the super parameterization framework are presented. Finally, outstanding challenges and issues not resolved by this approach are discussed.

Development of a large-eddy simulation subgrid model based on artificial neural networks: a case study of turbulent channel flow

“…One way forward could be to adjust the training procedure such that it reflects better the a posteriori simulation. A potential elegant way to achieve this may be the online learning procedure proposed by Rasp (2020), where our ANN SGS model would be directly trained in an online a posteriori LES simulation. This would require a simultaneously running DNS that is continuously kept in sync with the LES by constant forcing, such that the ANN can learn directly from the DNS how its predictions should be adjusted for the full LES dynamics and its own errors.…”

Robustness of Neural Network Emulations of Radiative Transfer Parameterizations in a State-of-the-Art General Circulation Model

“…An NN optimization via random search over hyperparameter space resulted in considerable improvements in stability of subgrid physics emulators in the Super-parameterized Community Atmospheric Model version 3.0 (Ott et al, 2020). A coupled online learning approach was proposed where a high-resolution simulation is nudged to the output of a parallel lower-resolution hybrid model run, and the ML-component of the latter is retrained to emulate tendencies of the former, helping to eliminate biases and unstable feedback loops (Rasp, 2020). Random forests approach was successfully used to build a stable ML parameterization of convection (Yuval and O'Gorman, 2020).…”

Combining data assimilation and machine learning to infer unresolved scale parametrization

“…Note that the same approximation was made in a similar setting by [8]. The optimization can now be performed using the approximate loss function…”

“…This has been achieved using two approaches. The first consists in learning a subgrid parameterization of a model from existing physicsbased expensive parametrization schemes [3,4], or from the differences between high-and lowresolution simulations [5][6][7][8]. In those approaches, the unresolved part of the model is represented by an ML process while the core of the model is derived from ODEs.…”