Capturing missing physics in climate model parameterizations using neural differential equations

Understand

We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models.

• NDEs overcome some of the limitations of traditional neural networks (NNs) in fluid dynamical applications in that they can readily incorporate conservation laws and boundary conditions and are stable when integrated over time.
• We advocate a method that employs a 'residual' approach, in which the NN is used to improve upon an existing parameterization through the representation of residual fluxes which are not captured by the base parameterization.
• This reduces the amount of training required and providing a method for capturing up-gradient and nonlocal fluxes.