Reproduce “4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models” on OpenResearch

About this paper

Kylen Solvik, Stephen G. Penny, Stephan Hoyer

A data assimilation method, Backprop-4DVar, integrates automatic differentiation and machine learning optimization techniques to enable 4D-Var implementation without manual adjoint models for both numerical and machine learning forecast models. Tested by Google Research and the University of Colorado Boulder, it achieved assimilation accuracy comparable to conventional 4D-Var while demonstrating near-linear computational scaling and up to an order of magnitude faster runtimes for high-dimensional systems.

Key insights

• Automatic differentiation provides a computationally efficient and practical alternative to manually coding tangent linear and adjoint models for 4D-Var, significantly simplifying its implementation.
• By adopting machine learning optimization concepts like backpropagation and Hessian approximation, 4D-Var can be effectively applied to differentiable ML forecast models, enabling their use in real-time data assimilation cycles.
• The use of an approximate Hessian within Backprop-4DVar can yield substantial computational speed-ups, particularly for high-dimensional systems, while maintaining assimilation accuracy comparable to conventional methods.

Summary by alphaXiv.