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Abstract

Differentiable Earth system models (ESMs) enable powerful applications such as sensitivity analysis, gradient-based calibration, state estimation, boundary flux inversions, uncertainty quantification, and online machine learning. Reverse-mode automatic differentiation (AD) efficiently provides gradients for such tasks, yet models have rarely included this capability because of complex, bespoke numerical algorithms. As part of the Differentiable programming in Julia for Earth system modeling (DJ4Earth) initiative, we present improved capabilities of the AD tool Enzyme.jl and the new compiler transpilation tool Reactant.jl, augmented by sophisticated checkpointing algorithms, which, together make general-purpose AD tractable and efficient for full-fledged ESM components written in Julia. Operating at the low-level virtual machine intermediate representation or multi-level intermediate representation compiler levels, these frameworks support mutable memory, custom kernels, and compiler optimizations before and after differentiation. Julia-specific challenges related to just-in-time compilation and garbage collection are handled efficiently. Reactant further enables automatic performance portability across central processing units, graphics processing units, and tensor processing units, facilitating use of emerging AI-customized high-performance computing architectures. We demonstrate these frameworks on four Julia-based ESM components featuring diverse spatial discretizations and numerical algorithms: the rotating-sphere shallow water model ShallowWaters.jl, the finite-volume ocean model Oceananigans.jl, the finite-element ice sheet model DJUICE.jl, and the spectral atmospheric model SpeedyWeather.jl. Across these ESM components, our tools compute efficient and correct gradients. These results establish a foundation for differentiable, high-performance and performance-portable ESMs that can integrate neural networks for unresolved processes, trained online, enabling next-generation hybrid physics–machine learning ESMs constrained by physical dynamics and observations.