DJ4Earth: Differentiable, and Performance‐Portable Earth System Modeling via Program Transformations

Journal article

Plain Language Summary: Earth system models are computer programs that simulate how Earth's atmosphere, ocean, ice, and biosphere interact and evolve. These models consist of millions of lines of code and rely on uncertain inputs. To improve accuracy, scientists adjust these inputs to minimize the difference between simulations and observations, measured by a “cost function.” Another computer program can efficiently determine how changes in each input affect the outcome. This calculation, called the gradient of the cost function, would be extremely time‐consuming to code manually. Instead, we use an automatic differentiation (AD) tool called Enzyme, which computes these gradients efficiently and updates them automatically whenever the model changes. As computing systems evolve rapidly, especially those optimized for artificial intelligence (AI), another tool called Reactant enables models to run efficiently across different hardware, from central processing units to graphics processing units and AI accelerators. We demonstrate these methods on four Earth system model components written in the modern programming language Julia: a shallow water model, an ocean model, an ice sheet model, and an atmospheric model. For each, the code generated via AD produces correct gradients of the cost function. This work lays the foundation for combining these differentiated models with machine learning to improve model accuracy efficiently.

Authors: Moses, WS; Cheng, G; Churavy, V; Gelbrecht, M; Klöwer, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Wiley
• Journal: Journal of Advances in Modeling Earth Systems
• Volume: 18
• Issue: 5
• Article number: e2025MS005615
• Publication date: 2026-05-18
• Acceptance date: 2026-04-20
• DOI: 10.1029/2025ms005615
• EISSN: 1942-2466
• ISSN: 1942-2466
• Language: English
• Keywords: differentiable programming; DJ4Earth; Earth system modeling; hybrid data assimilation/machine learning; reverse‐mode automatic differentiation; online learning