# Systematic LLM Translation of Legacy Scientific Code to Differentiable Frameworks: Application to a Land Surface Model

arXiv: https://arxiv.org/abs/2606.07681 · HTML: https://mlsanity.com/paper/2606.07681/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 53 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 16 of 16)

- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows](https://mlsanity.com/paper/2203.13760/) (2022)
- [Differentiable Programming for Earth System Modeling](https://mlsanity.com/paper/2208.13825/) (2022)
- [Leveraging Large Language Models for Code Translation and Software Development in Scientific Computing](https://mlsanity.com/paper/2410.24119/) (2024)
- [LLM-Assisted Translation of Legacy FORTRAN Codes to C++: A Cross-Platform Study](https://mlsanity.com/paper/2504.15424/) (2025)
- [Joint Parameter and Parameterization Inference with Uncertainty Quantification through Differentiable Programming](https://mlsanity.com/paper/2403.02215/) (2024)
- [Proof-of-concept: Using ChatGPT to Translate and Modernize an Earth System Model from Fortran to Python/JAX](https://mlsanity.com/paper/2405.00018/) (2024)
- [From Legacy Fortran to Portable Kokkos: An Autonomous Agentic AI Workflow](https://mlsanity.com/paper/2509.12443/) (2025)
- [Fortran2CPP: Automating Fortran-to-C++ Translation using LLMs via Multi-Turn Dialogue and Dual-Agent Integration](https://mlsanity.com/paper/2412.19770/) (2024)
- [Towards fully differentiable neural ocean model with Veros](https://mlsanity.com/paper/2511.17427/) (2025)

## Built on by (most cited first, 2 of 2)

- [A Fortran General-Purpose Transpiler: Proof of Concept](https://mlsanity.com/paper/2608.00130/) (2026)
- [Recursive Improvement of a Differentiable Scientific Software Ecosystem](https://mlsanity.com/paper/2610.04561/) (2026)

## Abstract (arXiv)

Differentiable programming offers transformative capabilities for scientific modeling, enabling gradient-based parameter estimation, sensitivity analysis, and data assimilation. Yet, migrating legacy codebases into differentiable frameworks remains a challenge. We present a five-phase LLM-based agentic pipeline that translates legacy Fortran into JAX: static dependency analysis determines module translation order from the full call graph; iterative compile-repair loops correct errors autonomously; and a Fortran reference oracle enforces numerical parity at the module level before integration and gradient verification. We instantiate and evaluate the pipeline on CLM-ml-v2, a 19,000-line Fortran land surface model, and analyze agent behavior across 73 module translation tasks. The resulting differentiable model computes the complete Jacobian in a single backward pass, recovers physical parameters in eight times fewer steps than gradient-free optimization, and achieves a 24 times wall-clock speedup over sequential Fortran at ensemble size N=2,048. Both the translated model and pipeline infrastructure are released as a reusable framework for differentiating other Earth system model components.