# Recursive Improvement of a Differentiable Scientific Software Ecosystem

arXiv: https://arxiv.org/abs/2610.04561 · HTML: https://mlsanity.com/paper/2610.04561/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 61 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Builds on (most cited first, 19 of 19)

- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [SWE-agent: Agent-Computer Interfaces Enable Automated Software Engineering](https://mlsanity.com/paper/2405.15793/) (2024)
- [OpenHands: An Open Platform for AI Software Developers as Generalist Agents](https://mlsanity.com/paper/2407.16741/) (2024)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [MLE-bench: Evaluating Machine Learning Agents on Machine Learning Engineering](https://mlsanity.com/paper/2410.07095/) (2024)
- [Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agents](https://mlsanity.com/paper/2505.22954/) (2025)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [ScienceAgentBench: Toward Rigorous Assessment of Language Agents for Data-Driven Scientific Discovery](https://mlsanity.com/paper/2410.05080/) (2024)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [SciCode: A Research Coding Benchmark Curated by Scientists](https://mlsanity.com/paper/2407.13168/) (2024)
- [LLM Agents Making Agent Tools](https://mlsanity.com/paper/2502.11705/) (2025)
- [Don't Unroll Adjoint: Differentiating SSA-Form Programs](https://mlsanity.com/paper/1810.07951/) (2018)
- [Instead of Rewriting Foreign Code for Machine Learning, Automatically Synthesize Fast Gradients](https://mlsanity.com/paper/2010.01709/) (2020)
- [RExBench: Can coding agents autonomously implement AI research extensions?](https://mlsanity.com/paper/2506.22598/) (2025)
- [SWE-bench Science: Can Coding Agents Resolve Engineering Tasks in Science?](https://mlsanity.com/paper/2608.19799/) (2026)
- [A Benchmark of Selected Algorithmic Differentiation Tools on Some Problems in Computer Vision and Machine Learning](https://mlsanity.com/paper/1807.10129/) (2018)
- [ScienceIDE: Turning World's Scientific Codebase into Agent Learnable Environments](https://mlsanity.com/paper/2609.19134/) (2026)
- [Systematic LLM Translation of Legacy Scientific Code to Differentiable Frameworks: Application to a Land Surface Model](https://mlsanity.com/paper/2606.07681/) (2026)

## Abstract (arXiv)

Differentiable programming connects scientific computation with gradient-based inference, learning and design. Extending these capabilities across a heterogeneous software ecosystem requires specialized effort to implement derivatives, integrate interfaces and evaluate quality. AI coding agents can accelerate this transformation, but translating their capabilities into useful scientific software requires identifying research needs and evaluating how well implementations meet them. We present an environment for agent-driven evolution of differentiable scientific software that connects demand identification, development and quality evaluation. A unified differentiation interface exposes reusable derivative rules alongside existing numerical routines, allowing research tasks to share these capabilities. Research requirements guide development, with implementations assessed through independent derivative checks, workflow tests and performance evaluation. Validated software, research programs and tests become shared resources for subsequent studies. We construct and validate automatic differentiation extensions across 20 packages spanning physical, chemical and biological modeling, with research workflows demonstrating reuse across tasks. Benchmarks demonstrate computational savings over finite differences in gradient evaluation and complete parameter estimation. Research-driven revisions make previously unsupported workflows differentiable, correct derivatives of scientific observables and eliminate redundant computation. Quantum-control and thermal-design studies revise objectives in response to physical evaluation, improving designs while reusing existing derivatives. This work provides a practical approach to expanding differentiable programming across established scientific software and organizing AI agents around the recursive improvement of a shared computational ecosystem.