Recursive Improvement of a Differentiable Scientific Software Ecosystem

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.