# An Agentic AI Workflow to Simplify Parameter Estimation of Complex Differential Equation Systems

arXiv: https://arxiv.org/abs/2509.07283 · HTML: https://mlsanity.com/paper/2509.07283/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2025.

## Built on by (most cited first, 1 of 1)

- [ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms](https://mlsanity.com/paper/2512.03476/) (2025)

## Abstract (arXiv)

Parameter identification for mechanistic Ordinary Differential Equation (ODE) models underpins prediction and control in several applications, yet remains a manual and labor-intensive process: datasets are noisy and partial, models can be stiff and complex, and differentiable implementations demand framework expertise. An agentic AI workflow is presented that converts a lightweight, human-readable specification into a compiled, parallel, and differentiable model calibration pipeline. Users supply an XML description of the problem and fill in a Python code skeleton; the agent automatically validates consistency between problem definition and code, and auto-corrects pathologies in the input deck. It transforms Python callables into pure JAX functions for efficient just-in-time compilation and parallelization. The system then orchestrates a two-stage search comprising global exploration of the parameter space followed by gradient-based refinement. The result is an AD-native, reproducible workflow that lowers the barrier to advanced calibration while preserving expert control. An open-source implementation with a documented API and examples is released, enabling rapid movement from problem statement to interpretable ODE models with minimal effort.