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

Abstract

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.