An Agentic AI Workflow to Simplify Parameter Estimation of Complex Differential Equation Systems (2509.07283v1)

Abstract: Parameter identification for mechanistic Ordinary Differential Equation (ODE) models underpins prediction and control in several applications, yet remains a labor-intensive and brittle process: datasets are noisy and partial, models can be stiff or misspecified, 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 calibration pipeline. Users supply an XML description of the problem and fill in a Python code skeleton; the agent automatically validates consistency between spec and code, and auto-remediates common pathologies. 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 fitted, auditable models with minimal boilerplate.