Physics-Enforced Neural Ordinary Differential Equation for Chemical Kinetics Optimization in Reaction-Diffusion Systems

TL;DR

This paper introduces a physics-informed neural ODE model for chemical kinetics in reaction-diffusion systems, enabling accurate, robust, and efficient parameter estimation even with noisy data.

Contribution

It embeds Arrhenius-structured reaction neurons into a differentiable framework, explicitly modeling diffusion coupling for improved kinetics calibration.

Findings

Reproduces species profiles with near-reference accuracy.

More robust than pure chemistry Neural ODEs, especially under noisy data.

Provides substantial speedups in gradient evaluation.

Abstract

Calibrating chemical kinetics in a reaction-diffusion system is challenging because of complex dynamics governed by tightly coupled chemistry and transport, while experimental observations are often sparse and noisy. We propose a physics consistent diffusion-chemistry coupled neural ordinary differential equation (Diff-Chem Neural ODE) that embeds Arrhenius-structured reaction neurons into a fully differentiable streamline formulation and explicitly accounts for diffusion coupling. This design enables direct gradient-based analysis of kinetic parameters without sampling-based pretraining. We validate this method on burner-stabilized flat and stagnation reacting flows using mechanisms spanning different stiffness ranges. The proposed method reproduces species profiles with near-reference accuracy, whereas a pure chemistry Neural ODE that neglects diffusion coupling may misplace ignition and generate an incorrect thin reaction zone. Diff-Chem Neural ODE is more robust than pure chemistry Neural ODE and provides substantial speedups for gradient evaluation compared with fully discretized computations. In kinetics refinement, optimizing only a limited set of "primal" species reduces the loss by over 98% and simultaneously recovers unobserved variables, demonstrating physically consistent global control. Finally, tests with 1-20% noise in the objective show stable convergence without local overfitting, supporting its applicability under noisy measurements.