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

2026-03-30

AI Summary

Calibrating chemical kinetic parameters in reaction-diffusion systems is highly challenging due to strong process coupling, sparse data, and significant noise. This work proposes a physically consistent diffusion-chemistry coupled neural ordinary differential equation (Diff-Chem Neural ODE), which embeds reaction neurons with an Arrhenius structure into a differentiable streamline framework to explicitly model the coupling between diffusion and reaction. The approach enables direct gradient-based optimization of key kinetic parameters without pretraining. It represents the first neural ODE formulation to achieve explicit, physics-consistent coupling of diffusion and chemical kinetics, accurately reconstructing full-species concentration fields by optimizing only a few observable species. The method demonstrates robust convergence under 1–20% noise, achieving over 98% loss reduction, and substantially outperforms purely chemical Neural ODEs that neglect diffusion, while offering significantly higher gradient computation efficiency than fully discretized approaches.

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.

Problem

• chemical kinetics calibration
• reaction-diffusion systems
• sparse and noisy observations
• diffusion-chemistry coupling
• kinetic parameter optimization

Innovation

• Neural ODE
• reaction-diffusion systems
• chemical kinetics optimization
• physics-informed learning
• diffusion-chemistry coupling