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A Posteriori Evaluation of a Physics-Constrained Neural Ordinary Differential Equations Approach Coupled with CFD Solver for Modeling Stiff Chemical Kinetics

Tadbhagya Kumar, Anuj Kumar, Pinaki Pal

TL;DR

CFD simulations of turbulent reacting flows are hampered by stiff chemical kinetics, making detailed mechanisms costly and difficult to couple with solvers. The authors formulate a physics-informed NeuralODE (PC-NODE) by embedding elemental mass-conservation constraints into the training loss, enabling stable, accurate surrogates for stiff chemistry. They train and validate the approach on a hydrogen–air autoignition system using Cantera data, and demonstrate through a posteriori 3D CFD coupling that PC-NODE outperforms purely data-driven NeuralODEs and offers roughly a 3× inference speedup over the full mechanism. The work provides a practical pathway for reliable, fast chemical kinetics surrogates in 3D reacting-flow simulations, with demonstrated robustness to unseen initial conditions.

Abstract

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. These models often require solving a system of coupled stiff ordinary differential equations (ODEs). While deep learning techniques have been experimented with to develop faster surrogate models, they often fail to integrate reliably with CFD solvers. This instability arises because deep learning methods optimize for training error without ensuring compatibility with ODE solvers, leading to accumulation of errors over time. Recently, NeuralODE-based techniques have offered a promising solution by effectively modeling chemical kinetics. In this study, we extend the NeuralODE framework for stiff chemical kinetics by incorporating mass conservation constraints directly into the loss function during training. This ensures that the total mass and the elemental mass are conserved, a critical requirement for reliable downstream integration with CFD solvers. Proof-of-concept studies are performed with physics-constrained neuralODE (PC-NODE) approach for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions. Our results demonstrate that this enhancement not only improves the physical consistency with respect to mass conservation criteria but also ensures better robustness. Lastly, a posteriori studies are performed wherein the trained PC-NODE model is coupled with a 3D CFD solver for computing the chemical source terms. PC-NODE is shown to be more accurate relative to the purely data-driven neuralODE approach. Moreover, PC-NODE also exhibits robustness and generalizability to unseen initial conditions from within (interpolative capability) as well as outside (extrapolative capability) the training regime.

A Posteriori Evaluation of a Physics-Constrained Neural Ordinary Differential Equations Approach Coupled with CFD Solver for Modeling Stiff Chemical Kinetics

TL;DR

CFD simulations of turbulent reacting flows are hampered by stiff chemical kinetics, making detailed mechanisms costly and difficult to couple with solvers. The authors formulate a physics-informed NeuralODE (PC-NODE) by embedding elemental mass-conservation constraints into the training loss, enabling stable, accurate surrogates for stiff chemistry. They train and validate the approach on a hydrogen–air autoignition system using Cantera data, and demonstrate through a posteriori 3D CFD coupling that PC-NODE outperforms purely data-driven NeuralODEs and offers roughly a 3× inference speedup over the full mechanism. The work provides a practical pathway for reliable, fast chemical kinetics surrogates in 3D reacting-flow simulations, with demonstrated robustness to unseen initial conditions.

Abstract

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. These models often require solving a system of coupled stiff ordinary differential equations (ODEs). While deep learning techniques have been experimented with to develop faster surrogate models, they often fail to integrate reliably with CFD solvers. This instability arises because deep learning methods optimize for training error without ensuring compatibility with ODE solvers, leading to accumulation of errors over time. Recently, NeuralODE-based techniques have offered a promising solution by effectively modeling chemical kinetics. In this study, we extend the NeuralODE framework for stiff chemical kinetics by incorporating mass conservation constraints directly into the loss function during training. This ensures that the total mass and the elemental mass are conserved, a critical requirement for reliable downstream integration with CFD solvers. Proof-of-concept studies are performed with physics-constrained neuralODE (PC-NODE) approach for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions. Our results demonstrate that this enhancement not only improves the physical consistency with respect to mass conservation criteria but also ensures better robustness. Lastly, a posteriori studies are performed wherein the trained PC-NODE model is coupled with a 3D CFD solver for computing the chemical source terms. PC-NODE is shown to be more accurate relative to the purely data-driven neuralODE approach. Moreover, PC-NODE also exhibits robustness and generalizability to unseen initial conditions from within (interpolative capability) as well as outside (extrapolative capability) the training regime.
Paper Structure (5 sections, 7 equations, 2 figures)

This paper contains 5 sections, 7 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Physics-constrained neuralODE (PC-NODE) framework for stiff chemical kinetics
  3. Proof-of-concept study
  4. Results and Discussion
  5. Cantera-NODE a posteriori studies

Figures (2)

  • Figure 1: Mean squared error (computed between ground truth and predictions) evolution for the two cases trained with MSE loss function (Eq. \ref{['MSELoss']}) and PC-NODE loss function (Eq. \ref{['pinnloss']}).
  • Figure 2: Temporal predictions from PC-NODE model for temperature and species mass fractions ($Y_{H_2}, Y_{H_2O}$) at initial temperatures: a) 1000 K, and b) 1200 K, and various equivalence ratios ($\phi$). The solid lines represent the ground truth and markers represent the PC-NODE predictions.