[Paper Review] Hybrid Neural Network PDE Solvers for Reacting Flows

Nilam Tathawadekar, Nguyen Anh Khoa Doan+2 more|arXiv (Cornell University)|Nov 22, 2021

Combustion and flame dynamics29 references4 citations

TL;DR

This paper proposes a hybrid neural network-PDE solver that combines a non-reactive PDE solver with a neural network to correct for chemical reaction effects in reactive flow simulations. By applying neural network corrections at each time step, the method enables accurate, long-term simulation of planar and Bunsen flames with improved stability, generalization, and larger time steps compared to purely data-driven or full reactive PDE approaches.

ABSTRACT

Low-cost simulations of reactive flows are generally hard to achieve. Accurately modeling the propagation of a flame in more than one spatial dimension during statistically significant time windows usually comprises a large range of temporal and spatial scales, which entail high computational costs. Recent machine learning developments have shown great potential in accelerating such simulations. However, purely data-driven approaches, which only make use of an artificial neural network and data, often fail to accurately simulate the evolution of the reactive flow over a sufficiently long time and in a physically consistent manner. Therefore, we propose a hybrid approach that uses a neural network model in combination with a non-reactive PDE solver that provides partial physical information. In this study, we demonstrate that results obtained from non-reactive PDEs can be efficiently corrected at every time step by a hybrid neural network PDE solver model so that the effect of the chemical reactions on the flow field is correctly accounted for. For validation purposes, the obtained simulations of the hybrid model are successfully compared against results coming from a complete set of reactive PDEs, which are inherently more expensive. We demonstrate the validity of the proposed approach on a planar and a Bunsen-type flame at various operating conditions. The hybrid neural-network PDE approach correctly models the flame evolution of the cases under study for significantly long time windows, yields improved generalization, and allows for larger simulation time steps.

Motivation & Objective

• To address the high computational cost of long-time, multi-dimensional reactive flow simulations involving complex chemical reactions.
• To overcome the limitations of purely data-driven neural networks in maintaining physical consistency and long-term accuracy in reactive flow modeling.
• To develop a hybrid framework that leverages physical PDE solvers for baseline dynamics while using neural networks to model reaction-induced corrections.
• To validate the method on planar and Bunsen-type flames under various operating conditions for robustness and generalization.
• To enable larger time steps and improved simulation efficiency without sacrificing physical fidelity.

Proposed method

• A non-reactive PDE solver computes baseline flow dynamics at each time step, providing physically consistent intermediate states.
• A neural network is trained to predict the correction field required to account for chemical reactions in the flow.
• The correction is applied to the non-reactive solution at every time step, effectively injecting reaction effects into the simulation.
• The hybrid model is trained using data generated from a full set of reactive PDEs, ensuring physical accuracy in the target dynamics.
• The architecture is designed to generalize across different operating conditions and flame types.
• The method allows for larger time steps than standard reactive PDE solvers due to improved stability from the physical prior.

Experimental results

Research questions

• RQ1 Can a neural network effectively learn and correct for reaction-induced dynamics in reactive flows when guided by a non-reactive PDE solver?
• RQ2 Does the hybrid approach maintain physical consistency and long-term accuracy in flame simulations compared to purely data-driven models?
• RQ3 Can the hybrid model generalize across different flame types and operating conditions with minimal retraining?
• RQ4 To what extent does the hybrid model reduce computational cost while preserving accuracy relative to full reactive PDE simulations?
• RQ5 Can larger time steps be used in the hybrid simulation without compromising stability or accuracy?

Key findings

• The hybrid model successfully simulates flame evolution for significantly longer time windows than purely data-driven neural networks, maintaining physical consistency.
• The method achieves accurate results comparable to full reactive PDE solvers, validating its physical fidelity.
• The model demonstrates improved generalization across various operating conditions and flame geometries, including planar and Bunsen-type flames.
• Larger simulation time steps are feasible with the hybrid approach, enhancing computational efficiency.
• The neural network correction effectively captures complex reaction effects without requiring full reactive PDE solves at every step.
• The integration of physical PDE dynamics with learned corrections results in stable and accurate long-term simulations.