Physics-informed machine learning for combustion: A review

TL;DR

This review surveys physics-informed machine learning (PIML) applied to combustion, detailing how physical priors—conservation laws, thermodynamics, diffusion, chemical kinetics, and fluid dynamics—can be embedded in ML models to improve physical consistency and data efficiency. It proposes a taxonomy around representation models, optimization processes, and PDE systems, and covers applications from 0D chemical kinetics to reacting flows (laminar, turbulent, and supersonic), as well as other combustion-related domains. The paper highlights methods such as PINNs, neural ODEs, and neural operators (DeepONet, FNO, KC-NODE, ChemKAN), discusses hard vs soft constraints, surrogate modeling, and kinetics discovery, and surveys public data/resources to advance reproducibility. It also candidly addresses challenges like stiffness, multiscale coupling, and data-model discrepancies, offering practical guidelines and identifying opportunities for collaboration between combustion and AI communities. Overall, PIML provides a unified bridge linking physics, models, and data in combustion, enabling improved data usage, more accurate physical models, and robust ML-based predictions with potential for digital twins and accelerated design.

Abstract

Physics-informed machine learning (PIML) represents an emerging paradigm that integrates various forms of physical knowledge into machine learning (ML) components, thereby enhancing the physical consistency of ML models compared to purely data-driven paradigms. The field of combustion, characterized by a rich foundation of physical laws and abundant data, is undergoing a transformation due to PIML. This paper aims to provide a comprehensive overview of PIML for combustion, systematically outlining fundamental principles, significant contributions, key advancements, and available resources. The application of PIML in combustion is categorized into three domains: combustion chemical kinetics, combustion reacting flows, and other combustion-related scenarios. Additionally, current challenges, potential solutions, and practical guidelines for researchers and engineers will be discussed. A primary focus of this review is to demonstrate how combustion laws can be integrated into ML, either through soft or hard constraints, via loss functions or representation models, and within coordinate-to-variable or field-to-field paradigms. This paper shows that PIML offers a unified framework linking physics, model, and data in combustion--integrating physical knowledge in model-to-data simulation and reconstruction tasks, as well as data-to-model modeling tasks--resulting in enhanced data, improved physical models, and more reliable ML models. PIML for combustion presents significant opportunities for both the combustion and ML communities, encouraging greater collaboration and cross-disciplinary engagement.

Figures (13)

• Figure 1: (a) Physics, model, and data are three elements in combustion. Physics represents the real world, physical models and ML models try to represent physics, while data are value records and usually contain physics. Their mutual transformations constitute the forward and inverse problems, which are defined as generating data and modeling, respectively. These transformations also correspond to four basic paradigms of science, as labeled in the figure. (b) PIML can act as a unified bridge connecting physics, model, and data. PIML is constituted by physical model, ML model, and possible data, then each of them can be enhanced by the other two. Models can better represent physics, while data can better reflect physics. The dashed colored arrows represent optional implementations.
• Figure 2: Scenarios under different conditions of physical models and data. PIML is naturally suitable for scenarios where both some physical models and some data are available, which is the most common scenario in practice (indicated by the dashed part). The "$\approx$" sign means that which of the two is superior depends on the specific situation. Here only correct physical models and high-fidelity data are considered.
• Figure 3: Overview of PIML for combustion. Section \ref{['sec: PIML']}, Section \ref{['sec: combus_laws']}, and Section \ref{['sec: resource']} introduce PIML, combustion laws, and resources, respectively. Sections \ref{['sec: PIML_0Dcombus']} to \ref{['sec: PIML_other-combus']} introduce the PIML for combustion chemical kinetics, combustion reacting flows, and other combustion problems, respectively. (Some icons are from Flaticon)
• Figure 4: Schematic of PINNs for solving forward and inverse problems of PDEs. The red dashed parts only exist in inverse problems. The blue, green, yellow, and orange parts represent the representation model, optimization process, PDE system, and derivative computation, respectively.
• Figure 5: PIML for solving ODEs of chemical kinetics. (a) Stiff-PINN for the ROBER problem Ji202108_stiff-PINN. (b) Using the X-TFC algorithm to solve stiff chemical kinetics equations DeFlorio202206_stiff-X-TFC. (c) Kinetics-informed neural networks Gusmao202204_kINN. Figures are reprinted with permission.