Organizations: Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115, USA · School of Mechanical Engineering, University of Leeds, Leeds, UK
Abstract
High-fidelity experimental characterization of turbulent premixed flames remains limited by the cost and complexity of advanced diagnostics, particularly under elevated pressures and intense turbulence where measurements of coupled flame morphology and burning dynamics are sparse. Here, we develop a hierarchical multi-fidelity neural network framework (MuFiNNs) to address this challenge by integrating sparse high-fidelity experimental data with structured low-fidelity representations encoding dominant physical trends. The framework combines hierarchical low-fidelity construction with nonlinear multi-fidelity correction to learn coupled geometric and reactive flame behavior while recovering discrepancies that simplified models alone cannot capture. The methodology is applied to expanding turbulent premixed flames to predict three-dimensional flame wrinkling dynamics and turbulent mass burning velocity across varying fuels, pressures, and turbulence intensities. Using experimentally informed low-fidelity trend models with sparse high-fidelity measurements, MuFiNNs accurately reconstruct observed flame behavior, enable interpolation across unseen operating conditions, and demonstrate robust extrapolation beyond the training domain. Importantly, the framework remains effective in noisy, weakly structured, or experimentally inaccessible regimes where conventional data-driven approaches often fail. These results show that hierarchical multi-fidelity learning provides a scalable and physically grounded strategy for predictive combustion modeling in data-limited regimes. More broadly, this work establishes multi-fidelity scientific machine learning as a practical framework for extracting physically meaningful predictive models from sparse experiments, particularly for instability-dominated and turbulence-sensitive reactive flows where high-fidelity data acquisition is demanding.
Turbulent combustion simulations are crucial for many scientific and engineering systems. However, the high cost to fully resolve the complex multiscale and multiphysics behavior makes direct simulation typically infeasible. The equivalent reactor network (ERN) approach attempts to improve computational efficiency by replacing a multidimensional turbulent simulation with a series of much cheaper 0-D and 1-D chemical reactors, providing a surrogate model that retains detailed chemistry at the cost of simplified flow physics. However, their development remains a challenge, often requiring either expert analysis, or automated approaches that sacrifice accuracy. In this work, we develop an automated machine-learning-assisted framework for constructing ERNs of the Sandia-D turbulent methane/air flame. Principal component analysis is first used to reduce high-dimensional thermochemical computational fluid dynamics (CFD) data to a low-dimensional latent space, where k-means clustering identifies physically interpretable flame regions used to initialize a reactor-network graph. This initialization is then refined using finite-difference gradient descent wrapped around non-differentiable Cantera reactor simulations. Across 30 RANS simulations spanning a range of pilot temperatures and inlet methane compositions, the optimized 7-reactor ERN achieves a maximum-temperature R2 score of 0.7945 while preserving a ∼6000× speedup over the CFD solver. Outlet CO prediction remains more challenging, with a final R2 score of −0.4183, but improves substantially from the unoptimized clustering initialization. These results show that unsupervised thermochemical feature extraction can provide effective physics-informed initializations for ERN construction, while gradient-based refinement can significantly improve predictive accuracy without manual reactor-network design.
This paper presents a physics-guided machine learning (PGML) framework for fuel density prediction, integrating physics constraints and domain knowledge into deep learning models to enhance model accuracy and stability. We explore three deep learning architectures -- ConvLSTM, Adaptive Fourier Neural Operator (AFNONet), and Video Vision Transformer (ViViT) -- to model the spatiotemporal evolution of fuel density. Our approach incorporates differentiable physics-informed terms in the loss function, including a mass-conserving fuel transport term and a rate-of-spread estimation. Experimental results, averaged across multiple independent trials, demonstrate that the proposed PGML framework outperforms purely data-driven baselines without physics constraints in both accuracy and stability. This framework enables computationally efficient, physically plausible fire forecasting to support adaptive prescribed burn management.
A novel convolutional autoencoder and neural ODE (CAE-NODE) framework is proposed for a reduced-order model (ROM) applied to transient 2D counterflow flames, as an extension of AE-NODE methods in homogeneous reactive systems to spatially resolved flows. The multidimensional thermochemical fields (256 x 256 grid, 21 variables) obtained from direct numerical simulations (DNS) are used in training the CAE, where convolutional layers learned the underlying spatial correlations, allowing the CAE to construct an unsupervised 3D latent manifold that is physically meaningful, smooth, and continuous in time. This results in a compression ratio of over 400,000 times. The NODE then subsequently learns the continuous-time dynamics on the latent manifold, enabling the prediction of the full temporal evolution of the flames by integrating forward in time from an initial condition. The results demonstrate that the CAE-NODE can accurately capture the entire transient process, including ignition, flame propagation, and the gradual transition to a non-premixed condition, with excellent agreement with the DNS, while adhering to conservation principles at virtually no computational cost compared to the reference DNS. Predictions remain accurate at strain rates outside the training range. Moreover, despite being unsupervised, the learned latent manifold is highly correlated with the flame-state descriptors such as the progress variable, mixture fraction, and the scalar dissipation rate. This study, for the first time, highlights the potential of CAE-NODE for surrogate modeling of unsteady dynamics of multi-dimensional reacting flows.
Mert Yakup Baykan, Weitao Liu, Mohammad Rafi Malik +4