Resolution-invariant temperature and species field reconstruction using factorized Fourier neural operator (F-FNO) for turbulent jet flames

This paper presents a resolution-invariant deep learning approach to reconstruct complete thermo-chemical scalar fields, including both temperature and species fields, from a single measurable scalar field. The study focuses on auto-ignition-stabilized turbulent non-premixed jet flames under various boundary conditions. Specifically, we employ the factorized Fourier neural operator (F-FNO) to reconstruct temperature and species fields from OH spatial data, significantly reducing model parameters and mitigating overfitting. Resolution-invariant evaluations demonstrate that the model outperforms both convolutional and FNO architectures, with frequency domain analysis highlighting its ability to capture multiscale, fast-evolving phenomena. While statistical comparisons reveal a slight underestimation of upstream fluctuations, correlation and transient analyses confirm the model’s capacity to accurately represent flame structures and dynamic processes. Furthermore, transfer learning demonstrates the model’s ability to extend from vitiated to hot air co-flow conditions with only a small additional dataset and minimal fine-tuning. This reconstruction method bridges correlations between different physical quantities, facilitating the parameterization of implicit governing equations between fields within a neural operator framework. It enables the inference of unmeasured fields based on limited data from either experiments or simulations. Novelty and Significance Statement This work introduces a resolution-invariant factorized Fourier neural operator (F-FNO) for reconstructing complete thermo-chemical scalar fields from a single measurable scalar field across a wide range of conditions. The novelty and significance of this approach lies in several key aspects: First, it extends the traditional value–to–value machine learning framework to field–to–field predictions, which more effectively resolve the spatial distributions of different scalar fields. Second, while prior field reconstruction methods focus on temperature and velocity fields, this work broadens the scope to include complete thermo-chemical scalar field reconstruction. Third, unlike most machine learning approaches that are limited to the training resolution, the current model can be trained on lower resolutions and applied to higher resolutions in a zero-shot manner. Finally, this work combines pre-training and fine-tuning to enable rapid adaptation to scarce-data scenarios.