Multi-task latent diffusion model for reconstructing high-fidelity turbulent non-premixed NH3/H2/N2 flames from sparse observations

Abstract

Motivated by both computational and experimental needs, reconstructing high-fidelity turbulent flame fields from low-fidelity, sparse, and damaged observations has emerged as a critical challenge. Turbulence–chemistry interactions produce complex spatiotemporal dynamics, making it challenging to reconstruct multicomponent and multiscale fields, especially with highly sparse data. Furthermore, deterministic models, which are typically designed for single tasks, often perform poorly under out-of-distribution conditions. To overcome these limitations, the current work adopts the diffusion model as a powerful generative inverse problem solver, highlighting its high-quality reconstructions and ability to handle multiple tasks without retraining. Specifically, we first employ a multiscale convolutional autoencoder to construct a latent space that effectively preserves turbulent flame structures while reducing both training and sampling costs. Within this latent space, the diffusion model is trained to learn the data distribution efficiently. The pre-trained generative model, which can unconditionally generate turbulent flame fields, then serves as a repository of flame generation. By incorporating the sparse conditional data using the diffusion posterior sampling algorithm, the model can flexibly adapt to various turbulent flame reconstruction tasks without retraining. The approach is validated on a dataset of two high-pressure turbulent non-premixed NH${}_3$/H${}_2$/N${}_2$ jet flames with ammonia cracking ratios of 14% and 28%. The proposed method exhibits high accuracy levels, demonstrates robustness to sparsity and noise levels, and provides an effective tool of uncertainty evaluation.

Novelty and significance statement

The novelty of this work lies in the application of the latent diffusion model with posterior sampling to reconstruct turbulent reacting flows from sparse observations. Diffusion in the latent space significantly reduces both training and sampling costs, while posterior sampling ensures adaptability to various flame generation scenarios without retraining. The significance of this model lies in its multi-task capability and flexibility. First, the pre-trained unconditional generative model effectively captures both flame structures and thermo-chemical correlations. Second, it generates high-fidelity, complete thermo-chemical fields from a single downsampled scalar field. Third, it handles highly sparse and noisy data, outperforming traditional deterministic models. Finally, it also demonstrates the capability to recover large areas of damaged data.