Deep learning-based surrogate models have received wide attention for efficient and cost-effective predictions of fluid flows and combustion, while their hyperparameter settings often lack generalizable guidelines. This study examines two different types of surrogate models, convolutional autoencoder (CAE)-based reduced order models (ROMs) and fully connected autoencoder (FCAE)-based ROMs, for emulating hydrogen-enriched combustion from a triple-coaxial nozzle jet. The performances of these ROMs are discussed in detail, with an emphasis on key hyperparameters, including the number of network layers in the encoder (l), latent vector dimensionality (dim), and convolutional stride (s). The results indicate that a larger l is essential for capturing features in strongly nonlinear flowfields, whereas a smaller l is more effective for less nonlinear distributions, as additional layers may cause overfitting. Specifically, when employing CAE-based ROMs to predict the spatial distribution for H₂ ($X_{H_2}$) with weak nonlinearity, the reconstruction absolute average relative deviation (AARD) from the two-layer model was marginally higher than that of three- and four-layer models, whereas the prediction AARD was approximately 5% lower. A smaller dim yields better performance in weakly nonlinear flowfields but may increase local errors in some cases due to excessive feature compression. A CAE-based ROM with a dim = 10 achieved a notably lower AARD of 4.01% for $X_{H_2}$ prediction. A smaller s may enhance the spatial resolution yet raise computational costs. Under identical hyperparameters, the CAE-based ROM outperformed the FCAE-based ROM in both cost-effectiveness and accuracy, achieving a 35 times faster training speed and lower absolute average relative deviation in prediction. These findings provide important guidelines for hyperparameter selection in training autoencoder (AE)-based ROMs for hydrogen-enriched combustion and other similar engineering design problems.

The parameter optimization of a multi-component isotope separation cascade is a multi-dimensional problem, involving many variables such as cut for stages, feed stage and separation factors. In this paper, a novel metaheuristic algorithm called butterfly optimization algorithm (BOA) is applied for the first time in cascade optimization field. Different objective functions are introduced like D function and a combination of D function and total flow rates. BOA method solves the problem of a 20-stage square cascade optimization to separate Xenon isotopes with the aim of getting the greatest D value or the least flow rates. The optimization results show that the optimal cut is close to the sum of the concentrations of the lightest N′_C isotopes. A 21-stage step cascade is optimized as well to obtain the best working conditions to separate ⁷²Ge and the cut θ is consistent with the experiment results. The calculation results indicate that BOA shows good performance in terms of calculation stability, speed and convergence to global optimum compared with traditional optimization methods and other metaheuristic algorithm like TLBO.