Deep Residual Networks for Flamelet/progress Variable Tabulation with Application to a Piloted Flame with Inhomogeneous Inlet

Criteria to switch from tabulation to neural networks in computational combustion

“…For example suppose N p =4, N v =8, N = 50 and that the table resolution is 50x100x50x100. Then we find using the analysis in section 3 that the most expensive structure is the four-layer network [4,23,27,8]. Under these conditions we have 0.37 ≤ T tab /T ann ≤ 4.24 and 204290.1 ≤ M tab /M ann ≤ 1801801.8.…”

“…In [27] an alternative approach based on deep neural networks with skip connections was employed. The authors reported a memory gain of about 55 when compared to classic tabulation which is much lower than the memory gains reported in the previous studies-perhaps due the increased complexity of the network.…”

“…Overall, the consensus between all studies in the literature is that the use of neural networks reduces the memory requirements and can ease the solving of problems featuring numerous degrees of freedom, for instance soot particle size distribution [28]. In terms of inference time, only the work in [25] reports a reduction in comparison to classic tabulation, as well as the work in [27], however it is not clear whether the comparison in [27] was made on the same basis as with tabulation (the authors reported that the networks were ran on a Graphics Processing Units (GPU) but it is not clear whether the classic tabulation approach was also ran on a GPU).…”

Clustering-Enhanced Deep Learning Method for Computation of Full Detailed Thermochemical States via Solver-Based Adaptive Sampling

“…However, research on this approach has so far been limited to simple cases, necessitating further extensions and investigations. Moreover, several studies also combine machine learning methods and traditional approaches to tackle the complex fuel problems, including using a data-driven method to reduce the full chemistry to a subspace manifold by linear and non-linear models − and using neural networks to predict the flamelet-generated manifolds. − …”

Co-optimized machine-learned manifold models for large eddy simulation of turbulent combustion

“…The primary advantage of this approach is that the amount of memory required to store the neural network is greatly reduced relative to the amount required to store the tables in traditional methods; it is nearly constant with manifold dimensionality as opposed to scaling exponentially [26] . With the trend toward higher manifold dimensionality in flamelet-based models to account for more complex physics, as well as the trend toward heterogeneous architectures in scientific computing, the past few years have seen an explosion of interest in using ANNs to replace flamelet tabulation [27][28][29][30][31][32] . A similar approach has been applied to replace the linear reconstruction process for PCA, and has become the prefered approach for PCA-based models [33][34][35] : first, a truncated set of PCs is generated using PCA on a set of thermochemical state data, and subsequently a nonlinear regression (e.g., a neural network) is fit to predict the desired outputs based on these components.…”