Tabulated chemistry models are widely used to simulate large-scale turbulent fires in applications including energy generation and fire safety. Tabulation via piecewise Cartesian interpolation suffers from the curse-of-dimensionality, leading to a prohibitive exponential growth in parameters and memory usage as more dimensions are considered. Artificial neural networks (ANNs) have attracted attention for constructing surrogates for chemistry models due to their ability to perform high-dimensional approximation. However, due to well-known pathologies regarding the realization of suboptimal local minima during training, in practice they do not converge and provide unreliable accuracy. Partition of unity networks (POUnets) are a recently introduced family of ANNs which preserve notions of convergence while performing high-dimensional approximation, discovering a mesh-free partition of space which may be used to perform optimal polynomial approximation. In this work, we assess their performance with respect to accuracy and model complexity in reconstructing unstructured flamelet data representative of nonadiabatic pool fire models. Our results show that POUnets can provide the desirable accuracy of classical spline-based interpolants with the low memory footprint of traditional ANNs while converging faster to significantly lower errors than ANNs. For example, we observe POUnets obtaining target accuracies in two dimensions with 40 to 50 times less memory and roughly double the compression in three dimensions. We also address the practical matter of efficiently training accurate POUnets by studying convergence over key hyperparameters, the impact of partition/basis formulation, and the sensitivity to initialization.

Adcock, Christiane A.; Ananthan, Shreyas A.; Berger-Vergiat, Luc B.; Brazell, Michael B.; Brunhart-Lupo, Nicholas B.; Hu, Jonathan J.; Knaus, Robert C.; Melvin, Jeremy M.; Moser, Bob M.; Mullowney, Paul M.; Rood, Jon R.; Sharma, Ashesh S.; Thomas, Stephen T.; Vijayakumar, Ganesh V.; Williams, Alan B.; Wilson, Robert V.; Yamazaki, Ichitaro Y.; Sprague, Michael S.

Isocontours of Q-criterion with velocity visualized in the wake for two NREL 5-MW turbines operating under uniform-inflow wind speed of 8 m/s. Simulation performed with the hybrid-Nalu-Wind/AMR-Wind solver.

Adcock, Christiane A.; Ananthan, Shreyas A.; Berget-Vergiat, Luc B.; Brazell, Michael B.; Brunhart-Lupo, Nicholas B.; Hu, Jonathan J.; Knaus, Robert C.; Melvin, Jeremy M.; Moser, Bob M.; Mullowney, Paul M.; Rood, Jon R.; Sharma, Ashesh S.; Thomas, Stephen T.; Vijayakumar, Ganesh V.; Williams, Alan B.; Wilson, Robert V.; Yamazaki, Ichitaro Y.; Sprague, Michael S.

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines, capturing the thin boundary layers, and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources.