A TVD neural network closure and application to turbulent combustion
This work addresses the challenge of ensuring physical consistency in neural network closures for turbulent combustion modeling, representing an incremental improvement by embedding TVD constraints directly into the training process.
The authors tackled the problem of neural network closures for governing equations failing when small errors violate physical constraints like boundedness, by introducing a total variation diminishing (TVD) neural network closure that strictly enforces non-oscillatory properties through parameter rescaling during training. The model successfully recovers hyperbolic phenomena and anti-diffusion, and in application to turbulent combustion, it suppresses spurious oscillations in scalar fields, outperforming simple penalization methods.
Trained neural networks (NN) have attractive features for closing governing equations. There are many methods that are showing promise, but all can fail in cases when small errors consequentially violate physical reality, such as a solution boundedness condition. A NN formulation is introduced to preclude spurious oscillations that violate solution boundedness or positivity. It is embedded in the discretized equations as a machine learning closure and strictly constrained, inspired by total variation diminishing (TVD) methods for hyperbolic conservation laws. The constraint is exactly enforced during gradient-descent training by rescaling the NN parameters, which maps them onto an explicit feasible set. Demonstrations show that the constrained NN closure model usefully recovers linear and nonlinear hyperbolic phenomena and anti-diffusion while enforcing the non-oscillatory property. Finally, the model is applied to subgrid-scale (SGS) modeling of a turbulent reacting flow, for which it suppresses spurious oscillations in scalar fields that otherwise violate the solution boundedness. It outperforms a simple penalization of oscillations in the loss function.