A TVD neural network closure and application to turbulent combustion

TL;DR

This paper introduces a TVD-constrained neural network closure method that enforces physical boundedness in turbulent combustion simulations, effectively preventing spurious oscillations and improving modeling accuracy.

Contribution

A novel neural network closure framework inspired by TVD methods that strictly enforces physical constraints during training, applied successfully to turbulent reacting flow modeling.

Findings

Successfully recovers hyperbolic phenomena and anti-diffusion.

Enforces non-oscillatory solutions in turbulent combustion.

Outperforms penalization methods in suppressing spurious oscillations.

Abstract

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.