[2023/11/30 9:30] Benjamin Sanderse

[APJansen]

Note changed time: 9:30

recording

Discovering physics models is an ongoing, fundamental challenge in computational science. In fluid flow problems, this problem is usually known as the “closure problem”, and the art is to discover a “closure model” that represents the effect of the small scales on the large scales. Well-known examples appear in large eddy simulations (LES) and in reduced-order models (ROMs). Recently, it appeared that highly accurate closure models can be constructed by using neural networks. However, integrating the neural network into the physics models (“neural closure models”) is typically prone to numerical instabilities as the training environment does not match the prediction environment. Instead, we investigate learning closure models while they are embedded in a discretized PDE solver by using differentiable programming software. This is a more difficult learning problem and we present several time integration strategies to deal with the adjoint problem. Furthermore, we present a new neural closure model form which allows us to preserve structure, namely kinetic energy conservation, and therefore non-linear stability bounds.