Structure-preserving SciML for discovering ODEs and SDEs in fluid flows
Benjamin Sanderse
Centrum Wiskunde & Informatica (CWI)
Scientific Computing
Discovering physics models is an ongoing, fundamental challenge in computational science and a crucial aspect of scientific machine learning. In fluid flow problems, this discovery problem is usually known as the “closure problem”, and the art is to discover a “closure model” that represents the effect of (unresolved) small scales on the large scales. Well-known examples appear in large eddy simulations (LES) and in reduced-order models (ROMs). Neural networks hold the promise of providing highly accurate closure models, but they have several important disadvantages, including lack of stability and consistency with physics (e.g. symmetries, conservation laws). In this talk I will explain how we achieve stable and accurate closure models through several new ingredients: (i) energy-conserving neural networks; (ii) group-equivariant and graph neural networks; (iii) a-posteriori and reinforcement learning; (iv) discretization consistency. In addition, I will show how generative approaches based on stochastic differential equations can be used to further improve modelling the effect of neglected scales and include a notion of uncertainty. I will also show how our differentiable physics framework in Julia can be used to tackle the closure problem.