Constraint-Aware Neural Networks for Riemann Problems
This work addresses the need for reliable neural network surrogates in simulations for domains like fluid dynamics, but it is incremental as it builds on existing methods to incorporate constraints.
The paper tackled the problem of ensuring physical constraints like mass or energy conservation in neural networks used for simulations, by proposing two strategies for constraint-aware neural networks and testing them on Riemann problems in compressible fluid flow, showing that reduced constraint deviation correlates with lower discretization errors across three model problems.
Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtain reliable results. However, standard machine learning algorithms are generally not tailored to respect such constraints. We propose two different strategies to generate constraint-aware neural networks. We test their performance in the context of front-capturing schemes for strongly nonlinear wave motion in compressible fluid flow. Precisely, in this context so-called Riemann problems have to be solved as surrogates. Their solution describes the local dynamics of the captured wave front in numerical simulations. Three model problems are considered: a cubic flux model problem, an isothermal two-phase flow model, and the Euler equations. We demonstrate that a decrease in the constraint deviation correlates with low discretization errors for all model problems, in addition to the structural advantage of fulfilling the constraint.