Robin Klein’s MSc thesis work on constraining hyper-reductions methods to be energy-conserving just got published in the Journal of Computational Physics. An outstanding achievement!

In this work, we show how the discrete empirical interpolation method (DEIM) can be adapted so that it conserves kinetic energy, an important quantity in the incompressible Navier-Stokes equations. The basic insight is that DEIM can be formulated as a minimization problem, and the energy conservation condition can be added as a constrained. The resulting constrained minimization problem can be solved exactly and leads to a stable method, also when integrating problems that are periodic in nature over long time periods. Accuracy is guaranteed by oversampling or by regularization, and slow Kolmogorov n-width decay is tackled by using principle interval decomposition, also in an energy-conserving manner.