Our new paper explores this question through a broad, open-source benchmark study of hyper-reduction methods for nonlinear finite element problems.
The attached figure highlights the main story:
1. a range of benchmark problems, from nonlinear diffusion and nonlinear elasticity to Sedov blast, Taylor–Green vortex, and triple-point problems
2. a visual comparison of sample mesh constructions, showing how methods such as S-OPT and EQP select very different structures
3. the resulting accuracy vs. online cost tradeoffs, summarized through Pareto fronts
In the paper, we compare DEIM, Q-DEIM, S-OPT, and EQP across these settings.
Key takeaways: there is no universally best hyper-reduction method. Performance depends strongly on the underlying physics, discretization, and even the time integrator. That said, EQP often shows strong performance when balancing accuracy and speedup, while other methods can be competitive depending on the scenario.
Larsson, A., Kim, M., Vales, C., Adriaenssens, S., Copeland, D. M., Choi, Y., & Cheung, S. W. (2026). Hyper-reduction methods for accelerating nonlinear finite element simulations: open source implementation and reproducible benchmarks. arXiv preprint arXiv:2602.23551.


