The hyper-reduction problem for reduced-order internal forces evaluation in transient, nonlinear, explicit dynamics is reformulated, employing Mixed-Integer Programming (MIP), taking into account consistency constraints. Constraint reduction is introduced. Resulting quadratures, as well as reduced runs, are compared against the standard Energy Conserving Sampling and Weighting (ECSW) scheme, on a reference example. Rather than searching for optimal performance, the goal is to provide a benchmark solution, for evaluation of heuristic hyper-reduction formulations along with a non-greedy approach.

中文翻译：

---

关于非线性动力学中超还原方案的混合整数公式的说明

考虑到一致性约束，采用混合整数规划（MIP），重新构造了瞬态，非线性，显式动力学中用于降阶内力评估的超还原问题。引入约束减少。在一个参考示例中，将所得的正交以及减少的运行次数与标准的节能采样和加权（ECSW）方案进行了比较。而不是寻求最佳性能，目标是提供一个基准解决方案，用于评估启发式超简化公式以及非贪婪方法。