We propose a novel Model Order Reduction framework that is able to handle solutions of hyperbolic problems characterized by multiple travelling discontinuities. By means of an optimization based approach, we introduce suitable calibration maps that allow us to transform the original solution manifold into a lower dimensional one. The novelty of the methodology is represented by the fact that the optimization process does not require the knowledge of the discontinuities location. The optimization can be carried out simply by choosing some reference control points, thus avoiding the use of some implicit shock tracking techniques, which would translate into an increased computational effort during the offline phase. In the online phase, we rely on a non-intrusive approach, where the coefficients of the projection of the reduced order solution onto the reduced space are recovered by means of an Artificial Neural Network. To validate the methodology, we present numerical results for the 1D Sod shock tube problem, for the 2D double Mach reflection problem, also in the parametric case, and for the triple point problem.

翻译：我们提出了一种新颖的模型降阶框架，能够处理以多个行进间断为特征的双曲问题解。通过基于优化的方法，我们引入了适当的校准映射，使得我们能够将原始解流形变换为更低维的流形。该方法的新颖之处在于优化过程无需已知间断位置信息。该优化仅需选择若干参考控制点即可实施，从而避免了使用某些隐式激波追踪技术——此类技术通常会导致离线阶段计算成本显著增加。在线阶段，我们采用非侵入式方法，通过人工神经网络恢复降阶解在降阶空间上投影的系数。为验证该方法，我们给出了二维Sod激波管问题、二维双马赫反射问题（包括参数化情形）以及三重点问题的数值结果。