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 optimization process does not require the knowledge of the discontinuities location. In the online phase, 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 and for the 2D double Mach reflection problem, also in the parametric case.

翻译：我们提出了一种新颖的模型降阶框架，能够处理具有多个行波间断的双曲问题解。通过基于优化的方法，我们引入了适当的校准映射，将原始解流形变换为低维流形。该优化过程无需预先了解间断位置。在线阶段，通过人工神经网络恢复降阶解投影至降阶空间的系数。为验证该方法，我们分别在一维Sod激波管问题和二维双马赫反射问题（含参数化情形）中给出了数值结果。