Data-Driven model order reduction for problems with parameter-dependent jump-discontinuities

We propose a data-driven model order reduction (MOR) technique for parametrized partial differential equations that exhibit parameter-dependent jump-discontinuities. Such problems have poor-approximability in linear space and therefore, are challenging standard MOR techniques. build upon the methodology of approximating map between parameter domain expansion coefficients reduced basis via regression. The online stage queries regression recovers approximation solution. to apply this transformed solution results from composing with spatial transform . Unlike (untransformed) solution, it is sufficiently regular along thus, well-approximable low-dimensional space. To recover an we efficient regression-based approximates inverse transform. Our method features decoupled offline stage, benchmark involving hyperbolic parabolic demonstrate its effectiveness. • Combination image registration reduction. Image aligns Regression coefficients. A de-transformation step Experiments report improvements over approximation.