A Nonlinear Physics-based Reduced Order Model with Convolutional-based Operator Compression

This paper presents a nonlinear reduced-order modeling approach that leverages convolutional operator compression to address the inherent limitations of projection-based ROMs constrained by the Kolmogorov N-width. The proposed method employs nonlinear approximation in the low-dimensional space, enabling more compact representations when solution manifolds exhibit slow N-width decay. Experimental results on parametrized PDE benchmarks demonstrate improved accuracy compared to traditional linear ROMs.