Structure-Informed Data-Driven Reduced-Order Modeling of Scalar Hyperbolic Conservation Laws via Kinetic Defect Measure

This arXiv paper addresses the challenge of reduced-order modeling for transport-dominated systems where moving fronts and shocks are poorly represented by low-dimensional linear subspaces. The authors propose a structure-informed data-driven ROM based on the kinetic defect formulation, which separates nonlinear dynamics into known characteristic transport and a kinetic entropy defect localized on the shock manifold. This approach leverages the mathematical structure of hyperbolic conservation laws to improve the fidelity of reduced-order models in capturing sharp gradients and discontinuities typical of compressible flow and related transport phenomena.