Manifold Approximation via Transported Subspaces (MATS)

We introduce a model reduction approach for time-dependent nonlinear scalar conservation laws. Our approach, Manifold Approximation via Transported Subspaces (MATS), exploits structure via a nonlinear approximation by transporting reduced subspaces along characteristic curves. The notion of Kolmogorov N-width is extended to account for this new nonlinear approximation. We also present an online efficient time-stepping algorithm based on MATS with costs independent of the dimension of the full model. Numerical results with stiff source terms demonstrate that reduced models based on MATS achieve orders of magnitude speedups compared to full models and traditional (linear) reduced models.