17 problems

Extension of the projected closed-loop ISS result. Under standard model-order-reduction assumptions, the closed-loop dynamics on the submanifold…

Let synthetic snapshots be generated by CDI and added to a snapshot set for constructing a proper orthogonal decomposition space. Let the sensor choice determine the information av…

SyCo-AE conjecture. The full-space constraint can be approximated by

Asymptotic sharpness conjecture. This upper bound is also asymptotically sharp.

Consider the proposed randomized local approximation procedure, which draws one random initial condition and computes one local basis function at each chosen time point. Assume tha…

Suppose a snapshot matrix is compressed by a singular value decomposition, particularly when no error estimator is available or evaluating one is very costly. Adaptive-enrichment c…

Let local approximation spaces in time be constructed from transfer operators and used to approximate the global solution trajectory. Global-error-bound conjecture. It should also…

The proposed reduced-order modeling ideas use randomized, time-parallel generation of reduced basis functions for a time-dependent problem. Computational-savings conjecture. The pr…

Vanishing-scale transfer-spectrum conjecture. For at least the considered test case, this independence result should transfer to

Reduced-oversampling conjecture. Less oversampling should already be sufficient to extract the significant modes.

Domain-independent local-space conjecture. In general, it should be possible to construct suitable local reduced spaces without knowledge of the global computational domain…

The full-order model (FOM) uses global proper orthogonal decomposition (POD) bases, and the conservative POD-DG model is observed to have better stability properties than the conse…

Delayed-interaction conjecture. We conjecture that for many systems the influence of fluid–fluid interactions will not be significant until after $\epsilon$ is already sufficiently…

Polynomial derivative and error-bound conjecture. A polynomial bound should exist for the derivatives of the singular components in terms of $k$, and consequently a polynomial or e…

The proposed error estimator is considered for parametrized equations and is evaluated using reduced spaces, tolerances, and quantile-based stopping criteria as described above. Ap…

Let $\boldsymbol{a}$ be the vector of reduced-order-model coefficients, and let $\tilde{A}$ and $\widetilde{B}$ denote the linear and nonlinear operators in the data-driven filtere…

Let $A$ and $B$ be the linear and nonlinear operators in a Galerkin reduced-order model, and let $\tilde{A}$ and $\widetilde{B}$ be the corresponding data-driven filtered reduced-o…