Feng Shi

Feng Shi, Guoping Liang, Yubo Zhao et al.

We present a new splitting method for time-dependent convection-dominated diffusion problems. The original convection diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a convection problem and a diffusion problem are solved successively. The scheme has the following nice features: the convection subproblem is solved explicitly and a multistep technique is introduced to essentially enlarge the stability region so that the resulting scheme behaves like an unconditionally stable scheme; the diffusion subproblem is always self-adjoint and coercive so that it can be solved efficiently using many existing optimal preconditioned iterative solvers. The scheme is then extended for Navier-Stokes equations, where the nonlinear convection is resolved by a linear explicit multistep scheme at the convection step, and only a generalized Stokes problem is needed to solve at the diffusion step with the resulting stiffness matrix being invariant in the time marching process. The new schemes are all free from tuning some stabilization parameters for the convection-dominated diffusion problems. Numerical simulations are presented to demonstrate the stability, convergence and performance of the single-step and multistep variants of the new scheme.

Yiling Chen, Shi Feng, Paul Kattuman et al.

How can we assess the reliability of a dataset without access to ground truth? We introduce the problem of reliability scoring for datasets collected from potentially strategic sources. The true data are unobserved, but we see outcomes of an unknown statistical experiment that depends on them. To benchmark reliability, we define ground-truth-based orderings that capture how much reported data deviate from the truth. We then propose the Gram determinant score, which measures the volume spanned by vectors describing the empirical distribution of the observed data and experiment outcomes. We show that this score preserves several ground-truth based reliability orderings and, uniquely up to scaling, yields the same reliability ranking of datasets regardless of the experiment -- a property we term experiment agnosticism. Experiments on synthetic noise models, CIFAR-10 embeddings, and real employment data demonstrate that the Gram determinant score effectively captures data quality across diverse observation processes.