Abstract Many modern statistical models are used for both insight and prediction when applied to data. When one should optimise parameters through a error loss function. Estimation methods based on multiple steps ahead forecast errors have been shown lead more robust less biased estimates of parameters. However, plausible explanation why this is the case lacking. In paper, we provide explanatio...

A class of one-step methods which obtain a block of r new values at each step are studied. The asymptotic behavior of both implicit and predictor-corrector procedures is examined.

Recent studies on knowledge base completion, the task of recovering missing relationships based on recorded relations, demonstrate the importance of learning embeddings from multi-step relations. However, due to the size of knowledge bases, learning multi-step relations directly on top of observed instances could be costly. In this paper, we propose Implicit ReasoNets (IRNs), which is designed ...

We study the question whether multistep methods or general multi-value methods can be symplectic. Already a precise understanding of symplecticity of such methods is a nontrivial task, because they advance the numerical solution in a higher dimensional space (in contrast to one-step methods). The essential ingredient for the present study is the formal existence of an invariant manifold, on whi...

In this paper, we report a class of stabilized explicit-implicit domain decomposition (SEIDD) methods for the parallel solution of parabolic equations, based on the explicit-implicit domain decomposition (EIDD) methods. EIDD methods are globally non-iterative, non-overlapping domain decomposition methods which, when compared with Schwarz alternating algorithm based parabolic solvers, are comput...

We present an efficient numerical methodology for the 3D computation of incompressible multi-phase flows described by conservative phase field models. We focus here on the case of density matched fluids with different viscosity (Model H). The numerical method employs adaptive mesh refinements (AMR) in concert with an efficient semi-implicit time discretization strategy and a linear, multi-level...