Related papers: Adaptive grids as parametrized scale-free networks

Adaptive robust optimization problems have received significant attention in recent years, but remain notoriously difficult to solve when recourse decisions are discrete in nature. In this paper, we propose new reformulation techniques for…

This article proposes a new layered model to represent the spectrum assignment on flexible-grid optical networks. This model can reduce the time-complexity of existing routing and spectrum assignment methods by providing a data structure…

Scaled relative graphs have been originally introduced in the context of convex optimization and have recently gained attention in the control systems community for the graphical analysis of nonlinear systems. Of particular interest in…

This paper proposes a distributed framework for demand response and user adaptation in smart grid networks. In particular, we borrow the concept of congestion pricing in Internet traffic control and show that pricing information is very…

This paper constructs adaptive sparse grid collocation method onto arbitrary order piecewise polynomial space. The sparse grid method is a popular technique for high dimensional problems, and the associated collocation method has been well…

In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…

Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…

We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods…

Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…

We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…

We propose an information-based model for network dynamics in which imperfect information leads to networks where the different vertices have widely different number of edges to other vertices, and where the topology has hierarchical…

We study the sub-grid scale characteristics of a vorticity-transport-based approach for large-eddy simulations. In particular, we consider a multi-dimensional upwind scheme for the vorticity transport equations and establish its properties…

We construct a kinetic model for matter-radiation interactions whose hydrodynamic gradient expansion can be computed analytically up to infinite order in derivatives, in the fully nonlinear regime, and for arbitrary flows. The frequency…

Interpretability methods for deep neural networks mainly focus on the sensitivity of the class score with respect to the original or perturbed input, usually measured using actual or modified gradients. Some methods also use a…

Adaptive control is a classical control method for complex cyber-physical systems, including transportation networks. In this work, we analyze the convergence properties of such methods on exemplar graphs, both theoretically and…

In real applications of the linear model, the explanatory variables are very often naturally grouped, the most common example being the multivariate variance analysis. In the present paper, a quantile model with structure group is…

The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients…

Variational inequalities provide a framework through which many optimisation problems can be solved, in particular, saddle-point problems. In this paper, we study modifications to the so-called Golden RAtio ALgorithm (GRAAL) for variational…

This paper introduces adaptive Bregman proximal gradient algorithms for solving convex composite minimization problems without relying on global relative smoothness or strong convexity assumptions. Building upon recent advances in adaptive…