Related papers: An algebraic multiscale method for spatial network…
This paper introduces a chordal decomposition approach for scalable analysis of linear networked systems, including stability, $\mathcal{H}_2$ and $\mathcal{H}_{\infty}$ performance. Our main strategy is to exploit any sparsity within these…
Network analysis has played a key role in knowledge discovery and data mining. In many real-world applications in recent years, we are interested in mining multilayer networks, where we have a number of edge sets called layers, which encode…
This paper presents a neural network based semantic plane detection method utilizing polygon representations. The method can for example be used to solve room layout estimations tasks. The method is built on, combines and further develops…
A new modelling approach for the analysis of weighted networks with ordinal/polytomous dyadic values is introduced. Specifically, it is proposed to model the weighted network connectivity structure using a hierarchical multilayer…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…
In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
The clear understanding of the non-convex landscape of neural network is a complex incomplete problem. This paper studies the landscape of linear (residual) network, the simplified version of the nonlinear network. By treating the gradient…
We present a new methodology for decomposing flows with multiple transports that further extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to approximate transport-dominated flows by a sum of co-moving data fields.…
This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical homogenization, which compresses fine-scale coefficients into…
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…
In this paper we utilize the Proper Orthogonal Decomposition (POD) method for model order reduction in application to Smoluchowski aggregation equations with source and sink terms. In particular, we show in practice that there exists a…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
We study the finite element approximation of linear second-order elliptic partial differential equations in nondivergence form with highly heterogeneous diffusion and drift coefficients. A generalized Cordes condition is imposed to…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
Distributed linear algebraic equation over networks, where nodes hold a part of problem data and cooperatively solve the equation via node-to-node communications, is a basic distributed computation task receiving an increasing research…
Image segmentation relies heavily on neural networks which are known to be overconfident, especially when making predictions on out-of-distribution (OOD) images. This is a common scenario in the medical domain due to variations in…
We propose an online learning algorithm for a class of machine learning models under a separable stochastic approximation framework. The essence of our idea lies in the observation that certain parameters in the models are easier to…