相关论文: Neural network representation of microflows with B…

Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…

Graph neural networks (GNNs) have become a powerful tool for processing graph-structured data but still face challenges in effectively aggregating and propagating information between layers, which limits their performance. We tackle this…

Providing human-understandable insights into the inner workings of neural networks is an important step toward achieving more explainable and trustworthy AI. Existing approaches to such mechanistic interpretability typically require…

Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…

We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…

Despite rapid improvements in the performance of central processing unit (CPU), the calculation cost of simulating chemically reacting flow using CFD remains infeasible in many cases. The application of the convolutional neural networks…

The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However,…

In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation. While the mesh-free nature of PINNs offers significant advantages in handling…

The Gauss--Newton with approximated tensors (GNAT) method is a nonlinear model reduction method that operates on fully discretized computational models. It achieves dimension reduction by a Petrov--Galerkin projection associated with…

In this paper, we propose a numerical method for solving weakly compressible fluid flow based on a dynamical low-rank projector splitting. The low-rank splitting scheme is applied to the Boltzmann equation with BGK collision term, which…

Structural and topological information play a key role in modeling flow and transport through fractured rock in the subsurface. Discrete fracture network (DFN) computational suites such as dfnWorks are designed to simulate flow and…

The $L^2$ gradient flow of the Ginzburg-Landau free energy functional leads to the Allen Cahn equation that is widely used for modeling phase separation. Machine learning methods for solving the Allen-Cahn equation in its strong form suffer…

In this paper, we develop an $O((m \log k) {\rm MSF} (n,m,1))$-time algorithm to find a half-integral node-capacitated multiflow of the maximum total flow-value in a network with $n$ nodes, $m$ edges, and $k$ terminals, where ${\rm MSF}…

Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…

In Bayesian structure learning, we are interested in inferring a distribution over the directed acyclic graph (DAG) structure of Bayesian networks, from data. Defining such a distribution is very challenging, due to the combinatorially…

Gas network planning optimization under emission constraints prioritizes gas supply with the least CO$_2$ intensity. As this problem includes complex physical laws of gas flow, standard optimization solvers cannot guarantee convergence to a…

Flow delegation is a flexible technique to mitigate flow table capacity bottlenecks in Software-defined Networks (SDN). Such bottlenecks occur when SDN switches provide insufficient flow table capacity which leads to performance degradation…

We introduce a novel combination of Bayesian Models (BMs) and Neural Networks (NNs) for making predictions with a minimum expected risk. Our approach combines the best of both worlds, the data efficiency and interpretability of a BM with…

We consider a dissipative flow network that obeys the standard linear nodal flow conservation, and where flows on edges are driven by potential difference between adjacent nodes. We show that in the case when the flow is a monotonically…

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…