相关论文: GNN-based physics solver for time-independent PDEs

Graph Neural Networks (GNNs) are a new and increasingly popular family of deep neural network architectures to perform learning on graphs. Training them efficiently is challenging due to the irregular nature of graph data. The problem…

Parameter Estimation (PE) and State Estimation (SE) are the most wide-spread tasks in the system engineering. They need to be done automatically, fast and frequently, as measurements arrive. Deep Learning (DL) holds the promise of tackling…

Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn…

This paper introduces a novel two-stream deep model based on graph convolutional network (GCN) architecture and feed-forward neural networks (FFNN) for learning the solution of nonlinear partial differential equations (PDEs). The model aims…

The successful integration of machine learning models into decision support tools for grid operation hinges on effectively capturing the topological changes in daily operations. Frequent grid reconfigurations and N-k security analyses have…

Learning to reason about relations and dynamics over multiple interacting objects is a challenging topic in machine learning. The challenges mainly stem from that the interacting systems are exponentially-compositional, symmetrical, and…

Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics. However, they still encounter several challenges: 1) Physical laws abide by symmetry, which is a vital inductive bias accounting for model…

Although Finite Element Analysis (FEA) is an integral part of the product design lifecycle, the analysis is computationally expensive, making it unsuitable for many design optimization problems. The deep learning models can be a great…

One of the main challenges in solving time-dependent partial differential equations is to develop computationally efficient solvers that are accurate and stable. Here, we introduce a graph neural network approach to finding efficient PDE…

We explore the feasibility of combining Graph Neural Network-based policy architectures with Deep Reinforcement Learning as an approach to problems in systems. This fits particularly well with operations on networks, which naturally take…

Real-time particle transverse momentum ($p_T$) estimation in high-energy physics demands algorithms that are both efficient and accurate under strict hardware constraints. Static machine learning models degrade under high pileup and lack…

This work addresses the accurate and efficient simulation of physical phenomena governed by parametric Partial Differential Equations (PDEs) characterized by varying boundary conditions, where parametric instances modify not only the…

We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its…

Graph Neural Networks (GNNs) are emerging as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs). However, existing methodologies struggle to combine geometric…

In the last years, an increasing number of learning-based approaches have been proposed to tackle combinatorial optimization problems such as routing problems. Many of these approaches are based on graph neural networks (GNNs) or related…

We address the efficiency issue for the construction of a deep graph neural network (GNN). The approach exploits the idea of representing each input graph as a fixed point of a dynamical system (implemented through a recurrent neural…

Reinforcement learning is well known for its ability to model sequential tasks and learn latent data patterns adaptively. Deep learning models have been widely explored and adopted in regression and classification tasks. However, deep…

Graph Neural Networks (GNNs) is an architecture for structural data, and has been adopted in a mass of tasks and achieved fabulous results, such as link prediction, node classification, graph classification and so on. Generally, for a…

Data-centric methods have shown great potential in understanding and predicting spatiotemporal dynamics, enabling better design and control of the object system. However, deep learning models often lack interpretability, fail to obey…