arXiv subjects

Longxiang Jiang

Publications and source records attributed to Longxiang Jiang.

3 recordsLinked to original sources

arXiv2024

Combining physics-informed graph neural network and finite difference for solving forward and inverse spatiotemporal PDEs

The great success of Physics-Informed Neural Networks (PINN) in solving partial differential equations (PDEs) has significantly advanced our simulation and understanding of complex physical systems in science and engineering. However, many PINN-like methods are poorly scalable and are limited to in-sample scenarios. To address these challenges, this work proposes a novel discrete approach termed Physics-Informed Graph Neural Network (PIGNN) to solve forward and inverse nonlinear PDEs. In particular, our approach seamlessly integrates the strength of graph neural networks (GNN), physical equations and finite difference to approximate solutions of physical systems. Our approach is compared with the PINN baseline on three well-known nonlinear PDEs (heat, Burgers and FitzHugh-Nagumo). We demonstrate the excellent performance of the proposed method to work with irregular meshes, longer time steps, arbitrary spatial resolutions, varying initial conditions (ICs) and boundary conditions (BCs) by conducting extensive numerical experiments. Numerical results also illustrate the superiority of our approach in terms of accuracy, time extrapolability, generalizability and scalability. The main advantage of our approach is that models trained in small domains with simple settings have excellent fitting capabilities and can be directly applied to more complex situations in large domains.

math.NA↗

arXiv2023

PhyGNNet: Solving spatiotemporal PDEs with Physics-informed Graph Neural Network

Solving partial differential equations (PDEs) is an important research means in the fields of physics, biology, and chemistry. As an approximate alternative to numerical methods, PINN has received extensive attention and played an important role in many fields. However, PINN uses a fully connected network as its model, which has limited fitting ability and limited extrapolation ability in both time and space. In this paper, we propose PhyGNNet for solving partial differential equations on the basics of a graph neural network which consists of encoder, processer, and decoder blocks. In particular, we divide the computing area into regular grids, define partial differential operators on the grids, then construct pde loss for the network to optimize to build PhyGNNet model. What's more, we conduct comparative experiments on Burgers equation and heat equation to validate our approach, the results show that our method has better fit ability and extrapolation ability both in time and spatial areas compared with PINN.

cs.NE↗

arXiv2022

Confidence-Aware Active Feedback for Interactive Instance Search

Online relevance feedback (RF) is widely utilized in instance search (INS) tasks to further refine imperfect ranking results, but it often has low interaction efficiency. The active learning (AL) technique addresses this problem by selecting valuable feedback candidates. However, mainstream AL methods require an initial labeled set for a cold start and are often computationally complex to solve. Therefore, they cannot fully satisfy the requirements for online RF in interactive INS tasks. To address this issue, we propose a confidence-aware active feedback method (CAAF) that is specifically designed for online RF in interactive INS tasks. Inspired by the explicit difficulty modeling scheme in self-paced learning, CAAF utilizes a pairwise manifold ranking loss to evaluate the ranking confidence of each unlabeled sample. The ranking confidence improves not only the interaction efficiency by indicating valuable feedback candidates but also the ranking quality by modulating the diffusion weights in manifold ranking. In addition, we design two acceleration strategies, an approximate optimization scheme and a top-K search scheme, to reduce the computational complexity of CAAF. Extensive experiments on both image INS tasks and video INS tasks searching for buildings, landscapes, persons, and human behaviors demonstrate the effectiveness of the proposed method. Notably, in the real-world, large-scale video INS task of NIST TRECVID 2021, CAAF uses 25% fewer feedback samples to achieve a performance that is nearly equivalent to the champion solution. Moreover, with the same number of feedback samples, CAAF's mAP is 51.9%, significantly surpassing the champion solution by 5.9%. Code is available at https://github.com/nercms-mmap/caaf.

cs.CV↗