Jiaxin Li

Haixin Wang, Jiaxin Li, Anubhav Dwivedi et al.

Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural operators have emerged as a promising technique to solve elliptic PDEs more efficiently by directly mapping the input to solutions. However, existing networks typically cannot handle complex geometries and inhomogeneous boundary values present in the real world. Here we introduce Boundary-Embedded Neural Operators (BENO), a novel neural operator architecture that embeds the complex geometries and inhomogeneous boundary values into the solving of elliptic PDEs. Inspired by classical Green's function, BENO consists of two branches of Graph Neural Networks (GNNs) for interior source term and boundary values, respectively. Furthermore, a Transformer encoder maps the global boundary geometry into a latent vector which influences each message passing layer of the GNNs. We test our model extensively in elliptic PDEs with various boundary conditions. We show that all existing baseline methods fail to learn the solution operator. In contrast, our model, endowed with boundary-embedded architecture, outperforms state-of-the-art neural operators and strong baselines by an average of 60.96\%. Our source code can be found https://github.com/AI4Science-WestlakeU/beno.git.

Huizhi Zhu, Wenxia Xu, Jian Huang et al.

In this paper, we propose a graph neural network, DisGNet, for learning the graph distance matrix to address the forward kinematics problem of the Gough-Stewart platform. DisGNet employs the k-FWL algorithm for message-passing, providing high expressiveness with a small parameter count, making it suitable for practical deployment. Additionally, we introduce the GPU-friendly Newton-Raphson method, an efficient parallelized optimization method executed on the GPU to refine DisGNet's output poses, achieving ultra-high-precision pose. This novel two-stage approach delivers ultra-high precision output while meeting real-time requirements. Our results indicate that on our dataset, DisGNet can achieves error accuracys below 1mm and 1deg at 79.8\% and 98.2\%, respectively. As executed on a GPU, our two-stage method can ensure the requirement for real-time computation. Codes are released at https://github.com/FLAMEZZ5201/DisGNet.

Panhe Feng, Qi She, Lei Zhu et al.

Retrieving occlusion relation among objects in a single image is challenging due to sparsity of boundaries in image. We observe two key issues in existing works: firstly, lack of an architecture which can exploit the limited amount of coupling in the decoder stage between the two subtasks, namely occlusion boundary extraction and occlusion orientation prediction, and secondly, improper representation of occlusion orientation. In this paper, we propose a novel architecture called Occlusion-shared and Path-separated Network (OPNet), which solves the first issue by exploiting rich occlusion cues in shared high-level features and structured spatial information in task-specific low-level features. We then design a simple but effective orthogonal occlusion representation (OOR) to tackle the second issue. Our method surpasses the state-of-the-art methods by 6.1%/8.3% Boundary-AP and 6.5%/10% Orientation-AP on standard PIOD/BSDS ownership datasets. Code is available at https://github.com/fengpanhe/MT-ORL.

Jiaxin Li, Zijian Feng, Qi She et al.

In this paper, we propose MINE to perform novel view synthesis and depth estimation via dense 3D reconstruction from a single image. Our approach is a continuous depth generalization of the Multiplane Images (MPI) by introducing the NEural radiance fields (NeRF). Given a single image as input, MINE predicts a 4-channel image (RGB and volume density) at arbitrary depth values to jointly reconstruct the camera frustum and fill in occluded contents. The reconstructed and inpainted frustum can then be easily rendered into novel RGB or depth views using differentiable rendering. Extensive experiments on RealEstate10K, KITTI and Flowers Light Fields show that our MINE outperforms state-of-the-art by a large margin in novel view synthesis. We also achieve competitive results in depth estimation on iBims-1 and NYU-v2 without annotated depth supervision. Our source code is available at https://github.com/vincentfung13/MINE

Jiaxin Li, Yingcai Bi, Gim Hee Lee

Despite the recent active research on processing point clouds with deep networks, few attention has been on the sensitivity of the networks to rotations. In this paper, we propose a deep learning architecture that achieves discrete $\mathbf{SO}(2)$/$\mathbf{SO}(3)$ rotation equivariance for point cloud recognition. Specifically, the rotation of an input point cloud with elements of a rotation group is similar to shuffling the feature vectors generated by our approach. The equivariance is easily reduced to invariance by eliminating the permutation with operations such as maximum or average. Our method can be directly applied to any existing point cloud based networks, resulting in significant improvements in their performance for rotated inputs. We show state-of-the-art results in the classification tasks with various datasets under both $\mathbf{SO}(2)$ and $\mathbf{SO}(3)$ rotations. In addition, we further analyze the necessary conditions of applying our approach to PointNet based networks. Source codes at https://github.com/lijx10/rot-equ-net

Jiaxin Li, Yingcai Bi, Kun Li et al.

Driven by applications like Micro Aerial Vehicles (MAVs), driver-less cars, etc, localization solution has become an active research topic in the past decade. In recent years, Ultra Wideband (UWB) emerged as a promising technology because of its impressive performance in both indoor and outdoor positioning. But algorithms relying only on UWB sensor usually result in high latency and low bandwidth, which is undesirable in some situations such as controlling a MAV. To alleviate this problem, an Extended Kalman Filter (EKF) based algorithm is proposed to fuse the Inertial Measurement Unit (IMU) and UWB, which achieved 80Hz 3D localization with significantly improved accuracy and almost no delay. To verify the effectiveness and reliability of the proposed approach, a swarm of 6 MAVs is set up to perform a light show in an indoor exhibition hall. Video and source codes are available at https://github.com/lijx10/uwb-localization

Jiaxin Li, Ben M. Chen, Gim Hee Lee

This paper presents SO-Net, a permutation invariant architecture for deep learning with orderless point clouds. The SO-Net models the spatial distribution of point cloud by building a Self-Organizing Map (SOM). Based on the SOM, SO-Net performs hierarchical feature extraction on individual points and SOM nodes, and ultimately represents the input point cloud by a single feature vector. The receptive field of the network can be systematically adjusted by conducting point-to-node k nearest neighbor search. In recognition tasks such as point cloud reconstruction, classification, object part segmentation and shape retrieval, our proposed network demonstrates performance that is similar with or better than state-of-the-art approaches. In addition, the training speed is significantly faster than existing point cloud recognition networks because of the parallelizability and simplicity of the proposed architecture. Our code is available at the project website. https://github.com/lijx10/SO-Net