Graph Neural Network with Local Frame for Molecular Potential Energy Surface

Modeling molecular potential energy surface is of pivotal importance in science. Graph Neural Networks have shown great success in this field. However, their message passing schemes need special designs to capture geometric information and fulfill symmetry requirement like rotation equivariance, leading to complicated architectures. To avoid these designs, we introduce a novel local frame method to molecule representation learning and analyze its expressivity. Projected onto a frame, equivariant features like 3D coordinates are converted to invariant features, so that we can capture geometric information with these projections and decouple the symmetry requirement from GNN design. Theoretically, we prove that given non-degenerate frames, even ordinary GNNs can encode molecules injectively and reach maximum expressivity with coordinate projection and frame-frame projection. In experiments, our model uses a simple ordinary GNN architecture yet achieves state-of-the-art accuracy. The simpler architecture also leads to higher scalability. Our model only takes about 30% inference time and 10% GPU memory compared to the most efficient baselines.Comment: Learning on Graphs (LoG) 202

Neural Common Neighbor with Completion for Link Prediction

Despite its outstanding performance in various graph tasks, vanilla Message Passing Neural Network (MPNN) usually fails in link prediction tasks, as it only uses representations of two individual target nodes and ignores the pairwise relation between them. To capture the pairwise relations, some models add manual features to the input graph and use the output of MPNN to produce pairwise representations. In contrast, others directly use manual features as pairwise representations. Though this simplification avoids applying a GNN to each link individually and thus improves scalability, these models still have much room for performance improvement due to the hand-crafted and unlearnable pairwise features. To upgrade performance while maintaining scalability, we propose Neural Common Neighbor (NCN), which uses learnable pairwise representations. To further boost NCN, we study the unobserved link problem. The incompleteness of the graph is ubiquitous and leads to distribution shifts between the training and test set, loss of common neighbor information, and performance degradation of models. Therefore, we propose two intervention methods: common neighbor completion and target link removal. Combining the two methods with NCN, we propose Neural Common Neighbor with Completion (NCNC). NCN and NCNC outperform recent strong baselines by large margins. NCNC achieves state-of-the-art performance in link prediction tasks. Our code is available at https://github.com/GraphPKU/NeuralCommonNeighbor

Facilitating Graph Neural Networks with Random Walk on Simplicial Complexes

Node-level random walk has been widely used to improve Graph Neural Networks. However, there is limited attention to random walk on edge and, more generally, on $k$-simplices. This paper systematically analyzes how random walk on different orders of simplicial complexes (SC) facilitates GNNs in their theoretical expressivity. First, on $0$-simplices or node level, we establish a connection between existing positional encoding (PE) and structure encoding (SE) methods through the bridge of random walk. Second, on $1$-simplices or edge level, we bridge edge-level random walk and Hodge $1$-Laplacians and design corresponding edge PE respectively. In the spatial domain, we directly make use of edge level random walk to construct EdgeRWSE. Based on the spectral analysis of Hodge $1$-Laplcians, we propose Hodge1Lap, a permutation equivariant and expressive edge-level positional encoding. Third, we generalize our theory to random walk on higher-order simplices and propose the general principle to design PE on simplices based on random walk and Hodge Laplacians. Inter-level random walk is also introduced to unify a wide range of simplicial networks. Extensive experiments verify the effectiveness of our random walk-based methods.Comment: Accepted by NeurIPS 202

Efficient and Consistent Bundle Adjustment on Lidar Point Clouds

Bundle Adjustment (BA) refers to the problem of simultaneous determination of sensor poses and scene geometry, which is a fundamental problem in robot vision. This paper presents an efficient and consistent bundle adjustment method for lidar sensors. The method employs edge and plane features to represent the scene geometry, and directly minimizes the natural Euclidean distance from each raw point to the respective geometry feature. A nice property of this formulation is that the geometry features can be analytically solved, drastically reducing the dimension of the numerical optimization. To represent and solve the resultant optimization problem more efficiently, this paper then proposes a novel concept {\it point clusters}, which encodes all raw points associated to the same feature by a compact set of parameters, the {\it point cluster coordinates}. We derive the closed-form derivatives, up to the second order, of the BA optimization based on the point cluster coordinates and show their theoretical properties such as the null spaces and sparsity. Based on these theoretical results, this paper develops an efficient second-order BA solver. Besides estimating the lidar poses, the solver also exploits the second order information to estimate the pose uncertainty caused by measurement noises, leading to consistent estimates of lidar poses. Moreover, thanks to the use of point cluster, the developed solver fundamentally avoids the enumeration of each raw point (which is very time-consuming due to the large number) in all steps of the optimization: cost evaluation, derivatives evaluation and uncertainty evaluation. The implementation of our method is open sourced to benefit the robotics community and beyond.Comment: 30 pages, 15 figure

Crashworthiness Characterisation of the Car Front Bumper System Based on FEA Analysis

This thesis investigated different designs and material selections of vehicle front bumper system to improve the vehicle crashworthiness during the low impact speed (impact velocity=15km/h, 9.32mph) via FEA simulations. The primary purpose is to identify the most important parameters directly related to the improvement of crashworthiness using numerical parametric study. It is found the cross-section profile, curvature shape, material of the bumper beam, together with the connection to the crash box have been all identified that directly influence the crashworthiness performance of the front bumper system. The bumper system, including the sub-components such as bumper beam, crash box, and the connection methods were carried all the parameters, including a number of folds, curvature shapes and spot welds were in-built while creating them into the CAD models using Solidworks. The final assembled complete bumper system is then imported into the ANSYS for further geometry checks and adjustment. Solver Autodyn is used to perform the FEA simulation, and numbers of results files were generated. Results files such as force reaction, plastic work, and equivalent stress, normal stress was all exported it into the Excel for parametric analysis and discussions. Cross-section Profile-Out of proposed Single fold (fold 1) and Triple fold(fold 3) bumper beam profiles, Double fold (fold 2) bumper beam profile presented the best results of force reaction on both smoothness and force value, while the plastic work remained almost identical to profile fold 1 and 3 gained. Fold 2 profile is considered as a good performer since this profile regulated the deformation behaviour of the beam resulted in a smooth increasing force reaction curve. Where the force reaction curve on both fold 1 and fold 3 were fluctuated dramatically due to catastrophic structural failure. Material-In between structural steel and aluminium alloy used in the bumper beam, while the structural steel made bumper beam achieved good force reaction and plastic work. Switched to aluminium can achieve similar force reaction trend and rate with Cross-section neglectable amount of plastic work reduced. Particularly the weight of the bumper beam is dropped down to 5.357 kg while maintaining similar crashworthiness performance to the structural steel. Crash box Crash box connection- The bonded connection is considered as an ideal scenario and was xvii Sensitivity: Internal favoured in much other literature due to it simplifies the connection setting in the FEA environment since it automatically considers it as perfect contact. Three alternative connection methods were therefore proposed to simulate the more realistic scenario. It defined as welding connection that is constituted by a number of spot welds at left, right, top and bottom of the crash box. Since the bonded method contains no spot welds, a method of weld L+R was indicated by totally 4 spot welds appeared at both left and right side of the crash box. On top of this, 4 additional spot welds were added to the top and bottom of the crash box. Totally 4 spot welds were added only to both the top and bottom of the crash box to extend the comparison. While both bonded and weld L+R methods suffered from buckling effect to the crash box, particularly concentrated at the left and right side with high equivalent and normal stresses. It is discovered weld full method provided promising results by reducing the buckling effect to both left and right faces of the crash box, and also managed to lower the equivalent stress down to 336.48MPa and normal stress on the connection surface down to 66MPa. Weld T+B also observed similar performance when compared with both bonded and weld L+R methods. While registered with very small amount of equivalent and normal stresses, the buckling effect is significantly reduced. This thesis contributed the knowledge to the improvement of vehicle front bumper system. Particularly to the failure mode of both bumper beam and crash box, and offered the related optimisation.N/

An innovative vehicle-mounted GPR technique for fast and efficient monitoring of tunnel lining structural conditions

AbstractThe health status of a railway tunnel should be regularly inspected during its service period to ensure safe operation. Ground-penetrating radar (GPR) has been used as a key technique for tunnel detection; however, so far, the measurements of GPR are only obtainable in contact mode. Such methods cannot meet the requirements of the operational tunnel disease census and regular inspections. Therefore, a new method—vehicle-mounted GPR with long-range detection—has been developed. It consists of six channels. The distance from its air-launched antenna to the tunnel lining is approximately 0.93 m–2.25 m. The scanning rate of each channel is 976 1/s. When the sampling point interval is 5 cm, the maximum speed can reach up to 175 km/h. With its speed and air-launched antenna, this system has a significant advantage over existing methods. That is, for an electrified railway, there is no need for power outages. Indeed, the proposed system will not interrupt normal railway operation. Running tests were carried out on the Baoji–Zhongwei and Xiangfan–Chongqing railway lines, and very good results were obtained