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A discrete-module-finite element (DMFE) based hydroelasticity method has been proposed and well developed. Firstly, a freely floating flexible structure is discretized into several macro-submodules in two horizontal directions to perform a multi-rigid-body hydrodynamic analysis. Each macro-submodule is then abstracted to a lumped mass at the center of gravity that bears the external forces including inertia force, hydrodynamic force and hydrostatic force. Apart from external forces, all lumped masses are also subjected to structural forces that reflect the structural deformation features of the original flexible structure. The key to calculating the structural forces is derivation of the equivalent overall structural stiffness matrix with respect to the displacements of all lumped masses, which is tackled following the finite element procedure. More specifically, each macro-submodule is discretized into a number of microelements to derive the corresponding structural stiffness matrix, which is manipulated to a new one including only the nodes at the position of the lumped masses and surrounding boundaries by using the substructure approach, and subsequently the target overall stiffness matrix is obtained by combining together all macro-submodules. Finally, based on equivalence between external and structural forces, the DMFE method establishes the hydroelastic equation on all lumped masses with their displacements as unknown variables. Solving the equation gives the displacement response of all lumped masses. Displacement and structural force responses are first calculated on the interfaces of every two adjacent macro-submodules, after which at any given position of the flexible structure, the recovery of displacement is based on the structural stiffness matrix of the corresponding macro-submodule and the recovery of structural force uses the spline interpolation scheme., Comment: 51 pages, 36 figures, manuscripts for submission to journals

Recently Graph Injection Attack (GIA) emerges as a practical attack scenario on Graph Neural Networks (GNNs), where the adversary can merely inject few malicious nodes instead of modifying existing nodes or edges, i.e., Graph Modification Attack (GMA). Although GIA has achieved promising results, little is known about why it is successful and whether there is any pitfall behind the success. To understand the power of GIA, we compare it with GMA and find that GIA can be provably more harmful than GMA due to its relatively high flexibility. However, the high flexibility will also lead to great damage to the homophily distribution of the original graph, i.e., similarity among neighbors. Consequently, the threats of GIA can be easily alleviated or even prevented by homophily-based defenses designed to recover the original homophily. To mitigate the issue, we introduce a novel constraint -- homophily unnoticeability that enforces GIA to preserve the homophily, and propose Harmonious Adversarial Objective (HAO) to instantiate it. Extensive experiments verify that GIA with HAO can break homophily-based defenses and outperform previous GIA attacks by a significant margin. We believe our methods can serve for a more reliable evaluation of the robustness of GNNs., Comment: ICLR2022, 42 pages, 22 figures

Despite recent success in using the invariance principle for out-of-distribution (OOD) generalization on Euclidean data (e.g., images), studies on graph data are still limited. Different from images, the complex nature of graphs poses unique challenges to adopting the invariance principle. In particular, distribution shifts on graphs can appear in a variety of forms such as attributes and structures, making it difficult to identify the invariance. Moreover, domain or environment partitions, which are often required by OOD methods on Euclidean data, could be highly expensive to obtain for graphs. To bridge this gap, we propose a new framework, called Causality Inspired Invariant Graph LeArning (CIGA), to capture the invariance of graphs for guaranteed OOD generalization under various distribution shifts. Specifically, we characterize potential distribution shifts on graphs with causal models, concluding that OOD generalization on graphs is achievable when models focus only on subgraphs containing the most information about the causes of labels. Accordingly, we propose an information-theoretic objective to extract the desired subgraphs that maximally preserve the invariant intra-class information. Learning with these subgraphs is immune to distribution shifts. Extensive experiments on 16 synthetic or real-world datasets, including a challenging setting -- DrugOOD, from AI-aided drug discovery, validate the superior OOD performance of CIGA., Comment: NeurIPS2022, 46 pages, 72 figures