PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction

The use of machine learning in fluid dynamics is becoming more common to expedite the computation when solving forward and inverse problems of partial differential equations. Yet, a notable challenge with existing convolutional neural network (CNN)-based methods for data fidelity enhancement is their reliance on specific low-fidelity data patterns and distributions during the training phase. In addition, the CNN-based method essentially treats the flow reconstruction task as a computer vision task that prioritizes the element-wise precision which lacks a physical and mathematical explanation. This dependence can dramatically affect the models' effectiveness in real-world scenarios, especially when the low-fidelity input deviates from the training data or contains noise not accounted for during training. The introduction of diffusion models in this context shows promise for improving performance and generalizability. Unlike direct mapping from a specific low-fidelity to a high-fidelity distribution, diffusion models learn to transition from any low-fidelity distribution towards a high-fidelity one. Our proposed model - Physics-informed Residual Diffusion, demonstrates the capability to elevate the quality of data from both standard low-fidelity inputs, to low-fidelity inputs with injected Gaussian noise, and randomly collected samples. By integrating physics-based insights into the objective function, it further refines the accuracy and the fidelity of the inferred high-quality data. Experimental results have shown that our approach can effectively reconstruct high-quality outcomes for two-dimensional turbulent flows from a range of low-fidelity input conditions without requiring retraining.

ReRoGCRL: Representation-based Robustness in Goal-Conditioned Reinforcement Learning

While Goal-Conditioned Reinforcement Learning (GCRL) has gained attention, its algorithmic robustness against adversarial perturbations remains unexplored. The attacks and robust representation training methods that are designed for traditional RL become less effective when applied to GCRL. To address this challenge, we first propose the Semi-Contrastive Representation attack, a novel approach inspired by the adversarial contrastive attack. Unlike existing attacks in RL, it only necessitates information from the policy function and can be seamlessly implemented during deployment. Then, to mitigate the vulnerability of existing GCRL algorithms, we introduce Adversarial Representation Tactics, which combines Semi-Contrastive Adversarial Augmentation with Sensitivity-Aware Regularizer to improve the adversarial robustness of the underlying RL agent against various types of perturbations. Extensive experiments validate the superior performance of our attack and defence methods across multiple state-of-the-art GCRL algorithms. Our tool ReRoGCRL is available at https://github.com/TrustAI/ReRoGCRL.

U3DS$^3$: Unsupervised 3D Semantic Scene Segmentation

Contemporary point cloud segmentation approaches largely rely on richly annotated 3D training data. However, it is both time-consuming and challenging to obtain consistently accurate annotations for such 3D scene data. Moreover, there is still a lack of investigation into fully unsupervised scene segmentation for point clouds, especially for holistic 3D scenes. This paper presents U3DS$^3$, as a step towards completely unsupervised point cloud segmentation for any holistic 3D scenes. To achieve this, U3DS$^3$ leverages a generalized unsupervised segmentation method for both object and background across both indoor and outdoor static 3D point clouds with no requirement for model pre-training, by leveraging only the inherent information of the point cloud to achieve full 3D scene segmentation. The initial step of our proposed approach involves generating superpoints based on the geometric characteristics of each scene. Subsequently, it undergoes a learning process through a spatial clustering-based methodology, followed by iterative training using pseudo-labels generated in accordance with the cluster centroids. Moreover, by leveraging the invariance and equivariance of the volumetric representations, we apply the geometric transformation on voxelized features to provide two sets of descriptors for robust representation learning. Finally, our evaluation provides state-of-the-art results on the ScanNet and SemanticKITTI, and competitive results on the S3DIS, benchmark datasets.

Combating Bilateral Edge Noise for Robust Link Prediction

Although link prediction on graphs has achieved great success with the development of graph neural networks (GNNs), the potential robustness under the edge noise is still less investigated. To close this gap, we first conduct an empirical study to disclose that the edge noise bilaterally perturbs both input topology and target label, yielding severe performance degradation and representation collapse. To address this dilemma, we propose an information-theory-guided principle, Robust Graph Information Bottleneck (RGIB), to extract reliable supervision signals and avoid representation collapse. Different from the basic information bottleneck, RGIB further decouples and balances the mutual dependence among graph topology, target labels, and representation, building new learning objectives for robust representation against the bilateral noise. Two instantiations, RGIB-SSL and RGIB-REP, are explored to leverage the merits of different methodologies, i.e., self-supervised learning and data reparameterization, for implicit and explicit data denoising, respectively. Extensive experiments on six datasets and three GNNs with diverse noisy scenarios verify the effectiveness of our RGIB instantiations. The code is publicly available at: https://github.com/tmlr-group/RGIB.

DeepHGCN: Toward Deeper Hyperbolic Graph Convolutional Networks

Hyperbolic graph convolutional networks (HGCN) have demonstrated significant potential in extracting information from hierarchical graphs. However, existing HGCNs are limited to shallow architectures, due to the expensive hyperbolic operations and the over-smoothing issue as depth increases. Although in GCNs, treatments have been applied to alleviate over-smoothing, developing a hyperbolic therapy presents distinct challenges since operations should be carefully designed to fit the hyperbolic nature. Addressing the above challenges, in this work, we propose DeepHGCN, the first deep multi-layer HGCN architecture with dramatically improved computational efficiency and substantially alleviated over-smoothing effect. DeepHGCN presents two key enablers of deep HGCNs: (1) a novel hyperbolic feature transformation layer that enables fast and accurate linear maps; and (2) Techniques such as hyperbolic residual connections and regularization for both weights and features facilitated by an efficient hyperbolic midpoint method. Extensive experiments demonstrate that DeepHGCN obtains significant improvements in link prediction and node classification tasks compared to both Euclidean and shallow hyperbolic GCN variants.

Symplectic Structure-Aware Hamiltonian (Graph) Embeddings

In traditional Graph Neural Networks (GNNs), the assumption of a fixed embedding manifold often limits their adaptability to diverse graph geometries. Recently, Hamiltonian system-inspired GNNs are proposed to address the dynamic nature of such embeddings by incorporating physical laws into node feature updates. In this work, we present SAH-GNN, a novel approach that generalizes Hamiltonian dynamics for more flexible node feature updates. Unlike existing Hamiltonian-inspired GNNs, SAH-GNN employs Riemannian optimization on the symplectic Stiefel manifold to adaptively learn the underlying symplectic structure during training, circumventing the limitations of existing Hamiltonian GNNs that rely on a pre-defined form of standard symplectic structure. This innovation allows SAH-GNN to automatically adapt to various graph datasets without extensive hyperparameter tuning. Moreover, it conserves energy during training such that the implicit Hamiltonian system is physically meaningful. To this end, we empirically validate SAH-GNN's superior performance and adaptability in node classification tasks across multiple types of graph datasets.

Accelerated Distributed Aggregative Optimization

In this paper, we investigate a distributed aggregative optimization problem in a network, where each agent has its own local cost function which depends not only on the local state variable but also on an aggregated function of state variables from all agents. To accelerate the optimization process, we combine heavy ball and Nesterov's accelerated methods with distributed aggregative gradient tracking, and propose two novel algorithms named DAGT-HB and DAGT-NES for solving the distributed aggregative optimization problem. We analyse that the DAGT-HB and DAGT-NES algorithms can converge to an optimal solution at a global $\mathbf{R}-$linear convergence rate when the objective function is smooth and strongly convex, and when the parameters (e.g., step size and momentum coefficients) are selected within certain ranges. A numerical experiment on the optimal placement problem is given to verify the effectiveness and superiority of our proposed algorithms.

The Novel Adaptive Fractional Order Gradient Decent Algorithms Design via Robust Control

The vanilla fractional order gradient descent may oscillatively converge to a region around the global minimum instead of converging to the exact minimum point, or even diverge, in the case where the objective function is strongly convex. To address this problem, a novel adaptive fractional order gradient descent (AFOGD) method and a novel adaptive fractional order accelerated gradient descent (AFOAGD) method are proposed in this paper. Inspired by the quadratic constraints and Lyapunov stability analysis from robust control theory, we establish a linear matrix inequality to analyse the convergence of our proposed algorithms. We prove that the proposed algorithms can achieve R-linear convergence when the objective function is $\textbf{L-}$smooth and $\textbf{m-}$strongly-convex. Several numerical simulations are demonstrated to verify the effectiveness and superiority of our proposed algorithms.