The Gromov--Hausdorff distance measures the difference in shape between compact metric spaces and poses a notoriously difficult problem in combinatorial optimization. We introduce its quadratic relaxation over a convex polytope whose solutions provably deliver the Gromov--Hausdorff distance. The optimality guarantee is enabled by the fact that the search space of our approach is not constrained to a generalization of bijections, unlike in other relaxations such as the Gromov--Wasserstein distance. We suggest the Frank--Wolfe algorithm with $O(n^3)$-time iterations for solving the relaxation and numerically demonstrate its performance on metric spaces of hundreds of points. In particular, we obtain a new upper bound of the Gromov--Hausdorff distance between the unit circle and the unit hemisphere equipped with Euclidean metric. Our approach is implemented as a Python package dGH.
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Supernova (SN) plays an important role in galaxy formation and evolution. In high-resolution galaxy simulations using massively parallel computing, short integration timesteps for SNe are serious bottlenecks. This is an urgent issue that needs to be resolved for future higher-resolution galaxy simulations. One possible solution would be to use the Hamiltonian splitting method, in which regions requiring short timesteps are integrated separately from the entire system. To apply this method to the particles affected by SNe in a smoothed-particle hydrodynamics simulation, we need to detect the shape of the shell on and within which such SN-affected particles reside during the subsequent global step in advance. In this paper, we develop a deep learning model, 3D-MIM, to predict a shell expansion after a SN explosion. Trained on turbulent cloud simulations with particle mass $m_{\rm gas}$~=~1 M$_\odot$, the model accurately reproduces the anisotropic shell shape, where densities decrease by over 10 per cent by the explosion. We also demonstrate that the model properly predicts the shell radius in the uniform medium beyond the training dataset of inhomogeneous turbulent clouds. We conclude that our model enables the forecast of the shell and its interior where SN-affected particles will be present.
Proton auroras are widely observed on the day side of Mars, identified as a significant intensity enhancement in the hydrogen Ly alpha (121.6 nm) emission between 120 and 150~km altitudes. Solar wind protons penetrating as energetic neutral atoms into the Martian thermosphere are thought to be responsible for these auroras. Understanding proton auroras is therefore important for characterizing the solar wind interaction with the atmosphere of Mars. Recent observations of spatially localized "patchy" proton auroras suggest a possible direct deposition of protons into the atmosphere of Mars during unstable solar wind conditions. Here, we develop a purely data-driven model of proton auroras using Mars Atmosphere and Volatile EvolutioN (MAVEN) in situ observations and limb scans of Ly alpha emissions between 2014 and 2022. We train an artificial neural network that reproduces individual Ly alpha intensities with a Pearson correlation of 0.95 along with a faithful reconstruction of the observed Ly alpha emission altitude profiles. By performing a SHapley Additive exPlanations (SHAP) analysis, we find that Solar Zenith Angle, seasonal CO2 atmosphere variability, solar wind temperature, and density are the most important features for the modelled proton auroras. We also demonstrate that our model can serve as an inexpensive tool for simulating and characterizing Ly alpha response under a variety of seasonal and upstream solar wind conditions.
Nonlinear Model Predictive Control (NMPC) is a state-of-the-art approach for locomotion and manipulation which leverages trajectory optimization at each control step. While the performance of this approach is computationally bounded, implementations of direct trajectory optimization that use iterative methods to solve the underlying moderately-large and sparse linear systems, are a natural fit for parallel hardware acceleration. In this work, we introduce MPCGPU, a GPU-accelerated, real-time NMPC solver that leverages an accelerated preconditioned conjugate gradient (PCG) linear system solver at its core. We show that MPCGPU increases the scalability and real-time performance of NMPC, solving larger problems, at faster rates. In particular, for tracking tasks using the Kuka IIWA manipulator, MPCGPU is able to scale to kilohertz control rates with trajectories as long as 512 knot points. This is driven by a custom PCG solver which outperforms state-of-the-art, CPU-based, linear system solvers by at least 10x for a majority of solves and 3.6x on average.
Current robotic grasping methods often rely on estimating the pose of the target object, explicitly predicting grasp poses, or implicitly estimating grasp success probabilities. In this work, we propose a novel approach that directly maps gripper poses to their corresponding grasp success values, without considering objectness. Specifically, we leverage a Neural Radiance Field (NeRF) architecture to learn a scene representation and use it to train a grasp success estimator that maps each pose in the robot's task space to a grasp success value. We employ this learned estimator to tune its inputs, i.e., grasp poses, by gradient-based optimization to obtain successful grasp poses. Contrary to other NeRF-based methods which enhance existing grasp pose estimation approaches by relying on NeRF's rendering capabilities or directly estimate grasp poses in a discretized space using NeRF's scene representation capabilities, our approach uniquely sidesteps both the need for rendering and the limitation of discretization. We demonstrate the effectiveness of our approach on four simulated 3DoF (Degree of Freedom) robotic grasping tasks and show that it can generalize to novel objects. Our best model achieves an average translation error of 3mm from valid grasp poses. This work opens the door for future research to apply our approach to higher DoF grasps and real-world scenarios.
Cyber-Physical Systems (CPSs) play a central role in the behavior of a wide range of autonomous physical systems such as medical devices, autonomous vehicles, and smart homes, many of which are safety-critical. CPSs are often specified iteratively as a sequence of models at different levels that can be tested via simulation systems at early stages of their development cycle. One such model is a hybrid automaton; these are used frequently for CPS applications and have the advantage of encapsulating both continuous and discrete CPS behaviors. When testing CPSs, engineers can take advantage of these models to generate test cases that target both types of these behaviors. Moreover, since these models are constructed early in the development process for CPSs, they allow test cases to be generated early in that process for those CPSs, even before simulation models of the CPSs have been designed. One challenge when testing CPSs is that these systems may operate differently even under an identically applied test scenario. In such cases, we cannot employ test oracles that use predetermined deterministic behaviors; instead, test oracles should consider sets of desired behaviors in order to determine whether the CPS has behaved appropriately. In this paper we present a test case generation technique, HYTEST, that generates test cases based on hybrid models, accompanied by appropriate test oracles, for use in testing CPSs early in their development cycle. To evaluate the effectiveness and efficiency of HYTEST, we conducted an empirical study in which we applied the technique to several CPSs and measured its ability to detect faults in those CPSs and the amount of time required to perform the testing process. The results of the study show that HYTEST was able to detect faults more effectively and efficiently than the baseline techniques we compare it to.
Next Point-of-Interest (POI) recommendation is a critical task in location-based services that aim to provide personalized suggestions for the user's next destination. Previous works on POI recommendation have laid focused on modeling the user's spatial preference. However, existing works that leverage spatial information are only based on the aggregation of users' previous visited positions, which discourages the model from recommending POIs in novel areas. This trait of position-based methods will harm the model's performance in many situations. Additionally, incorporating sequential information into the user's spatial preference remains a challenge. In this paper, we propose Diff-POI: a Diffusion-based model that samples the user's spatial preference for the next POI recommendation. Inspired by the wide application of diffusion algorithm in sampling from distributions, Diff-POI encodes the user's visiting sequence and spatial character with two tailor-designed graph encoding modules, followed by a diffusion-based sampling strategy to explore the user's spatial visiting trends. We leverage the diffusion process and its reversed form to sample from the posterior distribution and optimized the corresponding score function. We design a joint training and inference framework to optimize and evaluate the proposed Diff-POI. Extensive experiments on four real-world POI recommendation datasets demonstrate the superiority of our Diff-POI over state-of-the-art baseline methods. Further ablation and parameter studies on Diff-POI reveal the functionality and effectiveness of the proposed diffusion-based sampling strategy for addressing the limitations of existing methods.
Industrial Time-Sensitive Networking (TSN) provides deterministic mechanisms for real-time and reliable flow transmission. Increasing attention has been paid to efficient scheduling for time-sensitive flows with stringent requirements such as ultra-low latency and jitter. In TSN, the fine-grained traffic shaping protocol, cyclic queuing and forwarding (CQF), eliminates uncertain delay and frame loss by cyclic traffic forwarding and queuing. However, it inevitably causes high scheduling complexity. Moreover, complexity is quite sensitive to flow attributes and network scale. The problem stems in part from the lack of an attribute mining mechanism in existing frame-based scheduling. For time-critical industrial networks with large-scale complex flows, a so-called hyper-flow graph based scheduling scheme is proposed to improve the scheduling scalability in terms of schedulability, scheduling efficiency and latency & jitter. The hyper-flow graph is built by aggregating similar flow sets as hyper-flow nodes and designing a hierarchical scheduling framework. The flow attribute-sensitive scheduling information is embedded into the condensed maximal cliques, and reverse maps them precisely to congestion flow portions for re-scheduling. Its parallel scheduling reduces network scale induced complexity. Further, this scheme is designed in its entirety as a comprehensive scheduling algorithm GH^2. It improves the three criteria of scalability along a Pareto front. Extensive simulation studies demonstrate its superiority. Notably, GH^2 is verified its scheduling stability with a runtime of less than 100 ms for 1000 flows and near 1/430 of the SOTA FITS method for 2000 flows.
Many low-Mach or all-Mach number codes are based on space discretizations which in combination with the first order explicit Euler method as time integration would lead to an unstable scheme. In this paper, we investigate how the choice of a suitable explicit time integration method can stabilize these schemes. We restrict ourselves to some old prototypical examples in order to find directions for further research in this field.
Graph Neural Networks (GNNs) have gained significant attention owing to their ability to handle graph-structured data and the improvement in practical applications. However, many of these models prioritize high utility performance, such as accuracy, with a lack of privacy consideration, which is a major concern in modern society where privacy attacks are rampant. To address this issue, researchers have started to develop privacy-preserving GNNs. Despite this progress, there is a lack of a comprehensive overview of the attacks and the techniques for preserving privacy in the graph domain. In this survey, we aim to address this gap by summarizing the attacks on graph data according to the targeted information, categorizing the privacy preservation techniques in GNNs, and reviewing the datasets and applications that could be used for analyzing/solving privacy issues in GNNs. We also outline potential directions for future research in order to build better privacy-preserving GNNs.
In the past few years, the emergence of pre-training models has brought uni-modal fields such as computer vision (CV) and natural language processing (NLP) to a new era. Substantial works have shown they are beneficial for downstream uni-modal tasks and avoid training a new model from scratch. So can such pre-trained models be applied to multi-modal tasks? Researchers have explored this problem and made significant progress. This paper surveys recent advances and new frontiers in vision-language pre-training (VLP), including image-text and video-text pre-training. To give readers a better overall grasp of VLP, we first review its recent advances from five aspects: feature extraction, model architecture, pre-training objectives, pre-training datasets, and downstream tasks. Then, we summarize the specific VLP models in detail. Finally, we discuss the new frontiers in VLP. To the best of our knowledge, this is the first survey on VLP. We hope that this survey can shed light on future research in the VLP field.
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