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Deep neural networks have received widespread attention due to their simplicity and flexibility in the fields of engineering and scientific calculation. In this work, we probe into solving a class of elliptic Partial Differential Equations (PDEs) with multiple scales by means of Fourier-based mixed physics informed neural networks(dubbed FMPINN), the solver of FMPINN is configured as a multi-scale deep neural networks. Unlike the classical PINN method, a dual (flux) variable about the rough coefficient of PDEs is introduced to avoid the ill-condition of neural tangent kernel matrix that resulted from the oscillating coefficient of multi-scale PDEs. Therefore, apart from the physical conservation laws, the discrepancy between the auxiliary variables and the gradients of multi-scale coefficients is incorporated into the cost function, then obtaining a satisfactory solution of PDEs by minimizing the defined loss through some optimization methods. Additionally, a trigonometric activation function is introduced for FMPINN, which is suited for representing the derivatives of complex target functions. Handling the input data by Fourier feature mapping, it will effectively improve the capacity of deep neural networks to solve high-frequency problems. Finally, by introducing several numerical examples of multi-scale problems in various dimensional Euclidean spaces, we validate the efficiency and robustness of the proposed FMPINN algorithm in both low-frequency and high-frequency oscillation cases.

Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment in practice. In this paper, we propose a set-boundary reachability method to investigate the safety verification problem of NNs from a topological perspective. Given an NN with an input set and a safe set, the safety verification problem is to determine whether all outputs of the NN resulting from the input set fall within the safe set. In our method, the homeomorphism property and the open map property of NNs are mainly exploited, which establish rigorous guarantees between the boundaries of the input set and the boundaries of the output set. The exploitation of these two properties facilitates reachability computations via extracting subsets of the input set rather than the entire input set, thus controlling the wrapping effect in reachability analysis and facilitating the reduction of computation burdens for safety verification. The homeomorphism property exists in some widely used NNs such as invertible residual networks (i-ResNets) and Neural ordinary differential equations (Neural ODEs), and the open map is a less strict property and easier to satisfy compared with the homeomorphism property. For NNs establishing either of these properties, our set-boundary reachability method only needs to perform reachability analysis on the boundary of the input set. Moreover, for NNs that do not feature these properties with respect to the input set, we explore subsets of the input set for establishing the local homeomorphism property and then abandon these subsets for reachability computations. Finally, some examples demonstrate the performance of the proposed method.

Spiking Neural Networks (SNNs) have garnered widespread interest for their energy efficiency and brain-inspired event-driven properties. While recent methods like Spiking-YOLO have expanded the SNNs to more challenging object detection tasks, they often suffer from high latency and low detection accuracy, making them difficult to deploy on latency sensitive mobile platforms. Furthermore, the conversion method from Artificial Neural Networks (ANNs) to SNNs is hard to maintain the complete structure of the ANNs, resulting in poor feature representation and high conversion errors. To address these challenges, we propose two methods: timesteps compression and spike-time-dependent integrated (STDI) coding. The former reduces the timesteps required in ANN-SNN conversion by compressing information, while the latter sets a time-varying threshold to expand the information holding capacity. We also present a SNN-based ultra-low latency and high accurate object detection model (SUHD) that achieves state-of-the-art performance on nontrivial datasets like PASCAL VOC and MS COCO, with about remarkable 750x fewer timesteps and 30% mean average precision (mAP) improvement, compared to the Spiking-YOLO on MS COCO datasets. To the best of our knowledge, SUHD is the deepest spike-based object detection model to date that achieves ultra low timesteps to complete the lossless conversion.

We study energy-efficient offloading strategies in a large-scale MEC system with heterogeneous mobile users and network components. The system is considered with enabled user-task handovers that capture the mobility of various mobile users. We focus on a long-run objective and online algorithms that are applicable to realistic systems. The problem is significantly complicated by the large problem size, the heterogeneity of user tasks and network components, and the mobility of the users, for which conventional optimizers cannot reach optimum with a reasonable amount of computational and storage power. We formulate the problem in the vein of the restless multi-armed bandit process that enables the decomposition of high-dimensional state spaces and then achieves near-optimal algorithms applicable to realistically large problems in an online manner. Following the restless bandit technique, we propose two offloading policies by prioritizing the least marginal costs of selecting the corresponding computing and communication resources in the edge and cloud networks. This coincides with selecting the resources with the highest energy efficiency. Both policies are scalable to the offloading problem with a great potential to achieve proved asymptotic optimality - approach optimality as the problem size tends to infinity. With extensive numerical simulations, the proposed policies are demonstrated to clearly outperform baseline policies with respect to power conservation and robust to the tested heavy-tailed lifespan distributions of the offloaded tasks.

The great learning ability of deep learning models facilitates us to comprehend the real physical world, making learning to simulate complicated particle systems a promising endeavour. However, the complex laws of the physical world pose significant challenges to the learning based simulations, such as the varying spatial dependencies between interacting particles and varying temporal dependencies between particle system states in different time stamps, which dominate particles' interacting behaviour and the physical systems' evolution patterns. Existing learning based simulation methods fail to fully account for the complexities, making them unable to yield satisfactory simulations. To better comprehend the complex physical laws, this paper proposes a novel learning based simulation model- Graph Networks with Spatial-Temporal neural Ordinary Equations (GNSTODE)- that characterizes the varying spatial and temporal dependencies in particle systems using a united end-to-end framework. Through training with real-world particle-particle interaction observations, GNSTODE is able to simulate any possible particle systems with high precisions. We empirically evaluate GNSTODE's simulation performance on two real-world particle systems, Gravity and Coulomb, with varying levels of spatial and temporal dependencies. The results show that the proposed GNSTODE yields significantly better simulations than state-of-the-art learning based simulation methods, which proves that GNSTODE can serve as an effective solution to particle simulations in real-world application.

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.

Edge computing facilitates low-latency services at the network's edge by distributing computation, communication, and storage resources within the geographic proximity of mobile and Internet-of-Things (IoT) devices. The recent advancement in Unmanned Aerial Vehicles (UAVs) technologies has opened new opportunities for edge computing in military operations, disaster response, or remote areas where traditional terrestrial networks are limited or unavailable. In such environments, UAVs can be deployed as aerial edge servers or relays to facilitate edge computing services. This form of computing is also known as UAV-enabled Edge Computing (UEC), which offers several unique benefits such as mobility, line-of-sight, flexibility, computational capability, and cost-efficiency. However, the resources on UAVs, edge servers, and IoT devices are typically very limited in the context of UEC. Efficient resource management is, therefore, a critical research challenge in UEC. In this article, we present a survey on the existing research in UEC from the resource management perspective. We identify a conceptual architecture, different types of collaborations, wireless communication models, research directions, key techniques and performance indicators for resource management in UEC. We also present a taxonomy of resource management in UEC. Finally, we identify and discuss some open research challenges that can stimulate future research directions for resource management in UEC.

Conventionally, spatiotemporal modeling network and its complexity are the two most concentrated research topics in video action recognition. Existing state-of-the-art methods have achieved excellent accuracy regardless of the complexity meanwhile efficient spatiotemporal modeling solutions are slightly inferior in performance. In this paper, we attempt to acquire both efficiency and effectiveness simultaneously. First of all, besides traditionally treating H x W x T video frames as space-time signal (viewing from the Height-Width spatial plane), we propose to also model video from the other two Height-Time and Width-Time planes, to capture the dynamics of video thoroughly. Secondly, our model is designed based on 2D CNN backbones and model complexity is well kept in mind by design. Specifically, we introduce a novel multi-view fusion (MVF) module to exploit video dynamics using separable convolution for efficiency. It is a plug-and-play module and can be inserted into off-the-shelf 2D CNNs to form a simple yet effective model called MVFNet. Moreover, MVFNet can be thought of as a generalized video modeling framework and it can specialize to be existing methods such as C2D, SlowOnly, and TSM under different settings. Extensive experiments are conducted on popular benchmarks (i.e., Something-Something V1 & V2, Kinetics, UCF-101, and HMDB-51) to show its superiority. The proposed MVFNet can achieve state-of-the-art performance with 2D CNN's complexity.

Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics system, learning molecular fingerprints, predicting protein interface, and classifying diseases require that a model to learn from graph inputs. In other domains such as learning from non-structural data like texts and images, reasoning on extracted structures, like the dependency tree of sentences and the scene graph of images, is an important research topic which also needs graph reasoning models. Graph neural networks (GNNs) are connectionist models that capture the dependence of graphs via message passing between the nodes of graphs. Unlike standard neural networks, graph neural networks retain a state that can represent information from its neighborhood with an arbitrary depth. Although the primitive graph neural networks have been found difficult to train for a fixed point, recent advances in network architectures, optimization techniques, and parallel computation have enabled successful learning with them. In recent years, systems based on graph convolutional network (GCN) and gated graph neural network (GGNN) have demonstrated ground-breaking performance on many tasks mentioned above. In this survey, we provide a detailed review over existing graph neural network models, systematically categorize the applications, and propose four open problems for future research.