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Physics-informed neural networks (PINNs) have successfully addressed various computational physics problems based on partial differential equations (PDEs). However, while tackling issues related to irregularities like singularities and oscillations, trained solutions usually suffer low accuracy. In addition, most current works only offer the trained solution for predetermined input parameters. If any change occurs in input parameters, transfer learning or retraining is required, and traditional numerical techniques also need an independent simulation. In this work, a physics-driven GraphSAGE approach (PD-GraphSAGE) based on the Galerkin method and piecewise polynomial nodal basis functions is presented to solve computational problems governed by irregular PDEs and to develop parametric PDE surrogate models. This approach employs graph representations of physical domains, thereby reducing the demands for evaluated points due to local refinement. A distance-related edge feature and a feature mapping strategy are devised to help training and convergence for singularity and oscillation situations, respectively. The merits of the proposed method are demonstrated through a couple of cases. Moreover, the robust PDE surrogate model for heat conduction problems parameterized by the Gaussian random field source is successfully established, which not only provides the solution accurately but is several times faster than the finite element method in our experiments.

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Existing grasp prediction approaches are mostly based on offline learning, while, ignoring the exploratory grasp learning during online adaptation to new picking scenarios, i.e., objects that are unseen or out-of-domain (OOD), camera and bin settings, etc. In this paper, we present an uncertainty-based approach for online learning of grasp predictions for robotic bin picking. Specifically, the online learning algorithm with an effective exploration strategy can significantly improve its adaptation performance to unseen environment settings. To this end, we first propose to formulate online grasp learning as an RL problem that will allow us to adapt both grasp reward prediction and grasp poses. We propose various uncertainty estimation schemes based on Bayesian uncertainty quantification and distributional ensembles. We carry out evaluations on real-world bin picking scenes of varying difficulty. The objects in the bin have various challenging physical and perceptual characteristics that can be characterized by semi- or total transparency, and irregular or curved surfaces. The results of our experiments demonstrate a notable improvement of grasp performance in comparison to conventional online learning methods which incorporate only naive exploration strategies. Video: //youtu.be/fPKOrjC2QrU

A reservoir computer (RC) is a recurrent neural network (RNN) framework that achieves computational efficiency where only readout layer training is required. Additionally, it effectively predicts nonlinear dynamical system tasks and has various applications. RC is effective for forecasting nonautonomous dynamical systems with gradual changes to the external drive amplitude. This study investigates the predictability of nonautonomous dynamical systems with rapid changes to the phase of the external drive. The forced Van der Pol equation was employed for the base model, implementing forecasting tasks with the RC. The study findings suggest that, despite hidden variables, a nonautonomous dynamical system with rapid changes to the phase of the external drive is predictable. Therefore, RC can offer better schedules for individual shift workers.

Many stochastic processes in the physical and biological sciences can be modelled as Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the diffusion term is configuration-dependent. One remedy is to construct a transform to a constant-diffusion process and sample the transformed process instead. In this work, we explain how coordinate-based and time-rescaling-based transforms can be used either individually or in combination to map a general class of variable-diffusion Brownian motion processes into constant-diffusion ones. The transforms are invertible, thus allowing recovery of the original dynamics. We motivate our methodology using examples in one dimension before then considering multivariate diffusion processes. We illustrate the benefits of the transforms through numerical simulations, demonstrating how the right combination of integrator and transform can improve computational efficiency and the order of convergence to the invariant distribution. Notably, the transforms that we derive are applicable to a class of multibody, anisotropic Stokes-Einstein diffusion that has applications in biophysical modelling.

Transfer learning for Bayesian optimisation has generally assumed a strong similarity between optimisation tasks, with at least a subset having similar optimal inputs. This assumption can reduce computational costs, but it is violated in a wide range of optimisation problems where transfer learning may nonetheless be useful. We replace this assumption with a weaker one only requiring the shape of the optimisation landscape to be similar, and analyse the recent method Prior Learning for Bayesian Optimisation - PLeBO - in this setting. By learning priors for the hyperparameters of the Gaussian process surrogate model we can better approximate the underlying function, especially for few function evaluations. We validate the learned priors and compare to a breadth of transfer learning approaches, using synthetic data and a recent air pollution optimisation problem as benchmarks. We show that PLeBO and prior transfer find good inputs in fewer evaluations.

Physics-informed neural networks (PINNs) provide a means of obtaining approximate solutions of partial differential equations and systems through the minimisation of an objective function which includes the evaluation of a residual function at a set of collocation points within the domain. The quality of a PINNs solution depends upon numerous parameters, including the number and distribution of these collocation points. In this paper we consider a number of strategies for selecting these points and investigate their impact on the overall accuracy of the method. In particular, we suggest that no single approach is likely to be ``optimal'' but we show how a number of important metrics can have an impact in improving the quality of the results obtained when using a fixed number of residual evaluations. We illustrate these approaches through the use of two benchmark test problems: Burgers' equation and the Allen-Cahn equation.

Traditional federated learning mainly focuses on parallel settings (PFL), which can suffer significant communication and computation costs. In contrast, one-shot and sequential federated learning (SFL) have emerged as innovative paradigms to alleviate these costs. However, the issue of non-IID (Independent and Identically Distributed) data persists as a significant challenge in one-shot and SFL settings, exacerbated by the restricted communication between clients. In this paper, we improve the one-shot sequential federated learning for non-IID data by proposing a local model diversity-enhancing strategy. Specifically, to leverage the potential of local model diversity for improving model performance, we introduce a local model pool for each client that comprises diverse models generated during local training, and propose two distance measurements to further enhance the model diversity and mitigate the effect of non-IID data. Consequently, our proposed framework can improve the global model performance while maintaining low communication costs. Extensive experiments demonstrate that our method exhibits superior performance to existing one-shot PFL methods and achieves better accuracy compared with state-of-the-art one-shot SFL methods on both label-skew and domain-shift tasks (e.g., 6%+ accuracy improvement on the CIFAR-10 dataset).

Graph neural networks (GNNs) have been demonstrated to be a powerful algorithmic model in broad application fields for their effectiveness in learning over graphs. To scale GNN training up for large-scale and ever-growing graphs, the most promising solution is distributed training which distributes the workload of training across multiple computing nodes. However, the workflows, computational patterns, communication patterns, and optimization techniques of distributed GNN training remain preliminarily understood. In this paper, we provide a comprehensive survey of distributed GNN training by investigating various optimization techniques used in distributed GNN training. First, distributed GNN training is classified into several categories according to their workflows. In addition, their computational patterns and communication patterns, as well as the optimization techniques proposed by recent work are introduced. Second, the software frameworks and hardware platforms of distributed GNN training are also introduced for a deeper understanding. Third, distributed GNN training is compared with distributed training of deep neural networks, emphasizing the uniqueness of distributed GNN training. Finally, interesting issues and opportunities in this field are discussed.

Graph neural networks (GNNs) have emerged as a powerful paradigm for embedding-based entity alignment due to their capability of identifying isomorphic subgraphs. However, in real knowledge graphs (KGs), the counterpart entities usually have non-isomorphic neighborhood structures, which easily causes GNNs to yield different representations for them. To tackle this problem, we propose a new KG alignment network, namely AliNet, aiming at mitigating the non-isomorphism of neighborhood structures in an end-to-end manner. As the direct neighbors of counterpart entities are usually dissimilar due to the schema heterogeneity, AliNet introduces distant neighbors to expand the overlap between their neighborhood structures. It employs an attention mechanism to highlight helpful distant neighbors and reduce noises. Then, it controls the aggregation of both direct and distant neighborhood information using a gating mechanism. We further propose a relation loss to refine entity representations. We perform thorough experiments with detailed ablation studies and analyses on five entity alignment datasets, demonstrating the effectiveness of AliNet.

Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.

Deep neural networks (DNNs) have been found to be vulnerable to adversarial examples resulting from adding small-magnitude perturbations to inputs. Such adversarial examples can mislead DNNs to produce adversary-selected results. Different attack strategies have been proposed to generate adversarial examples, but how to produce them with high perceptual quality and more efficiently requires more research efforts. In this paper, we propose AdvGAN to generate adversarial examples with generative adversarial networks (GANs), which can learn and approximate the distribution of original instances. For AdvGAN, once the generator is trained, it can generate adversarial perturbations efficiently for any instance, so as to potentially accelerate adversarial training as defenses. We apply AdvGAN in both semi-whitebox and black-box attack settings. In semi-whitebox attacks, there is no need to access the original target model after the generator is trained, in contrast to traditional white-box attacks. In black-box attacks, we dynamically train a distilled model for the black-box model and optimize the generator accordingly. Adversarial examples generated by AdvGAN on different target models have high attack success rate under state-of-the-art defenses compared to other attacks. Our attack has placed the first with 92.76% accuracy on a public MNIST black-box attack challenge.

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