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This paper introduces Eilmer, a general-purpose open-source compressible flow solver developed at the University of Queensland, designed to support research calculations in hypersonics and high-speed aerothermodynamics. Eilmer has a broad userbase in several university research groups and a wide range of capabilities, which are documented on the project's website, in the accompanying reference manuals, and in an extensive catalogue of example simulations. The first part of this paper describes the formulation of the code: the equations, physical models, and numerical methods that are used in a basic fluid dynamics simulation, as well as a handful of optional multi-physics models that are commonly added on to do calculations of hypersonic flow. The second section describes the processes used to develop and maintain the code, documenting our adherence to good programming practice and endorsing certain techniques that seem to be particularly helpful for scientific codes. The final section describes a half-dozen example simulations that span the range of Eilmer's capabilities, each consisting of some sample results and a short explanation of the problem being solved, which together will hopefully assist new users in beginning to use Eilmer in their own research projects.

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In this work, we consider the task of improving the accuracy of dynamic models for model predictive control (MPC) in an online setting. Even though prediction models can be learned and applied to model-based controllers, these models are often learned offline. In this offline setting, training data is first collected and a prediction model is learned through an elaborated training procedure. After the model is trained to a desired accuracy, it is then deployed in a model predictive controller. However, since the model is learned offline, it does not adapt to disturbances or model errors observed during deployment. To improve the adaptiveness of the model and the controller, we propose an online dynamics learning framework that continually improves the accuracy of the dynamic model during deployment. We adopt knowledge-based neural ordinary differential equations (KNODE) as the dynamic models, and use techniques inspired by transfer learning to continually improve the model accuracy. We demonstrate the efficacy of our framework with a quadrotor robot, and verify the framework in both simulations and physical experiments. Results show that the proposed approach is able to account for disturbances that are possibly time-varying, while maintaining good trajectory tracking performance.

We introduce a practical method to enforce linear partial differential equation (PDE) constraints for functions defined by neural networks (NNs), up to a desired tolerance. By combining methods in differentiable physics and applications of the implicit function theorem to NN models, we develop a differentiable PDE-constrained NN layer. During training, our model learns a family of functions, each of which defines a mapping from PDE parameters to PDE solutions. At inference time, the model finds an optimal linear combination of the functions in the learned family by solving a PDE-constrained optimization problem. Our method provides continuous solutions over the domain of interest that exactly satisfy desired physical constraints. Our results show that incorporating hard constraints directly into the NN architecture achieves much lower test error, compared to training on an unconstrained objective.

Inference by means of mathematical modeling from a collection of observations remains a crucial tool for scientific discovery and is ubiquitous in application areas such as signal compression, imaging restoration, and supervised machine learning. The inference problems may be solved using variational formulations that provide theoretically proven methods and algorithms. With ever-increasing model complexities and growing data size, new specially designed methods are urgently needed to recover meaningful quantifies of interest. We consider the broad spectrum of linear inverse problems where the aim is to reconstruct quantities with a sparse representation on some vector space; often solved using the (generalized) least absolute shrinkage and selection operator (lasso). The associated optimization problems have received significant attention, in particular in the early 2000's, because of their connection to compressed sensing and the reconstruction of solutions with favorable sparsity properties using augmented Lagrangians, alternating directions and splitting methods. We provide a new perspective on the underlying l1 regularized inverse problem by exploring the generalized lasso problem through variable projection methods. We arrive at our proposed variable projected augmented Lagrangian (vpal) method. We analyze this method and provide an approach for automatic regularization parameter selection based on a degrees of freedom argument. Further, we provide numerical examples demonstrating the computational efficiency for various imaging problems.

Zeroth-order optimization methods are developed to overcome the practical hurdle of having knowledge of explicit derivatives. Instead, these schemes work with merely access to noisy functions evaluations. The predominant approach is to mimic first-order methods by means of some gradient estimator. The theoretical limitations are well-understood, yet, as most of these methods rely on finite-differencing for shrinking differences, numerical cancellation can be catastrophic. The numerical community developed an efficient method to overcome this by passing to the complex domain. This approach has been recently adopted by the optimization community and in this work we analyze the practically relevant setting of dealing with computational noise. To exemplify the possibilities we focus on the strongly-convex optimization setting and provide a variety of non-asymptotic results, corroborated by numerical experiments, and end with local non-convex optimization.

Machine learning (ML) has recently been adopted in vehicular networks for applications such as autonomous driving, road safety prediction and vehicular object detection, due to its model-free characteristic, allowing adaptive fast response. However, most of these ML applications employ centralized learning (CL), which brings significant overhead for data transmission between the parameter server and vehicular edge devices. Federated learning (FL) framework has been recently introduced as an efficient tool with the goal of reducing transmission overhead while achieving privacy through the transmission of model updates instead of the whole dataset. In this paper, we investigate the usage of FL over CL in vehicular network applications to develop intelligent transportation systems. We provide a comprehensive analysis on the feasibility of FL for the ML based vehicular applications, as well as investigating object detection by utilizing image-based datasets as a case study. Then, we identify the major challenges from both learning perspective, i.e., data labeling and model training, and from the communications point of view, i.e., data rate, reliability, transmission overhead, privacy and resource management. Finally, we highlight related future research directions for FL in vehicular networks.

We consider the problem of creating assistants that can help agents - often humans - solve novel sequential decision problems, assuming the agent is not able to specify the reward function explicitly to the assistant. Instead of aiming to automate, and act in place of the agent as in current approaches, we give the assistant an advisory role and keep the agent in the loop as the main decision maker. The difficulty is that we must account for potential biases induced by limitations or constraints of the agent which may cause it to seemingly irrationally reject advice. To do this we introduce a novel formalization of assistance that models these biases, allowing the assistant to infer and adapt to them. We then introduce a new method for planning the assistant's advice which can scale to large decision making problems. Finally, we show experimentally that our approach adapts to these agent biases, and results in higher cumulative reward for the agent than automation-based alternatives.

With its powerful capability to deal with graph data widely found in practical applications, graph neural networks (GNNs) have received significant research attention. However, as societies become increasingly concerned with data privacy, GNNs face the need to adapt to this new normal. This has led to the rapid development of federated graph neural networks (FedGNNs) research in recent years. Although promising, this interdisciplinary field is highly challenging for interested researchers to enter into. The lack of an insightful survey on this topic only exacerbates this problem. In this paper, we bridge this gap by offering a comprehensive survey of this emerging field. We propose a unique 3-tiered taxonomy of the FedGNNs literature to provide a clear view into how GNNs work in the context of Federated Learning (FL). It puts existing works into perspective by analyzing how graph data manifest themselves in FL settings, how GNN training is performed under different FL system architectures and degrees of graph data overlap across data silo, and how GNN aggregation is performed under various FL settings. Through discussions of the advantages and limitations of existing works, we envision future research directions that can help build more robust, dynamic, efficient, and interpretable FedGNNs.

Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains is dramatically increasing in both size and complexity. Taken together, this suggests many exciting opportunities for deep learning applications in scientific settings. But a significant challenge to this is simply knowing where to start. The sheer breadth and diversity of different deep learning techniques makes it difficult to determine what scientific problems might be most amenable to these methods, or which specific combination of methods might offer the most promising first approach. In this survey, we focus on addressing this central issue, providing an overview of many widely used deep learning models, spanning visual, sequential and graph structured data, associated tasks and different training methods, along with techniques to use deep learning with less data and better interpret these complex models --- two central considerations for many scientific use cases. We also include overviews of the full design process, implementation tips, and links to a plethora of tutorials, research summaries and open-sourced deep learning pipelines and pretrained models, developed by the community. We hope that this survey will help accelerate the use of deep learning across different scientific domains.

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.

Federated learning (FL) is a machine learning setting where many clients (e.g. mobile devices or whole organizations) collaboratively train a model under the orchestration of a central server (e.g. service provider), while keeping the training data decentralized. FL embodies the principles of focused data collection and minimization, and can mitigate many of the systemic privacy risks and costs resulting from traditional, centralized machine learning and data science approaches. Motivated by the explosive growth in FL research, this paper discusses recent advances and presents an extensive collection of open problems and challenges.

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