亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Powder-based additive manufacturing has transformed the manufacturing industry over the last decade. In Laser Powder Bed Fusion, a specific part is built in an iterative manner in which two-dimensional cross-sections are formed on top of each other by melting and fusing the proper areas of the powder bed. In this process, the behavior of the melt pool and its thermal field has a very important role in predicting the quality of the manufactured part and its possible defects. However, the simulation of such a complex phenomenon is usually very time-consuming and requires huge computational resources. Flow-3D is one of the software packages capable of executing such simulations using iterative numerical solvers. In this work, we create three datasets of single-trail processes using Flow-3D and use them to train a convolutional neural network capable of predicting the behavior of the three-dimensional thermal field of the melt pool solely by taking three parameters as input: laser power, laser velocity, and time step. The CNN achieves a relative Root Mean Squared Error of 2% to 3% for the temperature field and an average Intersection over Union score of 80% to 90% in predicting the melt pool area. Moreover, since time is included as one of the inputs of the model, the thermal field can be instantly obtained for any arbitrary time step without the need to iterate and compute all the steps

Process synthesis experiences a disruptive transformation accelerated by digitization and artificial intelligence. We propose a reinforcement learning algorithm for chemical process design based on a state-of-the-art actor-critic logic. Our proposed algorithm represents chemical processes as graphs and uses graph convolutional neural networks to learn from process graphs. In particular, the graph neural networks are implemented within the agent architecture to process the states and make decisions. Moreover, we implement a hierarchical and hybrid decision-making process to generate flowsheets, where unit operations are placed iteratively as discrete decisions and corresponding design variables are selected as continuous decisions. We demonstrate the potential of our method to design economically viable flowsheets in an illustrative case study comprising equilibrium reactions, azeotropic separation, and recycles. The results show quick learning in discrete, continuous, and hybrid action spaces. Due to the flexible architecture of the proposed reinforcement learning agent, the method is predestined to include large action-state spaces and an interface to process simulators in future research.

Mean-field games (MFG) were introduced to efficiently analyze approximate Nash equilibria in large population settings. In this work, we consider entropy-regularized mean-field games with a finite state-action space in a discrete time setting. We show that entropy regularization provides the necessary regularity conditions, that are lacking in the standard finite mean field games. Such regularity conditions enable us to design fixed-point iteration algorithms to find the unique mean-field equilibrium (MFE). Furthermore, the reference policy used in the regularization provides an extra parameter, through which one can control the behavior of the population. We first consider a stochastic game with a large population of $N$ homogeneous agents. We establish conditions for the existence of a Nash equilibrium in the limiting case as $N$ tends to infinity, and we demonstrate that the Nash equilibrium for the infinite population case is also an $\epsilon$-Nash equilibrium for the $N$-agent system, where the sub-optimality $\epsilon$ is of order $\mathcal{O}\big(1/\sqrt{N}\big)$. Finally, we verify the theoretical guarantees through a resource allocation example and demonstrate the efficacy of using a reference policy to control the behavior of a large population.

In dynamical systems, it is advantageous to identify regions of flow which can exhibit maximal influence on nearby behaviour. Hyperbolic Lagrangian Coherent Structures have been introduced to obtain two-dimensional surfaces which maximise repulsion or attraction in three-dimensional dynamical systems with arbitrary time-dependence. However, the numerical method to compute them requires obtaining derivatives associated with the system, often performed through the approximation of divided differences, which can lead to significant numerical error and numerical noise. In this paper, we introduce a novel method for the numerical calculation of hyperbolic Lagrangian Coherent Structures using Differential Algebra called DA-LCS. As a form of automatic forward differentiation, it allows direct computation of the Taylor expansion of the flow, its derivatives, and the eigenvectors of the associated strain tensor, with all derivatives obtained algebraically and to machine precision. It does so without a priori information about the system, such as variational equations or explicit derivatives. We demonstrate that this can provide significant improvements in the accuracy of the Lagrangian Coherent Structures identified compared to finite-differencing methods in a series of test cases drawn from the literature. We also show how DA-LCS uncovers additional dynamical behaviour in a real-world example drawn from astrodynamics.

We study incentive designs for a class of stochastic Stackelberg games with one leader and a large number of (finite as well as infinite population of) followers. We investigate whether the leader can craft a strategy under a dynamic information structure that induces a desired behavior among the followers. For the finite population setting, under sufficient conditions, we show that there exist symmetric incentive strategies for the leader that attain approximately optimal performance from the leader's viewpoint and lead to an approximate symmetric (pure) Nash best response among the followers. Driving the follower population to infinity, we arrive at the interesting result that in this infinite-population regime the leader cannot design a smooth "finite-energy" incentive strategy, namely, a mean-field limit for such games is not well-defined. As a way around this, we introduce a class of stochastic Stackelberg games with a leader, a major follower, and a finite or infinite population of minor followers, where the leader provides an incentive only for the major follower, who in turn influences the rest of the followers through her strategy. For this class of problems, we are able to establish the existence of an incentive strategy with finitely many minor followers. We also show that if the leader's strategy with finitely many minor followers converges as their population size grows, then the limit defines an incentive strategy for the corresponding mean-field Stackelberg game. Examples of quadratic Gaussian games are provided to illustrate both positive and negative results. In addition, as a byproduct of our analysis, we establish existence of a randomized incentive strategy for the class mean-field Stackelberg games, which in turn provides an approximation for an incentive strategy of the corresponding finite population Stackelberg game.

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

Recent years have witnessed significant advances in technologies and services in modern network applications, including smart grid management, wireless communication, cybersecurity as well as multi-agent autonomous systems. Considering the heterogeneous nature of networked entities, emerging network applications call for game-theoretic models and learning-based approaches in order to create distributed network intelligence that responds to uncertainties and disruptions in a dynamic or an adversarial environment. This paper articulates the confluence of networks, games and learning, which establishes a theoretical underpinning for understanding multi-agent decision-making over networks. We provide an selective overview of game-theoretic learning algorithms within the framework of stochastic approximation theory, and associated applications in some representative contexts of modern network systems, such as the next generation wireless communication networks, the smart grid and distributed machine learning. In addition to existing research works on game-theoretic learning over networks, we highlight several new angles and research endeavors on learning in games that are related to recent developments in artificial intelligence. Some of the new angles extrapolate from our own research interests. The overall objective of the paper is to provide the reader a clear picture of the strengths and challenges of adopting game-theoretic learning methods within the context of network systems, and further to identify fruitful future research directions on both theoretical and applied studies.

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.

Graphs, which describe pairwise relations between objects, are essential representations of many real-world data such as social networks. In recent years, graph neural networks, which extend the neural network models to graph data, have attracted increasing attention. Graph neural networks have been applied to advance many different graph related tasks such as reasoning dynamics of the physical system, graph classification, and node classification. Most of the existing graph neural network models have been designed for static graphs, while many real-world graphs are inherently dynamic. For example, social networks are naturally evolving as new users joining and new relations being created. Current graph neural network models cannot utilize the dynamic information in dynamic graphs. However, the dynamic information has been proven to enhance the performance of many graph analytical tasks such as community detection and link prediction. Hence, it is necessary to design dedicated graph neural networks for dynamic graphs. In this paper, we propose DGNN, a new {\bf D}ynamic {\bf G}raph {\bf N}eural {\bf N}etwork model, which can model the dynamic information as the graph evolving. In particular, the proposed framework can keep updating node information by capturing the sequential information of edges, the time intervals between edges and information propagation coherently. Experimental results on various dynamic graphs demonstrate the effectiveness of the proposed framework.