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Coupled hydro-mechanical processes are of great importance to numerous engineering systems, e.g., hydraulic fracturing, geothermal energy, and carbon sequestration. Fluid flow in fractures is modeled after a Poiseuille law that relates the conductivity to the aperture by a cubic relation. Newton's method is commonly employed to solve the resulting discrete, nonlinear algebraic systems. It is demonstrated, however, that Newton's method will likely converge to nonphysical numerical solutions, resulting in estimates with a negative fracture aperture. A Quasi-Newton approach is developed to ensure global convergence to the physical solution. A fixed-point stability analysis demonstrates that both physical and nonphysical solutions are stable for Newton's method, whereas only physical solutions are stable for the proposed Quasi-Newton method. Additionally, it is also demonstrated that the Quasi-Newton method offers a contraction mapping along the iteration path. Numerical examples of fluid-driven fracture propagation demonstrate that the proposed solution method results in robust and computationally efficient performance.

相關內容

擬牛(niu)頓法(fa)(Quasi-Newton Methods)是求解(jie)非(fei)線性(xing)優化問(wen)題最有效(xiao)的(de)(de)(de)方(fang)法(fa)之(zhi)一,于20世(shi)紀(ji)50年代由美國Argonne國家實驗室的(de)(de)(de)物理(li)學家W. C. Davidon所提出來(lai)(lai)。Davidon設計(ji)的(de)(de)(de)這種(zhong)算法(fa)在(zai)當時看來(lai)(lai)是非(fei)線性(xing)優化領(ling)域最具創(chuang)造性(xing)的(de)(de)(de)發明之(zhi)一。不久R. Fletcher和M. J. D. Powell證(zheng)實了這種(zhong)新的(de)(de)(de)算法(fa)遠比其他(ta)方(fang)法(fa)快(kuai)速和可靠,使得非(fei)線性(xing)優化這門學科(ke)在(zai)一夜之(zhi)間突飛(fei)猛(meng)進。

Vision-and-Language Navigation (VLN) is a task where an agent navigates in an embodied indoor environment under human instructions. Previous works ignore the distribution of sample difficulty and we argue that this potentially degrade their agent performance. To tackle this issue, we propose a novel curriculum-based training paradigm for VLN tasks that can balance human prior knowledge and agent learning progress about training samples. We develop the principle of curriculum design and re-arrange the benchmark Room-to-Room (R2R) dataset to make it suitable for curriculum training. Experiments show that our method is model-agnostic and can significantly improve the performance, the generalizability, and the training efficiency of current state-of-the-art navigation agents without increasing model complexity.

One of the central problems in machine learning is domain adaptation. Unlike past theoretical work, we consider a new model for subpopulation shift in the input or representation space. In this work, we propose a provably effective framework for domain adaptation based on label propagation. In our analysis, we use a simple but realistic ``expansion'' assumption, proposed in \citet{wei2021theoretical}. Using a teacher classifier trained on the source domain, our algorithm not only propagates to the target domain but also improves upon the teacher. By leveraging existing generalization bounds, we also obtain end-to-end finite-sample guarantees on the entire algorithm. In addition, we extend our theoretical framework to a more general setting of source-to-target transfer based on a third unlabeled dataset, which can be easily applied in various learning scenarios.

Graph Neural Networks (GNN) is an emerging field for learning on non-Euclidean data. Recently, there has been increased interest in designing GNN that scales to large graphs. Most existing methods use "graph sampling" or "layer-wise sampling" techniques to reduce training time. However, these methods still suffer from degrading performance and scalability problems when applying to graphs with billions of edges. This paper presents GBP, a scalable GNN that utilizes a localized bidirectional propagation process from both the feature vectors and the training/testing nodes. Theoretical analysis shows that GBP is the first method that achieves sub-linear time complexity for both the precomputation and the training phases. An extensive empirical study demonstrates that GBP achieves state-of-the-art performance with significantly less training/testing time. Most notably, GBP can deliver superior performance on a graph with over 60 million nodes and 1.8 billion edges in less than half an hour on a single machine.

We present FAST NAVIGATOR, a general framework for action decoding, which yields state-of-the-art results on the recent Room-to-Room (R2R) Vision-and-Language navigation challenge of Anderson et. al. (2018). Given a natural language instruction and photo-realistic image views of a previously unseen environment, the agent must navigate from a source to a target location as quickly as possible. While all of current approaches make local action decisions or score entire trajectories with beam search, our framework seamlessly balances local and global signals when exploring the environment. Importantly, this allows us to act greedily, but use global signals to backtrack when necessary. Our FAST framework, applied to existing models, yielded a 17% relative gain over the previous state-of-the-art, an absolute 6% gain on success rate weighted by path length (SPL).

Safety and decline of road traffic accidents remain important issues of autonomous driving. Statistics show that unintended lane departure is a leading cause of worldwide motor vehicle collisions, making lane detection the most promising and challenge task for self-driving. Today, numerous groups are combining deep learning techniques with computer vision problems to solve self-driving problems. In this paper, a Global Convolution Networks (GCN) model is used to address both classification and localization issues for semantic segmentation of lane. We are using color-based segmentation is presented and the usability of the model is evaluated. A residual-based boundary refinement and Adam optimization is also used to achieve state-of-art performance. As normal cars could not afford GPUs on the car, and training session for a particular road could be shared by several cars. We propose a framework to get it work in real world. We build a real time video transfer system to get video from the car, get the model trained in edge server (which is equipped with GPUs), and send the trained model back to the car.

Vision-language navigation (VLN) is the task of navigating an embodied agent to carry out natural language instructions inside real 3D environments. In this paper, we study how to address three critical challenges for this task: the cross-modal grounding, the ill-posed feedback, and the generalization problems. First, we propose a novel Reinforced Cross-Modal Matching (RCM) approach that enforces cross-modal grounding both locally and globally via reinforcement learning (RL). Particularly, a matching critic is used to provide an intrinsic reward to encourage global matching between instructions and trajectories, and a reasoning navigator is employed to perform cross-modal grounding in the local visual scene. Evaluation on a VLN benchmark dataset shows that our RCM model significantly outperforms existing methods by 10% on SPL and achieves the new state-of-the-art performance. To improve the generalizability of the learned policy, we further introduce a Self-Supervised Imitation Learning (SIL) method to explore unseen environments by imitating its own past, good decisions. We demonstrate that SIL can approximate a better and more efficient policy, which tremendously minimizes the success rate performance gap between seen and unseen environments (from 30.7% to 11.7%).

Autonomous urban driving navigation with complex multi-agent dynamics is under-explored due to the difficulty of learning an optimal driving policy. The traditional modular pipeline heavily relies on hand-designed rules and the pre-processing perception system while the supervised learning-based models are limited by the accessibility of extensive human experience. We present a general and principled Controllable Imitative Reinforcement Learning (CIRL) approach which successfully makes the driving agent achieve higher success rates based on only vision inputs in a high-fidelity car simulator. To alleviate the low exploration efficiency for large continuous action space that often prohibits the use of classical RL on challenging real tasks, our CIRL explores over a reasonably constrained action space guided by encoded experiences that imitate human demonstrations, building upon Deep Deterministic Policy Gradient (DDPG). Moreover, we propose to specialize adaptive policies and steering-angle reward designs for different control signals (i.e. follow, straight, turn right, turn left) based on the shared representations to improve the model capability in tackling with diverse cases. Extensive experiments on CARLA driving benchmark demonstrate that CIRL substantially outperforms all previous methods in terms of the percentage of successfully completed episodes on a variety of goal-directed driving tasks. We also show its superior generalization capability in unseen environments. To our knowledge, this is the first successful case of the learned driving policy through reinforcement learning in the high-fidelity simulator, which performs better-than supervised imitation learning.

In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective function, and (2) the Lipschitz continuity of local individual functions. Under the local regularity assumption, we provide the first optimal first-order decentralized algorithm called multi-step primal-dual (MSPD) and its corresponding optimal convergence rate. A notable aspect of this result is that, for non-smooth functions, while the dominant term of the error is in $O(1/\sqrt{t})$, the structure of the communication network only impacts a second-order term in $O(1/t)$, where $t$ is time. In other words, the error due to limits in communication resources decreases at a fast rate even in the case of non-strongly-convex objective functions. Under the global regularity assumption, we provide a simple yet efficient algorithm called distributed randomized smoothing (DRS) based on a local smoothing of the objective function, and show that DRS is within a $d^{1/4}$ multiplicative factor of the optimal convergence rate, where $d$ is the underlying dimension.

The potential of graph convolutional neural networks for the task of zero-shot learning has been demonstrated recently. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, knowledge from distant nodes can get diluted when propagating through intermediate nodes, because current approaches to zero-shot learning use graph propagation schemes that perform Laplacian smoothing at each layer. We show that extensive smoothing does not help the task of regressing classifier weights in zero-shot learning. In order to still incorporate information from distant nodes and utilize the graph structure, we propose an Attentive Dense Graph Propagation Module (ADGPM). ADGPM allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants and an attention scheme is further used to weigh their contribution depending on the distance to the node. Finally, we illustrate that finetuning of the feature representation after training the ADGPM leads to considerable improvements. Our method achieves competitive results, outperforming previous zero-shot learning approaches.

In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.

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