We extend and analyze the deep neural network multigrid solver (DNN-MG) for the Navier-Stokes equations in three dimensions. The idea of the method is to augment of finite element simulations on coarse grids with fine scale information obtained using deep neural networks. This network operates locally on small patches of grid elements. The local approach proves to be highly efficient, since the network can be kept (relatively) small and since it can be applied in parallel on all grid patches. However, the main advantage of the local approach is the inherent good generalizability of the method. Since the network is only ever trained on small sub-areas, it never ``sees'' the global problem and thus does not learn a false bias. We describe the method with a focus on the interplay between finite element method and deep neural networks. Further, we demonstrate with numerical examples the excellent efficiency of the hybrid approach, which allows us to achieve very high accuracies on coarse grids and thus reduce the computation time by orders of magnitude.
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Networking：IFIP International Conferences on Networking。
Explanation：國際網絡會議。
Publisher：IFIP。
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We propose SeedAL, a method to seed active learning for efficient annotation of 3D point clouds for semantic segmentation. Active Learning (AL) iteratively selects relevant data fractions to annotate within a given budget, but requires a first fraction of the dataset (a 'seed') to be already annotated to estimate the benefit of annotating other data fractions. We first show that the choice of the seed can significantly affect the performance of many AL methods. We then propose a method for automatically constructing a seed that will ensure good performance for AL. Assuming that images of the point clouds are available, which is common, our method relies on powerful unsupervised image features to measure the diversity of the point clouds. It selects the point clouds for the seed by optimizing the diversity under an annotation budget, which can be done by solving a linear optimization problem. Our experiments demonstrate the effectiveness of our approach compared to random seeding and existing methods on both the S3DIS and SemanticKitti datasets. Code is available at //github.com/nerminsamet/seedal.
Neural networks (NNs) have been successfully deployed in various fields. In NNs, a large number of multiplyaccumulate (MAC) operations need to be performed. Most existing digital hardware platforms rely on parallel MAC units to accelerate these MAC operations. However, under a given area constraint, the number of MAC units in such platforms is limited, so MAC units have to be reused to perform MAC operations in a neural network. Accordingly, the throughput in generating classification results is not high, which prevents the application of traditional hardware platforms in extreme-throughput scenarios. Besides, the power consumption of such platforms is also high, mainly due to data movement. To overcome this challenge, in this paper, we propose to flatten and implement all the operations at neurons, e.g., MAC and ReLU, in a neural network with their corresponding logic circuits. To improve the throughput and reduce the power consumption of such logic designs, the weight values are embedded into the MAC units to simplify the logic, which can reduce the delay of the MAC units and the power consumption incurred by weight movement. The retiming technique is further used to improve the throughput of the logic circuits for neural networks. In addition, we propose a hardware-aware training method to reduce the area of logic designs of neural networks. Experimental results demonstrate that the proposed logic designs can achieve high throughput and low power consumption for several high-throughput applications.
The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that arises in various fields including transportation and logistics. The CVRP extends from the Vehicle Routing Problem (VRP), aiming to determine the most efficient plan for a fleet of vehicles to deliver goods to a set of customers, subject to the limited carrying capacity of each vehicle. As the number of possible solutions skyrockets when the number of customers increases, finding the optimal solution remains a significant challenge. Recently, a quantum-classical hybrid algorithm known as Quantum Approximate Optimization Algorithm (QAOA) can provide better solutions in some cases of combinatorial optimization problems, compared to classical heuristics. However, the QAOA exhibits a diminished ability to produce high-quality solutions for some constrained optimization problems including the CVRP. One potential approach for improvement involves a variation of the QAOA known as the Grover-Mixer Quantum Alternating Operator Ansatz (GM-QAOA). In this work, we attempt to use GM-QAOA to solve the CVRP. We present a new binary encoding for the CVRP, with an alternative objective function of minimizing the shortest path that bypasses the vehicle capacity constraint of the CVRP. The search space is further restricted by the Grover-Mixer. We examine and discuss the effectiveness of the proposed solver through its application to several illustrative examples.
For estimating the proportion of false null hypotheses in multiple testing, a family of estimators by Storey (2002) is widely used in the applied and statistical literature, with many methods suggested for selecting the parameter $\lambda$. Inspired by change-point concepts, our new approach to the latter problem first approximates the $p$-value plot with a piecewise linear function with a single change-point and then selects the $p$-value at the change-point location as $\lambda$. Simulations show that our method has among the smallest RMSE across various settings, and we extend it to address the estimation in cases of superuniform $p$-values. We provide asymptotic theory for our estimator, relying on the theory of quantile processes. Additionally, we propose an application in the change-point literature and illustrate it using high-dimensional CNV data.
Electronic Health Record (EHR) data frequently exhibits sparse characteristics, posing challenges for predictive modeling. Current direct imputation such as matrix imputation approaches hinge on referencing analogous rows or columns to complete raw missing data and do not differentiate between imputed and actual values. As a result, models may inadvertently incorporate irrelevant or deceptive information with respect to the prediction objective, thereby compromising the efficacy of downstream performance. While some methods strive to recalibrate or augment EHR embeddings after direct imputation, they often mistakenly prioritize imputed features. This misprioritization can introduce biases or inaccuracies into the model. To tackle these issues, our work resorts to indirect imputation, where we leverage prototype representations from similar patients to obtain a denser embedding. Recognizing the limitation that missing features are typically treated the same as present ones when measuring similar patients, our approach designs a feature confidence learner module. This module is sensitive to the missing feature status, enabling the model to better judge the reliability of each feature. Moreover, we propose a novel patient similarity metric that takes feature confidence into account, ensuring that evaluations are not based merely on potentially inaccurate imputed values. Consequently, our work captures dense prototype patient representations with feature-missing-aware calibration process. Comprehensive experiments demonstrate that designed model surpasses established EHR-focused models with a statistically significant improvement on MIMIC-III and MIMIC-IV datasets in-hospital mortality outcome prediction task. The code is publicly available at \url{//github.com/yhzhu99/SparseEHR} to assure the reproducibility.
Segmentation of planar regions from a single RGB image is a particularly important task in the perception of complex scenes. To utilize both visual and geometric properties in images, recent approaches often formulate the problem as a joint estimation of planar instances and dense depth through feature fusion mechanisms and geometric constraint losses. Despite promising results, these methods do not consider cross-task feature distillation and perform poorly in boundary regions. To overcome these limitations, we propose X-PDNet, a framework for the multitask learning of plane instance segmentation and depth estimation with improvements in the following two aspects. Firstly, we construct the cross-task distillation design which promotes early information sharing between dual-tasks for specific task improvements. Secondly, we highlight the current limitations of using the ground truth boundary to develop boundary regression loss, and propose a novel method that exploits depth information to support precise boundary region segmentation. Finally, we manually annotate more than 3000 images from Stanford 2D-3D-Semantics dataset and make available for evaluation of plane instance segmentation. Through the experiments, our proposed methods prove the advantages, outperforming the baseline with large improvement margins in the quantitative results on the ScanNet and the Stanford 2D-3D-S dataset, demonstrating the effectiveness of our proposals.
In neural network training, RMSProp and ADAM remain widely favoured optimization algorithms. One of the keys to their performance lies in selecting the correct step size, which can significantly influence their effectiveness. It is worth noting that these algorithms performance can vary considerably, depending on the chosen step sizes. Additionally, questions about their theoretical convergence properties continue to be a subject of interest. In this paper, we theoretically analyze a constant stepsize version of ADAM in the non-convex setting. We show sufficient conditions for the stepsize to achieve almost sure asymptotic convergence of the gradients to zero with minimal assumptions. We also provide runtime bounds for deterministic ADAM to reach approximate criticality when working with smooth, non-convex functions.
The application of Physics-Informed Neural Networks (PINNs) is investigated for the first time in solving the one-dimensional Countercurrent spontaneous imbibition (COUCSI) problem at both early and late time (i.e., before and after the imbibition front meets the no-flow boundary). We introduce utilization of Change-of-Variables as a technique for improving performance of PINNs. We formulated the COUCSI problem in three equivalent forms by changing the independent variables. The first describes saturation as function of normalized position X and time T; the second as function of X and Y=T^0.5; and the third as a sole function of Z=X/T^0.5 (valid only at early time). The PINN model was generated using a feed-forward neural network and trained based on minimizing a weighted loss function, including the physics-informed loss term and terms corresponding to the initial and boundary conditions. All three formulations could closely approximate the correct solutions, with water saturation mean absolute errors around 0.019 and 0.009 for XT and XY formulations and 0.012 for the Z formulation at early time. The Z formulation perfectly captured the self-similarity of the system at early time. This was less captured by XT and XY formulations. The total variation of saturation was preserved in the Z formulation, and it was better preserved with XY- than XT formulation. Redefining the problem based on the physics-inspired variables reduced the non-linearity of the problem and allowed higher solution accuracies, a higher degree of loss-landscape convexity, a lower number of required collocation points, smaller network sizes, and more computationally efficient solutions.
Explainable Artificial Intelligence (XAI) is transforming the field of Artificial Intelligence (AI) by enhancing the trust of end-users in machines. As the number of connected devices keeps on growing, the Internet of Things (IoT) market needs to be trustworthy for the end-users. However, existing literature still lacks a systematic and comprehensive survey work on the use of XAI for IoT. To bridge this lacking, in this paper, we address the XAI frameworks with a focus on their characteristics and support for IoT. We illustrate the widely-used XAI services for IoT applications, such as security enhancement, Internet of Medical Things (IoMT), Industrial IoT (IIoT), and Internet of City Things (IoCT). We also suggest the implementation choice of XAI models over IoT systems in these applications with appropriate examples and summarize the key inferences for future works. Moreover, we present the cutting-edge development in edge XAI structures and the support of sixth-generation (6G) communication services for IoT applications, along with key inferences. In a nutshell, this paper constitutes the first holistic compilation on the development of XAI-based frameworks tailored for the demands of future IoT use cases.
Recently, Mutual Information (MI) has attracted attention in bounding the generalization error of Deep Neural Networks (DNNs). However, it is intractable to accurately estimate the MI in DNNs, thus most previous works have to relax the MI bound, which in turn weakens the information theoretic explanation for generalization. To address the limitation, this paper introduces a probabilistic representation of DNNs for accurately estimating the MI. Leveraging the proposed MI estimator, we validate the information theoretic explanation for generalization, and derive a tighter generalization bound than the state-of-the-art relaxations.
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