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 a finite element simulation on coarse grids with fine scale information obtained using deep neural networks. The neural 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 generalizability of the method. Since the network only processes data of small sub-areas, it never ``sees'' the global problem and thus does not learn false biases. We describe the method with a focus on the interplay between the 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 accuracy with a coarse grid and thus reduce the computation time by orders of magnitude.
相關內容
Networking：IFIP International Conferences on Networking。
Explanation：國際網絡會議。
Publisher：IFIP。
SIT：
Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verification
We provide a systematic investigation of using physics-informed neural networks to compute Lyapunov functions. We encode Lyapunov conditions as a partial differential equation (PDE) and use this for training neural network Lyapunov functions. We analyze the analytical properties of the solutions to the Lyapunov and Zubov PDEs. In particular, we show that employing the Zubov equation in training neural Lyapunov functions can lead to approximate regions of attraction close to the true domain of attraction. We also examine approximation errors and the convergence of neural approximations to the unique solution of Zubov's equation. We then provide sufficient conditions for the learned neural Lyapunov functions that can be readily verified by satisfiability modulo theories (SMT) solvers, enabling formal verification of both local stability analysis and region-of-attraction estimates in the large. Through a number of nonlinear examples, ranging from low to high dimensions, we demonstrate that the proposed framework can outperform traditional sums-of-squares (SOS) Lyapunov functions obtained using semidefinite programming (SDP).
Dual Attention U-Net with Feature Infusion: Pushing the Boundaries of Multiclass Defect Segmentation
The proposed architecture, Dual Attentive U-Net with Feature Infusion (DAU-FI Net), addresses challenges in semantic segmentation, particularly on multiclass imbalanced datasets with limited samples. DAU-FI Net integrates multiscale spatial-channel attention mechanisms and feature injection to enhance precision in object localization. The core employs a multiscale depth-separable convolution block, capturing localized patterns across scales. This block is complemented by a spatial-channel squeeze and excitation (scSE) attention unit, modeling inter-dependencies between channels and spatial regions in feature maps. Additionally, additive attention gates refine segmentation by connecting encoder-decoder pathways. To augment the model, engineered features using Gabor filters for textural analysis, Sobel and Canny filters for edge detection are injected guided by semantic masks to expand the feature space strategically. Comprehensive experiments on a challenging sewer pipe and culvert defect dataset and a benchmark dataset validate DAU-FI Net's capabilities. Ablation studies highlight incremental benefits from attention blocks and feature injection. DAU-FI Net achieves state-of-the-art mean Intersection over Union (IoU) of 95.6% and 98.8% on the defect test set and benchmark respectively, surpassing prior methods by 8.9% and 12.6%, respectively. Ablation studies highlight incremental benefits from attention blocks and feature injection. The proposed architecture provides a robust solution, advancing semantic segmentation for multiclass problems with limited training data. Our sewer-culvert defects dataset, featuring pixel-level annotations, opens avenues for further research in this crucial domain. Overall, this work delivers key innovations in architecture, attention, and feature engineering to elevate semantic segmentation efficacy.
Targetless IMU-LiDAR extrinsic calibration methods are gaining significant attention as the importance of the IMU-LiDAR fusion system increases. Notably, existing calibration methods derive calibration parameters under the assumption that the methods require full motion in all axes. When IMU and LiDAR are mounted on a ground robot the motion of which is restricted to planar motion, existing calibration methods are likely to exhibit degraded performance. To address this issue, we present GRIL-Calib: a novel targetless Ground Robot IMU-LiDAR Calibration method. Our proposed method leverages ground information to compensate for the lack of unrestricted full motion. First, we propose LiDAR Odometry (LO) using ground plane residuals to enhance calibration accuracy. Second, we propose the Ground Plane Motion (GPM) constraint and incorporate it into the optimization for calibration, enabling the determination of full 6-DoF extrinsic parameters, including theoretically unobservable direction. Finally, unlike baseline methods, we formulate the calibration not as sequential two optimizations but as a single optimization (SO) problem, solving all calibration parameters simultaneously and improving accuracy. We validate our \textit{GRIL-Calib} by applying it to three public real-world datasets and comparing its performance with that of existing state-of-the-art methods in terms of accuracy and robustness. Our code is available at //github.com/Taeyoung96/GRIL-Calib.
Deep Equilibrium Models (DEQs) and Neural Ordinary Differential Equations (Neural ODEs) are two branches of implicit models that have achieved remarkable success owing to their superior performance and low memory consumption. While both are implicit models, DEQs and Neural ODEs are derived from different mathematical formulations. Inspired by homotopy continuation, we establish a connection between these two models and illustrate that they are actually two sides of the same coin. Homotopy continuation is a classical method of solving nonlinear equations based on a corresponding ODE. Given this connection, we proposed a new implicit model called HomoODE that inherits the property of high accuracy from DEQs and the property of stability from Neural ODEs. Unlike DEQs, which explicitly solve an equilibrium-point-finding problem via Newton's methods in the forward pass, HomoODE solves the equilibrium-point-finding problem implicitly using a modified Neural ODE via homotopy continuation. Further, we developed an acceleration method for HomoODE with a shared learnable initial point. It is worth noting that our model also provides a better understanding of why Augmented Neural ODEs work as long as the augmented part is regarded as the equilibrium point to find. Comprehensive experiments with several image classification tasks demonstrate that HomoODE surpasses existing implicit models in terms of both accuracy and memory consumption.
The performance improvement of deep networks significantly depends on their optimizers. With existing optimizers, precise and efficient recognition of the gradients trend remains a challenge. Existing optimizers predominantly adopt techniques based on the first-order exponential moving average (EMA), which results in noticeable delays that impede the real-time tracking of gradients trend and consequently yield sub-optimal performance. To overcome this limitation, we introduce a novel optimizer called fast-adaptive moment estimation (FAME). Inspired by the triple exponential moving average (TEMA) used in the financial domain, FAME leverages the potency of higher-order TEMA to improve the precision of identifying gradient trends. TEMA plays a central role in the learning process as it actively influences optimization dynamics; this role differs from its conventional passive role as a technical indicator in financial contexts. Because of the introduction of TEMA into the optimization process, FAME can identify gradient trends with higher accuracy and fewer lag issues, thereby offering smoother and more consistent responses to gradient fluctuations compared to conventional first-order EMA. To study the effectiveness of our novel FAME optimizer, we conducted comprehensive experiments encompassing six diverse computer-vision benchmarks and tasks, spanning detection, classification, and semantic comprehension. We integrated FAME into 15 learning architectures and compared its performance with those of six popular optimizers. Results clearly showed that FAME is more robust and accurate and provides superior performance stability by minimizing noise (i.e., trend fluctuations). Notably, FAME achieves higher accuracy levels in remarkably fewer training epochs than its counterparts, clearly indicating its significance for optimizing deep networks in computer-vision tasks.
Super-resolution (SR) techniques have recently been proposed to upscale the outputs of neural radiance fields (NeRF) and generate high-quality images with enhanced inference speeds. However, existing NeRF+SR methods increase training overhead by using extra input features, loss functions, and/or expensive training procedures such as knowledge distillation. In this paper, we aim to leverage SR for efficiency gains without costly training or architectural changes. Specifically, we build a simple NeRF+SR pipeline that directly combines existing modules, and we propose a lightweight augmentation technique, random patch sampling, for training. Compared to existing NeRF+SR methods, our pipeline mitigates the SR computing overhead and can be trained up to 23x faster, making it feasible to run on consumer devices such as the Apple MacBook. Experiments show our pipeline can upscale NeRF outputs by 2-4x while maintaining high quality, increasing inference speeds by up to 18x on an NVIDIA V100 GPU and 12.8x on an M1 Pro chip. We conclude that SR can be a simple but effective technique for improving the efficiency of NeRF models for consumer devices.
State space models (SSMs) are widely used to describe dynamic systems. However, when the likelihood of the observations is intractable, parameter inference for SSMs cannot be easily carried out using standard Markov chain Monte Carlo or sequential Monte Carlo methods. In this paper, we propose a particle Gibbs sampler as a general strategy to handle SSMs with intractable likelihoods in the approximate Bayesian computation (ABC) setting. The proposed sampler incorporates a conditional auxiliary particle filter, which can help mitigate the weight degeneracy often encountered in ABC. To illustrate the methodology, we focus on a classic stochastic volatility model (SVM) used in finance and econometrics for analyzing and interpreting volatility. Simulation studies demonstrate the accuracy of our sampler for SVM parameter inference, compared to existing particle Gibbs samplers based on the conditional bootstrap filter. As a real data application, we apply the proposed sampler for fitting an SVM to S&P 500 Index time-series data during the 2008 financial crisis.
Due to the limitations in the accuracy and robustness of current electroencephalogram (EEG) classification algorithms, applying motor imagery (MI) for practical Brain-Computer Interface (BCI) applications remains challenging. This paper proposed a model that combined a three-dimensional convolutional neural network (CNN) with a long short-term memory (LSTM) network with attention to classify MI-EEG signals. This model combined MI-EEG signals from different channels into three-dimensional features and extracted spatial features through convolution operations with multiple three-dimensional convolutional kernels of different scales. At the same time, to ensure the integrity of the extracted MI-EEG signal temporal features, the LSTM network was directly trained on the preprocessed raw signal. Finally, the features obtained from these two networks were combined and used for classification. Experimental results showed that this model achieved a classification accuracy of 92.7% and an F1-score of 0.91 on the public dataset BCI Competition IV dataset 2a, which were both higher than the state-of-the-art models in the field of MI tasks. Additionally, 12 participants were invited to complete a four-class MI task in our lab, and experiments on the collected dataset showed that the 3D-CLMI model also maintained the highest classification accuracy and F1-score. The model greatly improved the classification accuracy of users' motor imagery intentions, giving brain-computer interfaces better application prospects in emerging fields such as autonomous vehicles and medical rehabilitation.
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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