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Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks

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arXiv 2024年

作者： Hu, Zheyuan Kawaguchi, Kenji Zhang, Zhongqiang Em Karniadakis, George Department of Computer Science National University of Singapore 119077 Singapore Department of Mathematical Sciences Worcester Polytechnic Institute WorcesterMA01609 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory RichlandWA United States

Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus struggling with the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a promising solution due to their universal approximation, generalization ability, and mesh-free training. In principle, Monte Carlo fractional PINN (MC-fPINN) estimates fractional derivatives using Monte Carlo methods and thus could lift CoD. However, this may cause significant variance and errors, hence affecting convergence;in addition, MC-fPINN is sensitive to hyperparameters. In general, numerical methods and specifically PINNs for tempered fractional PDEs are under-developed. Herein, we extend MC-fPINN to tempered fractional PDEs to address these issues, resulting in the Monte Carlo tempered fractional PINN (MC-tfPINN). To reduce possible high variance and errors from Monte Carlo sampling, we replace the one-dimensional (1D) Monte Carlo with 1D Gaussian quadrature, applicable to both MC-fPINN and MC-tfPINN. We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100,000 dimensions. Our improved MC-fPINN/MC-tfPINN using quadrature consistently outperforms the original versions in accuracy and convergence speed in very high dimensions. © 2024, CC BY.

关键词： Monte Carlo methods

Graph Confidence Intercalibration Network for Intracranial Aneurysm Lesion Instance Segmentation in Dsa

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SSRN

SSRN 2024年

作者： Ye, Haili Mo, Yancheng Tang, Chen Liao, Mingqian Zhang, Xiaoqing Dai, Limeng Li, Baihua Liu, Jiang Research Institute of Trustworthy Autonomous Systems Department of Computer Science and Engineering Southern University of Science and Technology Shenzhen518055 China Department of Computer Science Loughborough University LoughboroughLE11 3TU United Kingdom School of Ophthalmology and Optometry Eye Hospital Wenzhou Medical University Wenzhou325027 China Center for High Performance Computing and Shenzhen Key Laboratory of Intelligent Bioinformatics Shenzhen Institute of Advanced Technology Chinese Academy of Sciences Shenzhen518055 China Shenzhen People’s Hospital Neurosurgery Department Shenzhen518020 China China

Intracranial aneurysm (IA) lesion segmentation is significant for its treatment and prognosis. Although exiting deep network-based instance methods have good IA lesion segmentation results based on digital subtraction angiography (DSA) images, they still face great challenges with instance confidence bias and imprecise boundary segmentation, which may negatively affect IA diagnosis. To tackle these problems, this paper proposes a novel graph confidence intercalibration network (GCINet) to automatically segment IA lesions from DSA images. To be specific, we design a graph confidence intercalibration (GCI) module to mitigate instance confidence bias by dynamically adjusting their confidence distributions. At the same time, we propose an edge space perception (ESP) module to correct ambiguous segmentation boundaries. Extensive experiments on a clinical IA-DSA and a publicly available LiTS dataset demonstrate that our GCINet outperforms state-of-the-art methods. Additionally, visual analysis and ablation studies are provided to verify the effectiveness of each module in GCINet. © 2024, The Authors. All rights reserved.

关键词： Image segmentation

Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Lévy Equations

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arXiv 2024年

作者： Hu, Zheyuan Zhang, Zhongqiang Karniadakis, George Em Kawaguchi, Kenji Department of Computer Science National University of Singapore Singapore119077 Singapore Department of Mathematical Sciences Worcester Polytechnic Institute WorcesterMA01609 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory RichlandWA United States

We introduce an innovative approach for solving high-dimensional Fokker-Planck-Lévy (FPL) equations in modeling non-Brownian processes across disciplines such as physics, finance, and ecology. We utilize a fractional score function and Physical-informed neural networks (PINN) to lift the curse of dimensionality (CoD) and alleviate numerical overflow from exponentially decaying solutions with dimensions. The introduction of a fractional score function allows us to transform the FPL equation into a second-order partial differential equation without fractional Laplacian and thus can be readily solved with standard physics-informed neural networks (PINNs). We propose two methods to obtain a fractional score function: fractional score matching (FSM) and score-fPINN for fitting the fractional score function. While FSM is more cost-effective, it relies on known conditional distributions. On the other hand, score-fPINN is independent of specific stochastic differential equations (SDEs) but requires evaluating the PINN model's derivatives, which may be more costly. We conduct our experiments on various SDEs and demonstrate numerical stability and effectiveness of our method in dealing with high-dimensional problems, marking a significant advancement in addressing the CoD in FPL equations. © 2024, CC BY.

关键词： Cost effectiveness

Exact Fit Attention in Node-Holistic Graph Convolutional Network for Improved EEG-Based Driver Fatigue Detection

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arXiv 2025年

作者： Xu, Meiyan Chen, Qingqing Chen, Duo Ding, Yi Wang, Jingyuan Gu, Peipei Pan, Yijie Huang, Deshuang Guo, Jiayang Zhang, Xun Department of Computer Science The Institute of Human Factors Engineering Minnan Normal University Zhangzhou363000 China School of Artificial Intelligence and Information Technology Nanjing University of Chinese Medicine Nanjing210023 China College of Computing and Data Science Nanyang Technological University Singapore School of Digital Media and Design Arts Beijing University of Posts and Telecommunications Beijing100088 China College of Software Engineering Zhengzhou University of Light Industry Zhengzhou450000 China Department of Computer Science and Technology Tsinghua University Beijing100084 China Eastern Institute for Advanced Study Eastern Institute of Technology Ningbo315200 China Ningbo Institute of Digital Twin Eastern Institute of Technology Ningbo315200 China National Institute for Data Science in Health and Medicine Xiamen University Xiamen361005 China

EEG-based fatigue monitoring can effectively reduce the incidence of related traffic accidents. In the past decade, with the advancement of deep learning, convolutional neural networks (CNN) have been increasingly used for EEG signal processing. However, due to the data’s non-Euclidean characteristics, existing CNNs may lose important spatial information from EEG, specifically channel correlation. Thus, we propose the node-holistic graph convolutional network (NHGNet), a model that uses graphic convolution to dynamically learn each channel’s features. With exact fit attention optimization, the network captures inter-channel correlations through a trainable adjacency matrix. The interpretability is enhanced by revealing critical areas of brain activity and their interrelations in various mental states. In validations on two public datasets, NHGNet outperforms the SOTAs. Specifically, in the intra-subject, NHGNet improved detection accuracy by at least 2.34% and 3.42%, and in the inter-subjects, it improved by at least 2.09% and 15.06%. Visualization research on the model revealed that the central parietal area plays an important role in detecting fatigue levels, whereas the frontal and temporal lobes are essential for maintaining vigilance. Copyright © 2025, The Authors. All rights reserved.

关键词： Electroencephalography

MIMO Beamforming and Signal Modulation Design for Federated Learning Optimization

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MIMO Beamforming and Signal Modulation Design for Federated ...

IEEE Conference on Global Communications (GLOBECOM)

作者： Nuocheng Yang Sihua Wang Mingzhe Chen Cong Shen Changchuan Yin Christopher G. Brinton Beijing Laboratory of Advanced Information Network Beijing University of Posts and Telecommunications Beijing China Department of Electrical and Computer Engineering Institute for Data Science and Computing University of Miami Coral Gables FL USA Charles L. Brown Department of Electrical and Computer Engineering University of Virginia Charlottesville VA USA School of Electrical and Computer Engineering Purdue University West Lafayette IN USA

In this paper, we consider the optimization of federated learning (FL) over a realistic wireless multiple-input multiple-output (MIMO) communication system with digital modulation and over-the-air computation (AirComp). In such a system, MIMO devices transmit their locally trained FL models to a parameter server (PS) using beamforming to maximize the number of devices scheduled for transmission. AirComp enables efficient wireless model aggregation by the PS in bandwidth-limited settings. However, wireless channel fading can produce distortions in AirComp-based FL. To tackle this challenge, we develop a novel aggregation scheme that combines digital modulation with AirComp to mitigate wireless fading while ensuring communication efficiency. We formulate this as a joint transmit-receive beamforming design optimization problem which dynamically adjusts the beamforming matrices to minimize the FL training loss with transmission errors. To solve this problem based on limited information at the PS, we employ an artificial neural network (ANN) to estimate the local FL models of all devices. Then, we derive a closed-form optimal design of the transmit and receive beamforming matrices based on predicted FL models. Numerical evaluations validate the advantages of the proposed methodology in terms of model training performance compared with baselines.

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KANsformer for Scalable Beamforming

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IEEE Transactions on Vehicular Technology 2025年

作者： Xie, Xinke Lu, Yang Chi, Chong-Yung Chen, Wei Ai, Bo Niyato, Dusit Beijing Jiaotong University State Key Laboratory of Advanced Rail Autonomous Operation Beijing100044 China Beijing Jiaotong University School of Computer Science and Technology Beijing100044 China National Tsing Hua University Institute of Communications Engineering Department of Electrical Engineering Hsinchu30013 Taiwan Beijing Jiaotong University School of Electronics and Information Engineering Beijing100044 China Nanyang Technological University College of Computing and Data Science 639798 Singapore

This paper proposes an unsupervised deep-learning (DL) approach by integrating Transformer and Kolmogorov-Arnold networks (KAN) termed KANsformer to realize scalable beamforming for mobile communication systems. Specifically, we consider a classic multi-input single-output energy efficiency maximization problem subject to the total power budget. The proposed KANsformer first extracts hidden features via a multi-head self-attention mechanism and then reads out the desired beamforming design via KAN. Numerical results are provided to evaluate the KANsformer in terms of generalization performance, transfer learning and ablation experiment. Overall, the KANsformer outperforms the existing benchmark DL approaches, and is adaptable to the variation in the number of mobile users with real-time and near-optimal inference. © 1967-2012 IEEE.

关键词： Budget control

CauSSL: Causality-inspired Semi-supervised Learning for Medical Image Segmentation

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CauSSL: Causality-inspired Semi-supervised Learning for Medi...

International Conference on computer Vision (ICCV)

作者： Juzheng Miao Cheng Chen Furui Liu Hao Wei Pheng-Ann Heng Department of Computer Science and Engineering The Chinese University of Hong Kong Center for Advanced Medical Computing and Analysis Harvard Medical School and Massachusetts General Hospital Zhejiang Lab Department of Biomedical Engineering The Chinese University of Hong Kong Institute of Medical Intelligence and XR The Chinese University of Hong Kong

Semi-supervised learning (SSL) has recently demonstrated great success in medical image segmentation, significantly enhancing data efficiency with limited annotations. However, despite its empirical benefits, there are still concerns in the literature about the theoretical foundation and explanation of semi-supervised segmentation. To explore this problem, this study first proposes a novel causal diagram to provide a theoretical foundation for the mainstream semi-supervised segmentation methods. Our causal diagram takes two additional intermediate variables into account, which are neglected in previous work. Drawing from this proposed causal diagram, we then introduce a causality-inspired SSL approach on top of co-training frameworks called CauSSL, to improve SSL for medical image segmentation. Specifically, we first point out the importance of algorithmic independence between two networks or branches in SSL, which is often overlooked in the literature. We then propose a novel statistical quantification of the uncomputable algorithmic independence and further enhance the independence via a min-max optimization process. Our method can be flexibly incorporated into different existing SSL methods to improve their performance. Our method has been evaluated on three challenging medical image segmentation tasks using both 2D and 3D network architectures and has shown consistent improvements over state-of-the-art methods. Our code is publicly available at: https://***/JuzhengMiao/CauSSL.

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CodeEnhance: A Codebook-Driven Approach for Low-Light Image Enhancement

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arXiv 2024年

作者： Wu, Xu Hou, XianXu Lai, Zhihui Zhou, Jie Zhang, Ya-Nan Pedrycz, Witold Shen, Linlin The Computer Vision Institute College of Computer Science and Software Engineering Shenzhen University Shenzhen518060 China Shenzhen Institute of Artificial Intelligence and Robotics for Society Shenzhen518060 China Guangdong Key Laboratory of Intelligent Information Processing Shenzhen University Shenzhen518060 China School of AI and Advanced Computing Xi’an Jiaotong-Liverpool University China National Engineering Laboratory for Big Data System Computing Technology Shenzhen University SZU Branch Shenzhen Institute of Artificial Intelligence and Robotics for Society Guangdong Shenzhen518060 China The Department of Electrical & Computer Engineering University of Alberta University of Alberta Canada

Low-light image enhancement (LLIE) aims to improve low-illumination images. However, existing methods face two challenges: (1) uncertainty in restoration from diverse brightness degradations;(2) loss of texture and color information caused by noise suppression and light enhancement. In this paper, we propose a novel enhancement approach, CodeEnhance, by leveraging quantized priors and image refinement to address these challenges. In particular, we reframe LLIE as learning an image-to-code mapping from low-light images to discrete codebook, which has been learned from high-quality images. To enhance this process, a Semantic Embedding Module (SEM) is introduced to integrate semantic information with low-level features, and a Codebook Shift (CS) mechanism, designed to adapt the pre-learned codebook to better suit the distinct characteristics of our low-light dataset. Additionally, we present an Interactive Feature Transformation (IFT) module to refine texture and color information during image reconstruction, allowing for interactive enhancement based on user preferences. Extensive experiments on both real-world and synthetic benchmarks demonstrate that the incorporation of prior knowledge and controllable information transfer significantly enhances LLIE performance in terms of quality and fidelity. The proposed CodeEnhance exhibits superior robustness to various degradations, including uneven illumination, noise, and color distortion. Copyright © 2024, The Authors. All rights reserved.

关键词： Image enhancement

Psychometrics for Hypnopaedia-Aware Machinery via Chaotic Projection of Artificial Mental Imagery

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arXiv 2024年

作者： Chang, Ching-Chun Gao, Kai Xu, Shuying Kordoni, Anastasia Leckie, Christopher Echizen, Isao National Institute of Informatics Chiyoda Tokyo Japan The Department of Information Engineering and Computer Science Feng Chia University Taichung Taiwan The Department of Psychology Lancaster University Lancaster United Kingdom The Department of Computing and Information Systems University of Melbourne MelbourneVIC Australia The Information and Society Research Division National Institute of Informatics The Department of Informatics Graduate University for Advanced Studies The Department of Information and Communication Engineering University of Tokyo Chiyoda Tokyo Japan

Neural backdoors represent insidious cybersecurity loopholes that render learning machinery vulnerable to unauthorised manipulations, potentially enabling the weaponisation of artificial intelligence with catastrophic consequences. A backdoor attack involves the clandestine infiltration of a trigger during the learning process, metaphorically analogous to hypnopaedia, where ideas are implanted into a subject's subconscious mind under the state of hypnosis or unconsciousness. When activated by a sensory stimulus, the trigger evokes conditioned reflex that directs a machine to mount a predetermined response. In this study, we propose a cybernetic framework for constant surveillance of backdoors threats, driven by the dynamic nature of untrustworthy data sources. We develop a self-aware unlearning mechanism to autonomously detach a machine's behaviour from the backdoor trigger. Through reverse engineering and statistical inference, we detect deceptive patterns and estimate the likelihood of backdoor infection. We employ model inversion to elicit artificial mental imagery, using stochastic processes to disrupt optimisation pathways and avoid convergent but potentially flawed patterns. This is followed by hypothesis analysis, which estimates the likelihood of each potentially malicious pattern being the true trigger and infers the probability of infection. The primary objective of this study is to maintain a stable state of equilibrium between knowledge fidelity and backdoor vulnerability. © 2024, CC BY.

关键词： Reverse engineering