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OPTIMAL TRANSPORT--INSPIRED DEEP LEARNING FRAMEWORK FOR SLOW-DECAYING KOLMOGOROV n-WIDTH PROBLEMS: EXPLOITING SINKHORN LOSS AND WASSERSTEIN KERNEL

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2025年第2期47卷 C235-C264页

作者： Khamlich, Moaad Pichi, Federico Rozza, Gianluigi SISSA mathLab Math Area I-34136 Trieste Italy Ecole Polytech Fed Lausanne Chair Computat Math & Simulat Sci CH-1015 Lausanne Switzerland

Reduced-order models (ROMs) are widely used in scientific computing to tackle highdimensional systems. However, traditional ROM methods may only partially capture the intrinsic geometric characteristics of the data. These characteristics encompass the underlying structure, relationships, and essential features crucial for accurate modeling. To overcome this limitation, we propose a novel ROM framework that integrates optimal transport (OT) theory and neural network-based methods. Specifically, we investigate the kernel proper orthogonal decomposition method exploiting the Wasserstein distance as the custom kernel, and we efficiently train the resulting neural network employing the Sinkhorn algorithm. By leveraging an OT-based nonlinear reduction, the presented framework can capture the geometric structure of the data, which is crucial for accurate learning of the reduced solution manifold. When compared with traditional metrics such as mean squared error or cross-entropy, exploiting the Sinkhorn divergence as the loss function enhances stability during training, robustness against overfitting and noise, and accelerates convergence. To showcase the approach's effectiveness, we conduct experiments on a set of challenging test cases exhibiting a slow decay of the Kolmogorov n-width. The results show that our framework outperforms traditional ROM methods in terms of accuracy and computational efficiency.

关键词： kernel proper orthogonal decomposition deep learning Wasserstein distance Sinkhorn loss convolutional autoencoders parameterized PDEs

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Dynamic feature capturing in a fluid flow reduced-order model using attention-augmented autoencoders

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2025年 149卷

作者： Beiki, Alireza Kamali, Reza Shiraz Univ Sch Mech Engn Shiraz Iran

This study looks into how adding adaptive attention to convolutional autoencoders can help reconstruct flow fields in fluid dynamics applications. The study compares the effectiveness of the proposed adaptive attention mechanism with the convolutional block attention module approach using two different sets of datasets. The analysis encompasses the evaluation of reconstruction loss, latent space characteristics, and the application of attention mechanisms to time series forecasting. Combining adaptive attention with involution layers enhances its ability to identify and highlight significant features, surpassing the capabilities of the convolutional block attention module. This result demonstrates an increase of over 20% in the accuracy of reconstruction. Latent space analysis shows the adaptive attention mechanism's complex and flexible encoding, which makes it easier for the model to represent different types of data. The study also looks at how attention works and how it affects time series forecasting. It shows that a new method that combines multi-head attention and bidirectional long-short-term memory works well for forecasting over 5 s of futures of flow fields. This research provides valuable insights into the role of attention mechanisms in improving model accuracy, generalization, and forecasting capabilities in the field of fluid dynamics.

关键词： Reduced-order modeling convolutional autoencoders Adaptive attention mechanisms Time series forecasting in fluid dynamics Flow field reconstruction

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Polytopic autoencoders with smooth clustering for reduced-order modeling of flows

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JOURNAL OF COMPUTATIONAL PHYSICS 2025年 521卷

作者： Heiland, Jan Kim, Yongho Otto von Guericke Univ Dept Math Univ Pl 2 D-39106 Magdeburg Germany Max Planck Inst Dynam Complex Tech Syst Sandtorstr 1 D-39106 Magdeburg Germany

With the advancement of neural networks, there has been a notable increase, both in terms of quantity and variety, in research publications concerning the application of autoencoders to reduced-order models. We propose a polytopic autoencoder architecture that includes a lightweight nonlinear encoder, a convex combination decoder, and a smooth clustering network. Supported by several proofs, the model architecture ensures that all reconstructed states lie within a polytope, accompanied by a metric indicating the quality of the constructed polytopes, referred to as polytope error. Additionally, it offers a minimal number of convex coordinates for polytopic linear-parameter varying systems while achieving acceptable reconstruction errors compared to proper orthogonal decomposition (POD). To validate our proposed model, we conduct simulations involving two flow scenarios with the incompressible Navier-Stokes equation. Numerical results demonstrate the guaranteed properties of the model, low reconstruction errors compared to POD, and the improvement in error using a clustering network.

关键词： convolutional autoencoders Clustering Convex polytope Model order reduction Linear parameter-varying (LPV) systems Polytopic LPV system

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Gravitational wave isolation with autoencoder neural network cascade

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NEURAL COMPUTING & APPLICATIONS 2024年第13期36卷 6993-7006页

作者： Sengupta, Mayank Spring Ford Area High Sch Spring Ford Sr High Sch 10 12 Grade Ctr Royersford PA 19468 USA

Detectors at the Laser Interferometer Gravitational Wave Observatory (LIGO), along with its sister detectors Virgo and Kamioka Gravitational Wave Detector (KAGRA), endlessly collect data to be analyzed in search of gravitational wave signals (GW signals) produced primarily by massive merger events involving colliding black holes and neutron stars. These detectors are the foundation upon which the new field of gravitational wave astronomy is built. However, the algorithms used to sift through this incoming data are extremely computationally expensive. They constantly run the risk of lagging behind the detectors, which would be catastrophic for astronomers searching for merger events, and their inherent rigidity becomes an obstruction to the expansion of these detectors' range and sensitivity. To simplify and expedite the process of detecting and isolating GW signals, this paper presents a neural network (NN) cascade to automatically isolate GW signals in raw LIGO data. Perfecting such a NN system would improve the speed and efficiency of detecting and analyzing GW signals. This study uses a 2-stage cascade of convolutional autoencoders (CAEs) to detect and reconstruct GW signals buried in LIGO data, finding that it is effective at accurately isolating GW signals with very low latency on just one graphics processing unit (GPU). Ultimately, it is found that it is practical and likely beneficial for astronomers to use such a cascade to process incoming LIGO data.

关键词： autoencoders convolutional autoencoders Gravitational waves Relativity

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Forged document detection and writer identification through unsupervised deep learning approach

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MULTIMEDIA TOOLS AND APPLICATIONS 2024年第6期83卷 18459-18478页

作者： Tyagi, Prachi Agarwal, Khushboo Jaiswal, Garima Sharma, Arun Rani, Ritu Indira Gandhi Delhi Tech Univ Women Delhi India Bennett Univ Greater Noida India

In recent years, there has been a significant increase in document forgery, which includes the fraudulent replication of currency, diplomas, and works of art. This has become a major issue due to the widespread usage of paper-based documentation. Handwriting is closely linked to document forgery and forensics as it possesses unique characteristics, including variations in text characters, pen pressure, writing angle, and stroke patterns, which makes it impossible to replicate accurately. As a result, handwriting serves as a personalized biometric that can be used to determine the authenticity of documents. However, traditional methods of writer identification are both time-consuming and destructive, requiring substantial expertise. To overcome these limitations, the study explores the potential of hyperspectral imaging (HSI) as a non-destructive and advanced approach for detecting and preventing document forgery. HSI provides detailed spectral information from a scene, making it possible to capture subtle spectral differences in handwriting samples. This imaging technique has diverse applications in various fields such as agriculture, environmental monitoring, remote sensing, forensics, document analysis, and medical imaging. Our study proposes a novel unsupervised approach, CAE-SVM that uses convolutional Autoencoder (CAE) for feature extraction and Support Vector Machine (SVM) for writer identification. It was tested on the UWA writing ink hyperspectral images dataset for blue and black inks which is available publicly and compared with state-of-the-art methods and CNN. The proposed approach achieved the highest accuracy of 92.78% for blue ink, surpassing existing methods. The study's results emphasize the efficacy of HSI as a potent forensic analysis tool for detecting and preventing document forgery.

关键词： Hyperspectral imaging Document forgery Writer identification convolutional autoencoders SVM

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Deep Learning for Reduced Sampling Spatial 3-D REM Reconstruction

IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY

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IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY 2024年 5卷 2287-2301页

作者： Ivanov, Antoni Tonchev, Krasimir Poulkov, Vladimir Manolova, Agata Tech Univ Sofia Fac Telecommun Sofia 1000 Bulgaria

Radio environment maps (REMs) have been established as an important tool in spectrum occupancy characterization toward more efficient coverage planning and design of resource allocation algorithms. The utilization of deep learning (DL) techniques for REM reconstruction, particularly when working with a limited number of samples, has garnered significant research attention owing to its speed and accuracy. This is particularly relevant for spatial three-dimensional REMs, which involve an exponential increase in the number of samples compared to the two-dimensional case. This paper presents a method for determining the optimal sampling grid resolution based on two key criteria, 1) the generated map's similarity to the covariance matrix mean (CMM) of measurements collected in real world (RW) scenarios, and 2) reduced computational complexity. Subsequently, three prominent DL models for REM reconstruction, are evaluated, with the convolutional autoencoder (CAE) achieving the best performance. To enhance its accuracy, a neural network (NN) design approach is introduced, which involves assessing the difference in CMM between the original example and the output for each layer in the NN architecture. This method identifies the layers that introduce the smallest difference and determines their optimal number of filters. Thus, the model's complexity is reduced, and the accuracy is improved. Normalized root mean square error of as little as -35 dB is achieved for a sampling rate of 30%.

关键词： convolutional autoencoders deep learning neural network design radio environment maps reduced sampling U-Net

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Deep learning of movement behavior profiles and their association with markers of cardiometabolic health

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BMC MEDICAL INFORMATICS AND DECISION MAKING 2024年第1期24卷 1页

作者： Farrahi, Vahid Collings, Paul J. Oussalah, Mourad TU Dortmund Univ Inst Sport & Sport Sci Dortmund Germany Luxembourg Inst Hlth Dept Precis Hlth Phys Act Sport & Hlth Res Grp Strassen Luxembourg Univ Oulu Fac Informat Technol & Elect Engn Ctr Machine Vis & Signal Anal Oulu Finland

Background Traditionally, existing studies assessing the health associations of accelerometer-measured movement behaviors have been performed with few averaged values, mainly representing the duration of physical activities and sedentary behaviors. Such averaged values cannot naturally capture the complex interplay between the duration, timing, and patterns of accumulation of movement behaviors, that altogether may be codependently related to health outcomes in adults. In this study, we introduce a novel approach to visually represent recorded movement behaviors as images using original accelerometer outputs. Subsequently, we utilize these images for cluster analysis employing deep convolutional autoencoders. Methods Our method involves converting minute-by-minute accelerometer outputs (activity counts) into a 2D image format, capturing the entire spectrum of movement behaviors performed by each participant. By utilizing convolutional autoencoders, we enable the learning of these image-based representations. Subsequently, we apply the K-means algorithm to cluster these learned representations. We used data from 1812 adult (20-65 years) participants in the National Health and Nutrition Examination Survey (NHANES, 2003-2006 cycles) study who worn a hip-worn accelerometer for 7 seven consecutive days and provided valid accelerometer data. Results Deep convolutional autoencoders were able to learn the image representation, encompassing the entire spectrum of movement behaviors. The images were encoded into 32 latent variables, and cluster analysis based on these learned representations for the movement behavior images resulted in the identification of four distinct movement behavior profiles characterized by varying levels, timing, and patterns of accumulation of movement behaviors. After adjusting for potential covariates, the movement behavior profile characterized as "Early-morning movers" and the profile characterized as "Highest activity" both had lower levels of i

关键词： convolutional autoencoders Cardiometabolic health Clustering Accelerometry Wearables

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Remove and recover: two stage convolutional autoencoder based sonar image enhancement algorithm

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MULTIMEDIA TOOLS AND APPLICATIONS 2023年第18期83卷 55963页

作者： Liu, Ting Yan, Shun Wang, Guofeng Dalian Maritime Univ Dalian 116026 Peoples R China Yiqiyin Hangzhou Technol CO LTD Hangzhou 310000 Peoples R China

High-quality forward-looking sonar images are the basic guarantee for underwater object detection and classification of autonomous underwater vehicle (AUV). However, the sonar image has been suffering from two main problem with complex and changeable underwater environment: high speckle noises and the lack of high frequency information. In this paper, a two-stage sonar image enhancement algorithm based on convolutional autoencoder is proposed to solve the above two problems to allow low-frequency sonar images to obtain resolutions approximate to high-frequency sonar images. For the high speckle noise, we proposed a convolutional denoising autoencoder based speckle reduction method for low-frequency sonar image to avoid noise enhanced as the image enhancement process. Skip connections and newly designed loss function is incorporated to better suppress noise with varying degrees. To solve the problem of insufficient high frequency information, a convolutional sparse autoencoder is further introduced to achieve image super resolution enhancement. In order to verify the effectiveness of the enhancement network proposed in this paper, we conducted extensive experimental analysis have been conducted from two aspects: image enhancement effect and underwater target detection effect. Specifically, underwater sonar images have been collected was conducted based on our self-owned AUV platform equipped with a dual frequency forward looking sonar in a water tank for network training. And three datasets are constructed for speckle reduction, high-frequency restoration, and underwater target detection. Through extensive experimental verification, our proposed enhancement method achieves high performance improvement on speckle reduction and high-frequency information restoration than the state-of-the-art image speckle reduction and image enhancement algorithms with a better PSNR, SSIM, and EPI. Finally, the YOLO V5 network model is used for underwater target detection and the exper

关键词： Underwater object detection Sonar image convolutional autoencoders Speckle reduction Image enhancement

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convolutional Autoencoder for Vision-Based Human Activity Recognition 15th

Convolutional Autoencoder for Vision-Based Human Activity Re...

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15th International Conference on Intelligent Human-Computer Interaction (IHCI)

作者： Jain, Surbhi Garg, Aishvarya Nigam, Swati Singh, Rajiv Shastri, Anshuman Singh, Irish Banasthali Vidyapith Dept Comp Sci Jaipur 304022 Rajasthan India Banasthali Vidyapith Dept Phys Sci Jaipur 304022 Rajasthan India Banasthali Vidyapith Ctr Artificial Intelligence Jaipur 304022 Rajasthan India Oregon Inst Technol Klamath Falls OR USA

ISBN: (纸本)9783031538292;9783031538308

Human activity recognition (HAR) is a crucial component for many current applications, including those in the healthcare, security, and entertainment sectors. At the current state of the art, deep learning outperformsmachine learning with its ability to automatically extract features. autoencoders (AE) and convolutional neural networks (CNN) are the types of neural networks that are known for their good performance in dimensionality reduction and image classification, respectively. As most of the methods introduced for classification purposes are limited to sensor based methods. This paper mainly focuses on vision based HAR where we present a combination of AE and CNN for the classification of labeled data, in which convolutional AE (conv-AE) is utilized for two functions: dimensionality reduction and feature extraction and CNN is employed for classifying the activities. For the proposed model's implementation, public benchmark datasets KTH andWeizmann are considered, on which we have attained a recognition rate of 96.3%, 94.89% for both, respectively. Comparative analysis is provided for the proposed model for the above-mentioned datasets.

关键词： Human Activity Recognition Deep Learning convolutional Neural Networks autoencoders convolutional autoencoders

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A convolutional Autoencoder Framework for Probabilistic Anomaly Detection on Infrastructure Systems

A Convolutional Autoencoder Framework for Probabilistic Anom...

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ASCE International Conference on Computing in Civil Engineering (I3CE)

作者： Gu, Yueyan Jazizadeh, Farrokh Virginia Tech Dept Civil & Environm Engn Blacksburg VA 24061 USA

ISBN: (数字)9780784485248

ISBN: (纸本)9780784485248

Data-driven autonomous anomaly detection, empowered by advanced sensing and machine learning techniques, has the potential to significantly reduce costs associated with infrastructure maintenance. In this paper, we studied the impact of probabilistic anomaly detection in the context of a proposed deep learning-empowered framework for multivariate time series anomaly detection. In this framework, two-dimensional convolutional autoencoders are utilized to learn the patterns of normal data and detect unseen anomalous data points that fail to be reconstructed by the well-trained autoencoders. Kernel density estimation was utilized to generate a probability distribution function based on raw window-based anomaly predictions. Our assessments showed promising performance in a real-world case study of Class I railroad track anomaly detection. We conducted a comparative study that proved our hypothesis that probabilistic anomaly detection outperforms the deterministic approach of anomaly detection using direct autoencoder output. Furthermore, the impact of multivariate time series data processing methods, autoencoder architecture, and anomaly score thresholds was also investigated.

关键词： Deep Learning convolutional autoencoders Anomaly Detection Railroad Track

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