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Solving the chemical master equation for stochastic biochemical systems: A variational autoencoder approach with effective reactions

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CHEMICAL ENGINEERING SCIENCE 2025年 311卷

作者： Zhou, Xinyi Lu, Jingyi Gao, Furong Cao, Zhixing East China Univ Sci & Technol State Key Lab Bioreactor Engn Shanghai 200237 Peoples R China Hong Kong Univ Sci & Technol Dept Chem & Biol Engn Hong Kong Peoples R China Queens Univ Dept Chem Engn Kingston ON K7L 3N6 Canada

The stochasticity of biochemical reactions at mesoscopic scale presents significant challenges to our understanding of the underpinnings. The Chemical Master Equation (CME) serves as a crucial tool for describing the dynamics of biochemical reactions, but solving the CME is notoriously difficult and often faces the curse of dimensionality. In this paper, we propose an efficient CME solver for stochastic biochemical dynamics leveraging the power of variational autoencoder (VAE). VAE is employed to find effective reactions from a group of elementary reactions, reducing the complexity of the system. By using VAE to find equivalent propensity for a set of complex reactions, we simplify the intermediate reactions, reducing the sample size and time for training. The trained VAE can predict the distributions of unseen time points, different reaction structures and unobserved species. We show a robust method that simplifies the resolution of CME, providing a powerful tool for analyzing stochastic biochemical systems.

关键词： variational autoencoder Stochastic biochemical dynamics Effective reaction

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Spatiotemporal subspace variational autoencoder with repair mechanism for traffic data imputation

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NEUROCOMPUTING 2025年 617卷

作者： Qian, Jialong Zhang, Shiqi Pian, Yuzhuang Chen, Xinyi Liu, Yonghong Sun Yat Sen Univ Sch Intelligent Syst Engn Shenzhen 510275 Guangdong Peoples R China Guangdong Prov Key Lab Intelligent TransportationS Guangzhou 510275 Guangdong Peoples R China Guangdong Prov Engn Res Ctr Traff Environm Monitor Guangzhou 510275 Guangdong Peoples R China

High-quality spatial-temporal traffic data is crucial for the functioning of modern smart transportation systems. However, the collection and storage of traffic data in real-world scenarios are often hindered by many factors, causing data loss that greatly affects decision-making. Different modes of data absence result in varying degrees of information loss, which introduces considerable challenges to the precise imputation of traffic data. Many existing studies are concentrate on two main aspects: the examination of data distribution and the extraction of spatiotemporal relationships. On the one hand, methods that focus on distribution fitting do not require a large volume of observational data but often fail to capture spatial-temporal relationships, leading to overly smooth results. On the other hand, methods that aim to identify spatial-temporal relationships, while offering higher accuracy in fitting, demand a substantial amount of high-quality historical data. Taking into account the merits and demerits of both two paradigm, we developed a novel unsupervised two-stage model simultaneously takes into account the spatiotemporal distribution and relationships, termed Spatiotemporal Subspace variational autoencoder with Repair Mechanism (SVAE-R). In stage one, we introduced the concept of spatiotemporal subspace, which not only mitigates the noise impact caused by data sparsity but also reduces the cost for the model to find the distribution. In stage two, we designed a simple repair structure to capture spatial-temporal relationships among data through graph convolution network(GCN) and gated recurrent units(GRU), revising the details of the data. We have evaluated our model on two authentic datasets, and it has exhibited a high degree of robustness, maintaining effective performance even under extreme data loss conditions.

关键词： Spatiotemporal traffic data Missing data imputation variational autoencoder Spatiotemporal subspace Graph neural networks

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Self-attention variational autoencoder-based method for incomplete model parameter imputation of digital twin building energy systems

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ENERGY AND BUILDINGS 2025年 328卷

作者： Lu, Jie Zhang, Chaobo Li, Bozheng Zhao, Yang Choudhary, Ruchi Langtry, Max Zhejiang Univ Inst Refrigerat & Cryogen Hangzhou Peoples R China Univ Cambridge Dept Engn Energy Efficient Cities Initiat Cambridge England Eindhoven Univ Technol Dept Built Environm Eindhoven Netherlands China United Engn Corp Ltd Hangzhou Peoples R China Zhejiang Univ Jiaxing Res Inst Key Lab Clean Energy & Carbon Neutral Zhejiang Pro Jiaxing Peoples R China

Digital twin models serve as the most crucial foundation for estimating the expected conservation effects of building energy systems. The establishment of digital twin models relies heavily on the detailed design parameters of building energy systems, including component topology, power, and efficiency. However, a considerable number of existing buildings lack complete modeling parameters. It is challenging to impute the incomplete parameters for building energy systems, since the different building energy systems have different modeling parameters and different amounts of incomplete parameters. To address this challenge, a self-attention variational autoencoder-based method is proposed. Its basic idea is to employ the self-attention mechanism to identify the key parameters within the entire parameters, and to learn the relationships between the incomplete parameters and the key parameters. The method comprises three steps: feature embedding, model building, and supervised learning. The feature embedding is employed to represent the features of building energy systems, with each feature carrying a physical meaning. A self-attention variational autoencoder model is then applied to impute the incomplete parameters based on the available parameters and the relationship between the incomplete parameters and the key parameters. Supervised learning is adopted to train the model based on the principles of the evidence lower bound. The evaluations are conducted using 350 various practical building energy systems sourced from the excellent design atlas in China. Three representative incomplete parameter imputation methods are selected as baseline models for performance comparison. The results indicate that the proposed method exhibits high imputation accuracy, good flexibility, and good interpretability.

关键词： Digital twin Incomplete model parameter imputation Multi-head self-attention variational autoencoder Feature embedding

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Deep Learning-Based variational autoencoder for Classification of Quantum and Classical States of Light

ADVANCED PHYSICS RESEARCH

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ADVANCED PHYSICS RESEARCH 2025年第2期4卷

作者： Bhupati, Mahesh Mall, Abhishek Kumar, Anshuman Jha, Pankaj K. Indian Inst Technol Dept Phys Lab Opt Quantum Mat LOQM Mumbai 400076 India Max Planck Inst Struct & Dynam Matter D-22761 Hamburg Germany Ctr Free Electron Laser Sci D-22761 Hamburg Germany Indian Inst Technol Ctr Excellence Quantum Informat Computat Sci & Tec Mumbai 400076 India Syracuse Univ Dept Elect Engn & Comp Sci Quantum Technol Lab QLT Syracuse NY 13210 USA

Advancements in optical quantum technologies have been enabled by the generation, manipulation, and characterization of light, with identification based on its photon statistics. However, characterizing light and its sources through single photon measurements requires efficient detectors and longer measurement times to obtain high-quality photon statistics. Here, a deep learning-based variational autoencoder (VAE) method is introduced for classifying single photon added coherent state (SPACS), single photon added thermal state (SPATS), and mixed states between coherent and SPACS as well as between thermal and SPATS of light. The semi-supervised learning-based VAE efficiently maps the photon statistics features of light to a lower dimension, enabling quasi-instantaneous classification with low average photon counts. The proposed VAE method is robust and maintains classification accuracy in the presence of losses inherent in an experiment, such as finite collection efficiency, non-unity quantum efficiency, finite number of detectors, etc. Additionally, leveraging the transfer learning capabilities of VAE enables successful classification of data of any quality using a single trained model. It is envisioned that such a deep learning methodology will enable better classification of quantum light and light sources even in poor detection. A deep learning-assisted variational autoencoder (VAE) is used to classify quantum and classical states of light, such as single photon-added coherent source (SPACS), single photon-added thermal source (SPATS), and their mixtures. The semi-supervised VAE efficiently maps photon statistics to a low-dimensional latent space, allowing for rapid and accurate classification even with minimal photon counts and experimental losses. Transfer learning improves robustness and adaptability to varying data quality. image

关键词： deep learning spacs spats variational autoencoder

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PT-VAE: variational autoencoder with prior concept transformation

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NEUROCOMPUTING 2025年 638卷

作者： Liu, Zitu Liu, Yue Yu, Zhenyao Yang, Zhengwei Fu, Qingshan Guo, Yike Liu, Qun Wang, Guoyin Shanghai Univ Sch Comp Engn & Sci Shanghai 200444 Peoples R China Imperial Coll London Dept Comp London SW7 2AZ England Chongqing Univ Posts & Telecommun Chongqing Key Lab Computat Intelligence Chongqing 400065 Peoples R China Shanghai Engn Res Ctr Intelligent Comp Syst Shanghai 200444 Peoples R China

Learning and disentangling coherent latent representations of variational autoencoders (VAEs) have recently attracted widespread attention. However, the latent space of the VAE model is constrained by the prior distribution, which can hinder the latent variables from accurately capturing semantic information, thereby limiting its disentanglement and interpretability. This paper proposes PT-VAE, which constructs the latent space by a well-constructed latent space rather than a carefully designed prior distribution to guide the latent variables. Firstly, we transform the initial constraints of the latent space into understandable latent variable distributions, the so-called prior concept, which can be introduced into the latent space. Then, we design the Gumbel softmax reparameterization trick to enhance the integration of the prior concept and latent variables. Furthermore, the training process of PT-VAE is guided by deriving a variational lower bound, which facilitates the construction of the latent space concept based on the prior concept. Compared with 8 state-of-the-art VAE models, the PT-VAE improves the average clustering accuracy by over 11 % on the Fashion MNSIT, MNIST, COIL20, and COIL10 datasets. Moreover, the PT-VAE elucidates the process of information aggregation within the model and uncovers disentangled representations. PT-VAE provides a novel and flexible approach to construct an interpretable latent space by embedding prior concepts and disentangling the latent variables.

关键词： variational autoencoder Deep learning interpretability Disentangled representation

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Generating Artificial Patients With Reliable Clinical Characteristics Using a Geometry-Based variational autoencoder: Proof-of-Concept Feasibility Study

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Journal of Medical Internet Research 2025年 27卷 e63130页

作者： Ferré, Fabrice Allassonnière, Stéphanie Chadebec, Clément Minville, Vincent Department of Anesthesia Intensive Care and Perioperative Medicine Purpan University Hospital Toulouse France Université Paris Cité Unité Mixte de Recherche S1138 Institut national de recherche en sciences et technologies du numérique Sorbonne University Paris France

Background: Artificial patient technology could transform health care by accelerating diagnosis, treatment, and mapping clinical pathways. Deep learning methods for generating artificial data in health care include data augmentation by variational autoencoders (VAE) technology. Objective: We aimed to test the feasibility of generating artificial patients with reliable clinical characteristics by using a geometry-based VAE applied, for the first time, on high-dimension, low-sample-size tabular data. Methods: Clinical tabular data were extracted from 521 real patients of the “MAX” digital conversational agent (BOTdesign) created for preparing patients for anesthesia. A 3-stage methodological approach was implemented to generate up to 10,000 artificial patients: training the model and generating artificial data, assessing the consistency and confidentiality of artificial data, and validating the plausibility of the newly created artificial patients. Results: We demonstrated the feasibility of applying the VAE technique to tabular data to generate large artificial patient cohorts with high consistency (fidelity scores>94%). Moreover, artificial patients could not be matched with real patients (filter similarity scores>99%, κ coefficients of agreement<0.2), thus guaranteeing the essential ethical concern of confidentiality. Conclusions: This proof-of-concept study has demonstrated our ability to augment real tabular data to generate artificial patients. These promising results make it possible to envisage in silico trials carried out on large cohorts of artificial patients, thereby overcoming the pitfalls usually encountered in in vivo trials. Further studies integrating longitudinal dynamics are needed to map patient trajectories. ©Fabrice Ferré, Stéphanie Allassonnière, Clément Chadebec, Vincent Minville.

关键词： Alzheimer disease anesthesia artificial data artificial intelligence data augmentation data science deep learning digital health health monitoring imaging magnetic resonance imaging medical imaging prediction variational autoencoder

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variational autoencoder-Based Framework for Retail Sales Prediction

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IEEE ACCESS 2024年 12卷 196391-196402页

作者： Li, Fuyu Wang, Lei Jin, Bo Dalian Univ Foreign Languages Dalian 116044 Peoples R China Dalian Univ Technol Dalian 116024 Peoples R China

Accurate retail sales prediction is crucial for supporting the intelligent operations and management of a retail sales organization. For example, intelligent inventory replenishment based on forecasted sales can help reduce inventory backlog and turnover periods, improving operational efficiency. This paper presents a variational autoencoder (VAE)-based framework for retail sales prediction, with three unique contributions. First, the framework leverages the clustering properties of the VAE in latent space to enhance feature learning. The data clustering module integrates correlation information across different samples to effectively extract both local and global ***, we design a restructured VAE to capture high-level local and global features essential for sales prediction. The use of multiple self-adaptive priors and corresponding posteriors diversifies the posterior space, facilitating effective learning of characteristic distributions across samples. This approach enhances the extraction of useful features from the original data. Finally, to mitigate abnormal prediction outcomes, we incorporate prior knowledge to adjust predictions that may be affected by the model's limited fitting capacity or insufficient training data in certain cases. Extensive experiments conducted in collaboration with a national retail chain in China demonstrate that our method outperforms state-of-the-art baseline methods and is practical for various operational and management tasks.

关键词： Feature extraction Predictive models Training Image reconstruction Data models Correlation Time series analysis Long short term memory Forecasting Accuracy Abnormal predictions calibrating regression task retail sales prediction variational autoencoder

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variational autoencoder-based anomaly detection in time series data for inventory record inaccuracy

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TURKISH JOURNAL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCES 2023年第1期31卷 163-179页

作者： Argun, Halil Alptekin, S. Emre Galatasaray Univ Ind Engn Istanbul Turkiye

Retail companies monitor inventory stock levels regularly and manage them based on forecasted sales to sustain their market position. Inventory accuracy, defined as the difference between the warehouse stock records and the actual inventory, is critical for preventing stockouts and shortages. The root causes of inventory inaccuracy are the employee or customer theft, product damage or spoilage, and wrong shipments. In this paper, we aim at detecting inaccurate stocks of one of Turkey's largest supermarket chain using the variational autoencoder (VAE), which is an unsupervised learning method. Based on the findings, we showed that VAE is able to model the underlying probability distribution of data, regenerate the pattern from time series data, and detect anomalies. Hence, it reduces time and effort to manually label the inaccuracy in data. Since the distribution of inventory data depends on selected product/product categories, we had to use a parametric approach to handle potential differences. For individual products, we built univariate time series, whereas for product categories we built multivariate time series. The experimental results show that the proposed approaches can detect anomalies both in the low and high inventory quantities.

关键词： Inventory record inaccuracy variational autoencoder anomaly detection time series data

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variational autoencoder based bipartite network embedding by integrating local and global structure

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INFORMATION SCIENCES 2020年第0期519卷 9-21页

作者： Jiao, Pengfei Tang, Minghu Liu, Hongtao Wang, Yaping Lu, Chunyu Wu, Huaming Tianjin Univ Ctr Biosafety Res & Strategy Tianjin Peoples R China Tianjin Univ Coll Intelligence & Comp Tianjin Peoples R China Tianjin Univ Ctr Appl Math Tianjin Peoples R China

As a powerful tool for machine learning on the graph, network embedding, which projects nodes into low-dimensional spaces, has a variety of applications on complex networks. Most current methods and models are not suitable for bipartite networks, which have two different types of nodes and there are no links between nodes of the same type. Furthermore, the only existing methods for bipartite network embedding ignore the internal mechanism and highly nonlinear structures of links. Therefore, in this paper, we propose a new deep learning method to learn the node embedding for bipartite networks based on the widely used autoencoder framework. Moreover, we carefully devise a node-level triplet including two types of nodes to assign the embedding by integrating the local and global structures. Meanwhile, we apply the variational autoencoder (VAE), a deep generation model with natural advantages in data generation and reconstruction, to enhance the node embedding for the highly nonlinear relationships between nodes and complex features. Experiments on some widely used datasets show the effectiveness of the proposed model and corresponding algorithm compared with some baseline network (and bipartite) embedding techniques. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Bipartite network embedding Local and global structure variational autoencoder Nonlinear structure

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variational autoencoder With Optimizing Gaussian Mixture Model Priors

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IEEE ACCESS 2020年 8卷 43992-44005页

作者： Guo, Chunsheng Zhou, Jialuo Chen, Huahua Ying, Na Zhang, Jianwu Zhou, Di Hangzhou Dianzi Univ Telecommun Engn Hangzhou 310018 Peoples R China Hangzhou Dianzi Univ Video Anal & Proc Team Hangzhou 310018 Zhejiang Peoples R China Zhejiang Univ Technol Co Ltd Hangzhou 310051 Peoples R China

The latent variable prior of the variational autoencoder (VAE) often utilizes a standard Gaussian distribution because of the convenience in calculation, but has an underfitting problem. This paper proposes a variational autoencoder with optimizing Gaussian mixture model priors. This method utilizes a Gaussian mixture model to construct prior distribution, and utilizes the Kullback-Leibler (KL) distance between posterior and prior distribution to implement an iterative optimization of the prior distribution based on the data. The greedy algorithm is used to solve the KL distance for defining the approximate variational lower bound solution of the loss function, and for realizing the VAE with optimizing Gaussian mixture model priors. Compared with the standard VAE method, the proposed method obtains state-of-the-art results on MNIST, Omniglot, and Frey Face datasets, which shows that the VAE with optimizing Gaussian mixture model priors can learn a better model.

关键词： Gaussian mixture model Gaussian distribution Training Standards Neural networks Aggregates variational autoencoder Gaussian mixture model Kullback-Leibler distance

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