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The neural Ordinary Differential Equation (ODE) model has shown success in learning complex continuous-time processes from observations on discrete time stamps. In this work, we consider the modeling and forecasting of time series data that…

Machine Learning · Statistics 2023-06-05 Yixuan Tan , Liyan Xie , Xiuyuan Cheng

The use of deep learning techniques in detecting anomalies in time series data has been an active area of research with a long history of development and a variety of approaches. In particular, reconstruction-based unsupervised anomaly…

Artificial Intelligence · Computer Science 2023-02-21 Jinsheng Yang , Yuanhai Shao , ChunNa Li

Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena both in time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade…

Fluid Dynamics · Physics 2020-10-05 Hamidreza Eivazi , Hadi Veisi , Mohammad Hossein Naderi , Vahid Esfahanian

The recurrent neural network and its variants have shown great success in processing sequences in recent years. However, this deep neural network has not aroused much attention in anomaly detection through predictively process monitoring.…

Machine Learning · Computer Science 2023-09-06 Jiaqi Qiu , Yu Lin , Inez Zwetsloot

Recent advances in digitization have led to the availability of multivariate time series data in various domains, enabling real-time monitoring of operations. Identifying abnormal data patterns and detecting potential failures in these…

Machine Learning · Computer Science 2023-10-10 Fan Wang , Keli Wang , Boyu Yao

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

Numerical Analysis · Mathematics 2026-05-11 Andrew Tagg , Andrew Frandsen , Andrew Ning

Recurrent Neural Networks (RNNs) are widely used for online regression due to their ability to generalize nonlinear temporal dependencies. As an RNN model, Long-Short-Term-Memory Networks (LSTMs) are commonly preferred in practice, as these…

Machine Learning · Computer Science 2021-06-01 N. Mert Vural , Fatih Ilhan , Selim F. Yilmaz , Salih Ergüt , Suleyman S. Kozat

This work introduces Neural Chronos Ordinary Differential Equations (Neural CODE), a deep neural network architecture that fits a continuous-time ODE dynamics for predicting the chronology of a system both forward and backward in time. To…

Machine Learning · Computer Science 2025-03-27 C. Coelho , M. Fernanda P. Costa , L. L. Ferrás

Time series prediction can be generalized as a process that extracts useful information from historical records and then determines future values. Learning long-range dependencies that are embedded in time series is often an obstacle for…

Neural and Evolutionary Computing · Computer Science 2018-10-25 Yuxiu Hua , Zhifeng Zhao , Rongpeng Li , Xianfu Chen , Zhiming Liu , Honggang Zhang

Long Short-Term Memory (LSTM) is a popular approach to boosting the ability of Recurrent Neural Networks to store longer term temporal information. The capacity of an LSTM network can be increased by widening and adding layers. However,…

Machine Learning · Statistics 2017-12-14 Zhen He , Shaobing Gao , Liang Xiao , Daxue Liu , Hangen He , David Barber

Methods based on ordinary differential equations (ODEs) are widely used to build generative models of time-series. In addition to high computational overhead due to explicitly computing hidden states recurrence, existing ODE-based models…

Machine Learning · Statistics 2023-02-07 Linqi Zhou , Michael Poli , Winnie Xu , Stefano Massaroli , Stefano Ermon

Time series forecasting is prevalent in various real-world applications. Despite the promising results of deep learning models in time series forecasting, especially the Recurrent Neural Networks (RNNs), the explanations of time series…

Machine Learning · Computer Science 2023-08-29 Chaoqun Wang , Yijun Li , Xiangqian Sun , Qi Wu , Dongdong Wang , Zhixiang Huang

We investigate anomaly detection in an unsupervised framework and introduce Long Short Term Memory (LSTM) neural network based algorithms. In particular, given variable length data sequences, we first pass these sequences through our LSTM…

Signal Processing · Electrical Eng. & Systems 2020-02-25 Tolga Ergen , Ali Hassan Mirza , Suleyman Serdar Kozat

Using historical data to predict future events has many applications in the real world, such as stock price prediction; the robot localization. In the past decades, the Convolutional long short-term memory (LSTM) networks have achieved…

Machine Learning · Computer Science 2022-12-20 Dexun Li

Recurrent neural networks (RNNs) are particularly well-suited for modeling long-term dependencies in sequential data, but are notoriously hard to train because the error backpropagated in time either vanishes or explodes at an exponential…

Machine Learning · Computer Science 2019-08-28 Anil Kag , Ziming Zhang , Venkatesh Saligrama

Univariate time series (UTS), where each timestamp records a single variable, serve as crucial indicators in web systems and cloud servers. Anomaly detection in UTS plays an essential role in both data mining and system reliability…

Machine Learning · Computer Science 2026-02-11 Lingpei Zhang , Qingming Li , Yong Yang , Jiahao Chen , Rui Zeng , Chenyang Lyu , Shouling Ji

Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory…

In this study, we explore the application of an artificial recurrent neural network (RNN) called Long Short-Term Memory (LSTM) as an alternative to a turbulent Reynolds-Averaged Navier-Stokes (RANS) model. The LSTM models are utilized to…

Fluid Dynamics · Physics 2023-07-27 Hugo D. Pasinato , Nicólas F. Moguilner Reh

Through continuous observation and modeling of normal behavior in networks, Anomaly-based Network Intrusion Detection System (A-NIDS) offers a way to find possible threats via deviation from the normal model. The analysis of network traffic…

Networking and Internet Architecture · Computer Science 2019-06-13 Nguyen Thanh Van , Tran Ngoc Thinh , Le Thanh Sach

Transient computational fluid dynamics (CFD) remains expensive when long horizons and multi-scale turbulence are involved. Data-driven surrogates promise relief, yet many degrade over multiple steps or drift from physical behavior. This…

Fluid Dynamics · Physics 2025-12-01 Blaise Madiega , Mathieu Olivier