Cyclic models and recurrent neural networks

2019 ◽  
pp. 183-205
Author(s):  
Thomas P. Trappenberg
Keyword(s):  
Neural Networks ◽  
Dynamical Systems ◽  
Bayesian Networks ◽  
Recurrent Neural Networks ◽  
Directed Graphs ◽  
First Principle ◽  
Temporal Modeling ◽  
Cyclic Graphs ◽  
Cyclic Models

This chapter discusses models with cyclic dependencies. There are two principle architectures that are discussed. The first principle architecture of cyclic graphs comprises directed graphs similar to the Bayesian networks except that they include loops. Formally, such networks represent dynamical systems in the wider context and therefore represent some form of temporal modeling. The second type of models have connections between neurons that are bi-directional. These types of networks will be discussed in the context of stochastic units in the second half of this chapter.

scholarly journals An empirical study on temporal modeling for online action detection

2021 ◽  
Author(s):  
Wen Wang ◽  
Xiaojiang Peng ◽  
Yu Qiao ◽  
Jian Cheng
Keyword(s):  
Neural Networks ◽  
Empirical Study ◽  
Recurrent Neural Networks ◽  
State Of The Art ◽  
Deep Convolutional Neural Networks ◽  
Temporal Modeling ◽  
Action Detection ◽  
Modeling Methods ◽  
Feature Extractor ◽  
First Time

AbstractOnline action detection (OAD) is a practical yet challenging task, which has attracted increasing attention in recent years. A typical OAD system mainly consists of three modules: a frame-level feature extractor which is usually based on pre-trained deep Convolutional Neural Networks (CNNs), a temporal modeling module, and an action classifier. Among them, the temporal modeling module is crucial which aggregates discriminative information from historical and current features. Though many temporal modeling methods have been developed for OAD and other topics, their effects are lack of investigation on OAD fairly. This paper aims to provide an empirical study on temporal modeling for OAD including four meta types of temporal modeling methods, i.e. temporal pooling, temporal convolution, recurrent neural networks, and temporal attention, and uncover some good practices to produce a state-of-the-art OAD system. Many of them are explored in OAD for the first time, and extensively evaluated with various hyper parameters. Furthermore, based on our empirical study, we present several hybrid temporal modeling methods. Our best networks, i.e. , the hybridization of DCC, LSTM and M-NL, and the hybridization of DCC and M-NL, which outperform previously published results with sizable margins on THUMOS-14 dataset (48.6% vs. 47.2%) and TVSeries dataset (84.3% vs. 83.7%).

scholarly journals Observation error covariance specification in dynamical systems for data assimilation using recurrent neural networks

2021 ◽  
Author(s):  
Sibo Cheng ◽  
Mingming Qiu
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Dynamical Systems ◽  
Data Assimilation ◽  
Recurrent Neural Networks ◽  
Time Series Data ◽  
Series Data ◽  
Observation Data ◽  
Observation Error ◽  
Error Covariance

AbstractData assimilation techniques are widely used to predict complex dynamical systems with uncertainties, based on time-series observation data. Error covariance matrices modeling is an important element in data assimilation algorithms which can considerably impact the forecasting accuracy. The estimation of these covariances, which usually relies on empirical assumptions and physical constraints, is often imprecise and computationally expensive, especially for systems of large dimensions. In this work, we propose a data-driven approach based on long short term memory (LSTM) recurrent neural networks (RNN) to improve both the accuracy and the efficiency of observation covariance specification in data assimilation for dynamical systems. Learning the covariance matrix from observed/simulated time-series data, the proposed approach does not require any knowledge or assumption about prior error distribution, unlike classical posterior tuning methods. We have compared the novel approach with two state-of-the-art covariance tuning algorithms, namely DI01 and D05, first in a Lorenz dynamical system and then in a 2D shallow water twin experiments framework with different covariance parameterization using ensemble assimilation. This novel method shows significant advantages in observation covariance specification, assimilation accuracy, and computational efficiency.

Learning Brain Dynamics with Coupled Low-Dimensional Nonlinear Oscillators and Deep Recurrent Networks

2021 ◽  
pp. 1-40
Author(s):  
Germán Abrevaya ◽  
Guillaume Dumas ◽  
Aleksandr Y. Aravkin ◽  
Peng Zheng ◽  
Jean-Christophe Gagnon-Audet ◽  
...  
Keyword(s):  
Neural Networks ◽  
Dynamical Systems ◽  
Brain Imaging ◽  
Recurrent Neural Networks ◽  
Practical Importance ◽  
Parameters Estimation ◽  
Training Data ◽  
Autoregressive Models ◽  
Unseen Data ◽  
Low Dimensional

Abstract Many natural systems, especially biological ones, exhibit complex multivariate nonlinear dynamical behaviors that can be hard to capture by linear autoregressive models. On the other hand, generic nonlinear models such as deep recurrent neural networks often require large amounts of training data, not always available in domains such as brain imaging; also, they often lack interpretability. Domain knowledge about the types of dynamics typically observed in such systems, such as a certain type of dynamical systems models, could complement purely data-driven techniques by providing a good prior. In this work, we consider a class of ordinary differential equation (ODE) models known as van der Pol (VDP) oscil lators and evaluate their ability to capture a low-dimensional representation of neural activity measured by different brain imaging modalities, such as calcium imaging (CaI) and fMRI, in different living organisms: larval zebrafish, rat, and human. We develop a novel and efficient approach to the nontrivial problem of parameters estimation for a network of coupled dynamical systems from multivariate data and demonstrate that the resulting VDP models are both accurate and interpretable, as VDP's coupling matrix reveals anatomically meaningful excitatory and inhibitory interactions across different brain subsystems. VDP outperforms linear autoregressive models (VAR) in terms of both the data fit accuracy and the quality of insight provided by the coupling matrices and often tends to generalize better to unseen data when predicting future brain activity, being comparable to and sometimes better than the recurrent neural networks (LSTMs). Finally, we demonstrate that our (generative) VDP model can also serve as a data-augmentation tool leading to marked improvements in predictive accuracy of recurrent neural networks. Thus, our work contributes to both basic and applied dimensions of neuroimaging: gaining scientific insights and improving brain-based predictive models, an area of potentially high practical importance in clinical diagnosis and neurotechnology.

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