Multivariate Time Series Forecasting With Dynamic Graph Neural ODEs

Jin, Ming; Zheng, Yu; Li, Yuanfang; Chen, Siheng; Yang, Bin; Pan, Shirui

doi:10.1109/tkde.2022.3221989

Cited by 49 publications

(12 citation statements)

References 23 publications

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“…We compare MFG-NRDE with 11 baselines, all of which effectively model the dynamics of traffic data along the temporal and spatial dimensions, including 4 NDEbased models: STG-ODE [5], MTG-ODE [6], STG-NCDE [7], STG-NRDE [8].…”

Section: Methodsmentioning

confidence: 99%

“…STGODE [5] melds TCNs with Continuous GNN for extracting traffic data dependencies and applies NODE solely in the spatial domain. MTGODE [6] deploys dual coupled ODEs to effectuate continuous information transmission in both spatial and temporal aspects, learning the intricate dynamics of time series data. However, all the aforementioned strategies share a common drawback: their dependence on the initial state when solving ODEs.…”

Section: Traffic Forecastingmentioning

confidence: 99%

“…In this framework, given the initial state at the current moment X 0 , the future state at t moment X t is predicted by solving the neural differential equation (NDE) X t = X 0 + t 0 f (X)dt. More NDE-based models [5][6][7][8] architectures are derived, which model dynamical systems and perform traffic forecasting in the form of solving differential equations.…”

Section: Introductionmentioning

confidence: 99%

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Multi-Frequency Graph Neural Rough Differential Equations for Traffic Forecasting

Wang,

Zang

2024

Preprint

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The burgeoning field of neural differential equations (NDEs) underscores a quest for models that not only boast interpretability and robustness but also function within a more generalized framework. Although the fusion of Neural Controlled Differential Equations (NCDEs) with Graph Neural Networks (GNNs) has marked significant strides in traffic forecasting, the prolonged integrative process requisite for long-term forecasts remains a detriment to model efficacy. Furthermore, while NCDEs exhibit prowess in extracting temporal trends within traffic fluctuations, the potential of spatial trend correlations has not been adequately investigated. To bridge this gap, we introduce the Multi-Frequency Graph Neural Rough Differential Equation (MFG-NRDE), an NDE-based model tailored for traffic forecasting. Our model is underpinned by the frequency principle in neural networks and leverages both wavelet and signature transforms. This dual approach not only truncates the integral length but also captures a more nuanced representation of high- and low-frequency temporal features. Complementing this temporal focus, we integrate a novel methodology for dynamically computing spatial correlations, harnessing the inherent trend characteristics of traffic variations to enhance spatial dimension analysis. Empirical validation across four real-world traffic flow datasets demonstrates the superior performance of our MFG-NRDE model, positioning it favorably against contemporary state-of-the-art baselines. This underscores the efficacy of our model in managing the intricate dynamics of traffic data forecasting, paving the way for more sophisticated and accurate predictive models in this domain.

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Section: Methodsmentioning

confidence: 99%

Section: Traffic Forecastingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multi-Frequency Graph Neural Rough Differential Equations for Traffic Forecasting

Wang,

Zang

2024

Preprint

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“…In order to overcome these issues and relax the smoothness constraints found in conventional GPS algorithms, researchers have tended to move into GNN modules that allow for more flexibility for static and time-varying data living on graphs. Recently, several GNNs have been successfully used for time series imputation [39], and to capture time series relations for traffic and multivariate forecasting [50]- [52]. Even though these methods have paved the way for exploring new avenues in the reconstruction of time-varying graph signals, they primarily focus on capturing positive correlations between time series with strong similarities.…”

Section: Related Workmentioning

confidence: 99%

Time-Varying Signals Recovery Via Graph Neural Networks

Castro-Correa

Giraldo

Mondal

et al. 2023

ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Reconstructing time-varying graph signals (or graph time-series imputation) is a critical problem in machine learning and signal processing with broad applications, ranging from missing data imputation in sensor networks to time-series forecasting. Accurately capturing the spatio-temporal information inherent in these signals is crucial for effectively addressing these tasks. However, existing approaches relying on smoothness assumptions of temporal differences and simple convex optimization techniques have inherent limitations. To address these challenges, we propose a novel approach that incorporates a learning module to enhance the accuracy of the downstream task. To this end, we introduce the Gegenbauer-based graph convolutional (GegenConv) operator, which is a generalization of the conventional Chebyshev graph convolution by leveraging the theory of Gegenbauer polynomials. By deviating from traditional convex problems, we expand the complexity of the model and offer a more accurate solution for recovering time-varying graph signals. Building upon GegenConv, we design the Gegenbauerbased time Graph Neural Network (GegenGNN) architecture, which adopts an encoder-decoder structure. Likewise, our approach also utilizes a dedicated loss function that incorporates a mean squared error component alongside Sobolev smoothness regularization. This combination enables GegenGNN to capture both the fidelity to ground truth and the underlying smoothness properties of the signals, enhancing the reconstruction performance. We conduct extensive experiments on real datasets to evaluate the effectiveness of our proposed approach. The experimental results demonstrate that GegenGNN outperforms state-of-the-art methods, showcasing its superior capability in recovering time-varying graph signals.

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“…Recently, some studies introduce Neural ODEs to to obtain spatialtemporal hidden states with continuous depth, thus greatly improving the representation ability of the model [30,[35][36][37]. Nonetheless, on the one hand, in technique, these studies do not introduce the view of system dynamics to associate the continuity with continuous physical time; on the other hand, in application, few studies pay attention to those actually happened but unrecorded information within recording intervals, and none of these studies focus on the significant but under-valued temporal super-resolution forecasting task.…”

Section: Traffic Flow Forecastingmentioning

confidence: 99%

Temporal super-resolution traffic flow forecasting via continuous-time network dynamics

et al. 2023

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Traffic flow forecasting is a critical task for Intelligent Transportation Systems. However, the existed forecasting can only be conducted at certain timestamps, because the data, is discretely collected at these timestamps. In contrast, traffic flow evolves in real-time via a continuous manner in real world. Therefore, an ideal forecasting paradigm should be performed at arbitrary timestamps instead of only at these certain timestamps. Considering the forecasting timestamps will no longer be restricted by these timestamps, we call such paradigm as temporal super-resolution forecasting. In this paper, we incorporate the idea of neural ordinary differential equations (Neural ODEs) to handle the problem, modeling the change rate of traffic flow on the Article Title urban road. Therefore, due to the continuous nature of ordinary differential equations, the traffic flow at arbitrary timestamps can be forecasted by performing definite integral for the change rate. The urban road is usually regarded as a network, and the change rate of which can be described by continuous-time network dynamics, we parameterize the network dynamics of the traffic flow to quantify the change rate. On these foundations, we propose Spatial-Temporal Continuous Dynamics Network (STCDN) to complete the temporal super-resolution forecasting task. Extensive experiments on public traffic flow datasets illustrate that our model can achieve high accuracy on temporal super-resolution forecasting, while ensuring its performance on conventional experimental settings at these certain timestamps.

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Multivariate Time Series Forecasting With Dynamic Graph Neural ODEs

Cited by 49 publications

References 23 publications

Multi-Frequency Graph Neural Rough Differential Equations for Traffic Forecasting

Multi-Frequency Graph Neural Rough Differential Equations for Traffic Forecasting

Time-Varying Signals Recovery Via Graph Neural Networks

Temporal super-resolution traffic flow forecasting via continuous-time network dynamics

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