Stochastic Modeling of Hydroclimatic Processes Using Vine Copulas

PSTFormer: A novel parallel spatial-temporal transformer for remaining useful life prediction of aeroengine

If the ordinary least squares (OLS) diagnostics discussed in the previous chapter indicate the existence of spatial lag or spatial error dependence, the researcher will wish to model the type of dependence indicated by these diagnostics. If the OLS diagnostics indicate the presence of a diffusion process, the researcher will wish to estimate a spatial lag model via maximum likelihood (ML) estimation or an instrumental variables specification incorporating instruments for the spatially lagged dependent variable. Alternatively, if the OLS diagnostics indicate the existence of spatial error dependence, the researcher may choose to estimate a more fully specified OLS model to model the spatial dependence or may choose to employ a ML or generalized method of moments (GMM) approach incorporating the spatial dependence in the errors. The spatial dependence diagnosed via the diagnostics discussed in Chapter 5 may alternatively be produced by spatial heterogeneity in the effects of covariates. If this is the only source of spatial dependence, modeling this heterogeneity will be sufficient to capture the spatial dependence. As a consequence, any specification search should also consider the possibility of spatial heterogeneity, which is the focus of Chapter 7. This chapter will first, however, examine alternative approaches for modeling spatial dependence if spatial heterogeneity is not present. This chapter begins by examining ML estimation of spatial lag models that derives from Ord (1975). Next, I explore alternative instrumental variables and GMM estimators for spatial lag dependence. Next, I turn to approaches for estimating spatial error models. I conclude by considering areas of concern in the estimation of spatial models. These include estimators for large sample sizes and diagnostics for continued spatial dependence. MAXIMUM LIKELIHOOD SPATIAL LAG ESTIMATION The mixed regressive, spatial autoregressive model, or spatial lag model, extends the pure spatial autoregressive model considered in Section 3.2 to include also the set of covariates and associated parameters: y = ρ W y +Xβ+e where X is again an N by K matrix of observations on the covariates, β is a K by 1 vector of parameters, and the remaining notation is as discussed in Section 3.2.

Traffic forecasting is a challenging task due to complex spatial and temporal dependencies across sensor locations and time. Interest in solving this task has increased, but current research focuses on manually constructing neural network architectures without the aid of neural architecture search (NAS). In our work, we explore evolutionary neural architecture search (ENAS) by deploying a genetic algorithm (GA) to find optimal neural network architectures for predicting traffic conditions. The search space for the GA consists of arbitrary combinations of dilated convolutions and graph convolutions for modelling temporal and spatial dependencies respectively, limited in complexity only by technical constraints. Experimental results show that model architectures obtained via GA are able to match the current state-of-the-art on traffic prediction benchmarks.

Understanding crowd behavior is a pivotal step toward urban scene analysis. This is considered a very challenging task and has rarely been addressed to date due to the complexity of motion dynamics co-occurring across a given scene, which involves spatial and temporal dependencies. Unlike the mainstream research, which usually treats the temporal and spatial dependencies in a crowd separately, this paper presents a deep end-to-end approach that jointly considers the spatiotemporal information, leading to a rich understanding of crowd behavior. We first extract the displacement information describing crowd motion patterns from tracklets/trajectories. This information is subsequently fed into a convolutional layer to learn the underlying motion patterns and create high-level representations. The derived representations are used as inputs to a long short-term memory-based architecture to learn the underlying spatiotemporal cues in a single operation for the entire crowd in a given scene. We evaluate our approach on a widely used, large-scale benchmark datasets for three critical applications: pedestrian path forecasting, destination estimation, and holistic crowd behavior classification. The results show a drastic improvement compared to recently trending works.

A latent variable representation of count data models to accommodate spatial and temporal dependence: Application to predicting crash frequency at intersections

Long-term prediction of physical systems on irregular unstructured meshes is extremely challenging due to the spatial complexityof meshes and the dynamic changes over time; namely, spatial dependence and temporal dependence. Recently, graph-based next-step prediction models have achieved great success in the task of modeling complex high-dimensional physical systems. However, due to these models ignoring the temporal dependence, they inevitably suffer from the effects of error accumulation. To capture the spatial and temporal dependence simultaneously, we propose a temporal graph network (TGN) to predict the long-term dynamics of complex physical systems. Specifically, we introduce an Encode-Process-Decode architecture to capture spatial dependence and create low-dimensional vector representations of system states. Additionally, a temporal model is introduced to learn the dynamic changes in the low-dimensional vector representations to capture temporal dependence. Our model can capture spatiotemporal correlations within physical systems. On some complex long-term prediction tasks in fluid dynamics, such as airfoil flow and cylinder flow, the prediction error of our method is significantly lower than the competitive GNN baseline. We show accurate phase predictions even for very long prediction sequences.

Simplified non-homogeneous Markov Chain (MC) models for generation of synthetic time series of wind speed (WS) and wind direction (WD) are proposed. The proposed models consider daily, monthly, and seasonal WS and WD characteristics. The accuracy and computational burden of the proposed models are compared with those of a complete model (CM), proposed by the same authors in a previous paper, trough numerical experiments based on field data.

Spatial sciences are confronted with increasing amounts of high-dimensional data. These data commonly exhibit spatial and temporal dimensions. To explore, extract, and generalize inherent patterns in large spatiotemporal data sets, clustering algorithms are indispensable. These clustering algorithms must account for the distinct special properties of space and time to outline meaningful clusters in such data sets. Therefore, this research develops a hierarchical method based on self-organizing maps. The hierarchical architecture permits independent modeling of spatial and temporal dependence. To exemplify the utility of the method, this research uses an artificial data set and a socio-economic data set of the Ostregion, Austria, from the years 1961 to 2001. The results for the artificial data set demonstrate that the proposed method produces meaningful clusters that cannot be achieved when disregarding differences in spatial and temporal dependence. The results for the socio-economic data set show that the proposed method is an effective and powerful tool for analyzing spatiotemporal patterns in a regional context.

Traditional resource (demand or supply) forecasting models mainly focus on modeling temporal dependency. However, spatio-temporal data include complex non-linear relational and spatial dependencies. In addition, dynamic contextual information also impacts resources. Methods that consider context assume that the impact of context on resources is fixed, which is not realistic. For example, in a bicycle-sharing system, bike supply in stations is affected by the weather, and that effect changes over time. We propose a novel graph-based context integrated relational model, Context Integrated Graph Neural Network (CIGNN), which models temporal, relational, spatial, and dynamic contextual dependencies for multi-step ahead resource forecasting. We define a resource graph, where nodes represent locations with associated resource time-series, and context graphs (one for each type of context), where nodes represent locations with associated contextual time-series. Assuming that various contexts have dynamic impact on resources, our proposed CIGNN model employs a novel fusion mechanism that jointly learns from multiple contextual time-series. To the best of our knowledge, CIGNN is the first approach that integrates dynamic contextual information using graph neural networks for resource forecasting. Empirical results on two real-world datasets demonstrate that CIGNN consistently outperforms state-of-the-art approaches.

Traffic forecasting has emerged as an important task for developing intelligent transportation systems. Recent works focus on representing traffic as graph operation and using graph neural networks for spatial–temporal prediction. Most of the approaches assume a predefined graph structure based on node distances. However, spatial dependencies change over time in many scenarios of traffic flow. In this regard, this study takes an investigation capturing the spatial and temporal dependencies with no prior knowledge structure of traffic road networks. Specifically, we propose a multi-step prediction model named Dynamic Spatial Transformer WaveNet Network (DSTWN) to capture the dynamic conditions and directions of traffic flow in which a temporal convolution layer is adopted for the long time sequence and a spatial transformer layer is proposed to capture the dynamic spatial dependencies. Furthermore, we introduce a new traffic dataset, which is collected from the vehicle detection system in an urban area (UVDS). In particular, compared with existing benchmark traffic data, UVDS contains more complicated spatial information, which is similar to many real-world scenarios of traffic flow. Experiments on both benchmark traffic datasets indicate the promising results of DSTWN compared with state-of-the-art models in this research field.

Landslide displacement prediction has garnered significant recognition as a pivotal component in realizing successful early warnings and implementing effective control measures. This task remains challenging as landslide deformation involves not only temporal dependency within time series data but also spatial dependence across various regions within landslides. The present study proposes a landslide spatiotemporal displacement forecasting model by introducing attention-based deep learning algorithms based on spatiotemporal analysis. The Maximal Information Coefficient (MIC) approach is employed to quantify the spatial and temporal correlations within the daily data of Global Navigation Satellite System (GNSS) observations. Based on the quantitative spatiotemporal analysis, the proposed prediction model combines a convolutional neural network (CNN) and long short-term memory (LSTM) network to capture spatial and temporal dependencies individually. Spatial–temporal attention mechanisms are implemented to optimize the model. Additionally, we develop a single-point prediction model using LSTM and a multiple-point prediction model using the CNN-LSTM without an attention mechanism to compare the forecasting capabilities of the attention-based CNN-LSTM model. The Outang landslide in the Three Gorges Reservoir Area (TGRA), characterized by a large and active landslide equipped with an advanced monitoring system, is taken as a studied case. The temporal MIC results shed light on the response times of monitored daily displacement to external factors, showing a lagging duration of between 10 and 50 days. The spatial MIC results indicate mutual influence among different locations within the landslide, particularly in the case of nearby sites experiencing significant deformation. The attention-based CNN-LSTM model demonstrates an impressive predictive performance across six monitoring stations within the Outang landslide area. Notably, it achieves a remarkable maximum coefficient of determination (R2) value of 0.9989, accompanied by minimum values for root mean squared error (RMSE), absolute mean error (MAE), and mean absolute percentage error (MAPE), specifically, 1.18 mm, 0.99 mm, and 0.33%, respectively. The proposed model excels in predicting displacements at all six monitoring points, whereas other models demonstrate strong performance at specific individual stations but lack consistent performance across all stations. This study, involving quantitative deformation characteristics analysis and spatiotemporal displacement prediction, holds promising potential for a more profound understanding of landslide evolution and a significant contribution to reducing landslide risk.

Dynamic multi-scale spatial–temporal graph convolutional network for traffic flow prediction

Statistical methods to bias correct global or regional climate model output are now common to get data closer to observations in distribution. However, most bias correction (BC) methods work for one variable and one location at a time and basically reproduce the temporal structure of the models. The intervariable, spatial, and temporal dependencies of the corrected data are usually poor compared to observations. Here, the authors propose a novel method for multivariate BC. The empirical copula–bias correction (EC–BC) combines a one-dimensional BC with a shuffling technique that restores an empirical multidimensional copula. Several BC methods are investigated and compared to high-resolution reference data over the French Mediterranean basin: notably, (i) a 1D BC method applied independently to precipitation and temperature fields, (ii) a recent conditional correction approach developed for producing correct two-dimensional intervariable structures, and (iii) the EC–BC method. Assessments are realized in terms of intervariable, spatial, and temporal dependencies, and an objective evaluation using the integrated quadratic distance (IQD) is presented. As expected, the 1D methods cannot produce correct multidimensional properties. The conditional technique appears efficient for intervariable properties but not for spatial and temporal dependencies. EC–BC provides realistic dependencies in all respects: intervariable, spatial, and temporal. The IQD results are clearly in favor of EC–BC. As many BC methods, EC–BC relies on a stationarity assumption and is only able to reproduce patterns inherited from historical data. However, because of its ease of coding, its speed of application, and the quality of its results, the EC–BC method is a very good candidate for all needs in multivariate bias correction.

Spatial-temporal forecasting has attracted tremendous attention in a wide\nrange of applications, and traffic flow prediction is a canonical and typical\nexample. The complex and long-range spatial-temporal correlations of traffic\nflow bring it to a most intractable challenge. Existing works typically utilize\nshallow graph convolution networks (GNNs) and temporal extracting modules to\nmodel spatial and temporal dependencies respectively. However, the\nrepresentation ability of such models is limited due to: (1) shallow GNNs are\nincapable to capture long-range spatial correlations, (2) only spatial\nconnections are considered and a mass of semantic connections are ignored,\nwhich are of great importance for a comprehensive understanding of traffic\nnetworks. To this end, we propose Spatial-Temporal Graph Ordinary Differential\nEquation Networks (STGODE). Specifically, we capture spatial-temporal dynamics\nthrough a tensor-based ordinary differential equation (ODE), as a result,\ndeeper networks can be constructed and spatial-temporal features are utilized\nsynchronously. To understand the network more comprehensively, semantical\nadjacency matrix is considered in our model, and a well-design temporal\ndialated convolution structure is used to capture long term temporal\ndependencies. We evaluate our model on multiple real-world traffic datasets and\nsuperior performance is achieved over state-of-the-art baselines.\n

Accurate prediction of short-term passenger inflow and outflow at subway stations is important for the real-time operation and effective management of urban transit systems. Existing studies widely acknowledge that such prediction relies on capturing the temporal dependencies inherent in historical flow data and the spatial correlations between the target station and surrounding factors influencing passenger demand. Building on this principle, we propose a dynamic spatial-temporal decomposition and gate fusion network that explicitly accounts for subway-bus transfer behaviours and effectively captures the spatial-temporal dependencies. The main contributions of this paper are two-fold: (1) We develop a gated cross-modal attention fusion module to capture the interactions between subway and bus stations through a dual-stream architecture. Unlike existing approaches that focus on general multi-modal flow prediction, this module is specifically designed to model the unique characteristics of subway-bus transfer behaviour; and (2) In contrast to prevailing deep learning methods that adopt unified architectures to model spatial and temporal dependencies, we propose a novel dual-path spatial-temporal adaptive gate fusion module to better capture the heterogeneity between these dependencies across subway and bus modes. Furthermore, we introduce a temporal decomposition module and a dynamic compressed causal graph convolution module to enhance temporal sensitivity and overcome the structural limitations of static network topologies, respectively. Numerical experiments on real-world data from Beijing, China, demonstrate that our model consistently outperforms state-of-the-art methods. The datasets and code implementation are released on https://github.com/liushan-seu/DST-DFN.