Nonlinear Temporal Dynamics Research Articles

Multi-Scale Spatio-Temporal Attention Networks for Network-Scale Traffic Learning and Forecasting.

Accurate and timely forecasting of traffic on local road networks is crucial for deploying effective dynamic traffic control, advanced route planning, and navigation services. This task is particularly challenging due to complex spatio-temporal dependencies arising from non-Euclidean spatial relations in road networks and non-linear temporal dynamics influenced by changing road conditions. This paper introduces the spatio-temporal network embedding (STNE) model, a novel deep learning framework tailored for learning and forecasting graph-structured traffic data over extended input sequences. Unlike traditional convolutional neural networks (CNNs), the model employs graph convolutional networks (GCNs) to capture the spatial characteristics of local road network topologies. Moreover, the segmentation of very long input traffic data into multiple sub-sequences, based on significant temporal properties such as closeness, periodicity, and trend, is performed. Multi-dimensional long short-term memory neural networks (MDLSTM) are utilized to flexibly access multi-dimensional context. Experimental results demonstrate that the STNE model surpasses state-of-the-art traffic forecasting benchmarks on two large-scale real-world traffic datasets.

A Spatial-Temporal Graph Convolutional Recurrent Network for Transportation Flow Estimation.

Accurate estimation of transportation flow is a challenging task in Intelligent Transportation Systems (ITS). Transporting data with dynamic spatial-temporal dependencies elevates transportation flow forecasting to a significant issue for operational planning, managing passenger flow, and arranging for individual travel in a smart city. The task is challenging due to the composite spatial dependency on transportation networks and the non-linear temporal dynamics with mobility conditions changing over time. To address these challenges, we propose a Spatial-Temporal Graph Convolutional Recurrent Network (ST-GCRN) that learns from both the spatial stations network data and time series of historical mobility changes in order to estimate transportation flow at a future time. The model is based on Graph Convolutional Networks (GCN) and Long Short-Term Memory (LSTM) in order to further improve the accuracy of transportation flow estimation. Extensive experiments on two real-world datasets of transportation flow, New York bike-sharing system and Hangzhou metro system, prove the effectiveness of the proposed model. Compared to the current state-of-the-art baselines, it decreases the estimation error by 98% in the metro system and 63% in the bike-sharing system.

Comparison of the Impact between Classical and Novel Strains of Rabbit Haemorrhagic Disease on Wild Rabbit Populations in Spain.

The outbreaks of two strains of rabbit haemorrhagic disease (RHD) (GI.1 and GI.2) in the Iberian Peninsula have caused substantial economic losses in commercial rabbitries and have affected the conservation of rabbit-sensitive predators due to the dramatic decline of their natural populations. However, the assessment of the impact of both RHD strains on wild rabbit populations has been limited to a few small-scale studies. Little is known about the overall impact within its native range. In this study, we described and compared the effects of GI.1 and GI.2 countrywide by using time series of hunting bag data widely available across the country and compared their trend during the first eight years after the first outbreak of GI.1 (i.e., 1998) and GI.2 (i.e., 2011), respectively. We used Gaussian generalised additive models (GAM) with the number of hunted rabbits as the response variable and year as the predictor to evaluate the non-linear temporal dynamics of the population at the national and regional community levels. The first GI.1 caused a population decline of around 53%, affecting most Spanish regional communities where the disease occurred. The positive trend observed after GI.1 in Spain ended with the initial outbreak of GI.2, which did not appear to cause a national population decline. In contrast, we found significant variability in the rabbit population trend among regional communities, where some increased, and others decreased. Such a disparity is unlikely to be explained by a single factor; rather, it appears to result from several factors, such as climatic conditions, host resistance improvement, virulence attenuation, or population density. Our study suggests that a national comprehensive hunting bag series could aid in elucidating the differences in the impact of emerging diseases on a large scale. Future research should focus on national longitudinal serological studies to shed light on the immunological status of rabbit populations in different regions to better understand the evolution of RHD strains and the resistance gained by the wild populations.

Dynamic adaptive spatio-temporal graph neural network for multi-node offshore wind speed forecasting

Multi-node offshore wind speed forecasting is a challenging task due to the complex dynamic spatial dependencies and highly nonlinear temporal dynamics present in the ocean. As deep learning advances, graph neural networks (GNNs) have great potential to capture spatial dependencies in ocean meteorology. However, existing GNN models usually use predefined or learned static graphs. They lack the ability to model dynamic spatial associations, which can limit the performance of GNNs. In this paper, we propose a dynamic adaptive spatio-temporal graph neural network (DASTGN) that uses dynamic graph convolution (DGCN) to capture dynamic spatial dependencies in offshore wind speed data. Based on the assumption that not only long-term static associations but also short-term dynamic associations exist in the spatial domain and that the importance of these two associations is different, we propose a dynamic adaptive graph generation module to generate static and dynamic graphs to model these two associations. Meanwhile, a matrix fusion mechanism is proposed to fuse them into the optimal dynamic graph, which is fed into the DGCN module. We employ a temporal convolution module to capture the nonlinear temporal dependencies. Finally, the above modules are integrated into a dedicated spatio-temporal convolution module to predict wind speed. Extensive experiments on real wind speed datasets in Chinese seas showed that the DASTGN improved the performance of the optimal baseline model by 3.05% and 3.69% in terms of the MAE and RMSE, respectively. To demonstrate that the DASTGN can effectively model dynamic spatial associations, the generated graph structure is visualized and analyzed. Finally, we present policy implications aimed at enhancing the security of the power system.

Learning spatiotemporal statistical shape models for non-linear dynamic anatomies.

Numerous clinical investigations require understanding changes in anatomical shape over time, such as in dynamic organ cycle characterization or longitudinal analyses (e.g., for disease progression). Spatiotemporal statistical shape modeling (SSM) allows for quantifying and evaluating dynamic shape variation with respect to a cohort or population of interest. Existing data-driven SSM approaches leverage information theory to capture population-level shape variations by learning correspondence-based (landmark) representations of shapes directly from data using entropy-based optimization schemes. These approaches assume sample independence and thus are unsuitable for sequential dynamic shape observations. Previous methods for adapting entropy-based SSM optimization schemes for the spatiotemporal case either utilize a cross-sectional design (ignoring within-subject correlation) or impose other limiting assumptions, such as the linearity of shape dynamics. Here, we present a principled approach to spatiotemporal SSM that relaxes these assumptions to correctly capture population-level shape variation over time. We propose to incorporate modeling the underlying time dependency into correspondence optimization via a regularized principal component polynomial regression. This approach is flexible enough to capture non-linear temporal dynamics while encoding population-specific spatial regularity. We demonstrate our method's efficacy on synthetic data and left atrium segmented from cardiac MRI scans. Our approach better captures the population modes of variation and a statistically significant time dependency than existing methods.

High-dimensional population inflow time series forecasting via an interpretable hierarchical transformer

Mobile device location data (MDLD) are emerging data sources in the transportation domain that contain large-scale, fine-grained information on population inflow. However, limited studies have built forecasting models based on large-scale MDLD-based population inflow time series. This task is challenging due to complex nonlinear temporal dynamics, high-dimensional time series structure (i.e. multiple time series with multi-shape inputs and outputs), and non-negligible impacts from various external factors. To address these challenges, this study introduces a deep learning framework, the Interpretable Hierarchical Transformer (IHTF), for nationwide county-level population inflow time series forecasting and interpretation. A variety of cutting-edge deep learning techniques are fused, including the variable selection network to incorporate external effects, the gated residual network to handle nonlinearity, and the transformer architecture to learn temporal dynamics. Different interior parameters, such as variable selection weight and temporal attention weight, are extracted to explain patterns learned by the framework. Numerical experiments show that IHTF outperforms extensive baseline models in forecasting accuracy. In addition, feature importance generated by IHTF is similar to the tree-based model, LightGBM, but exhibits a more even distribution, among which point-of-interests (POIs) count, county location, median household income, and percentage of accommodation and food services are the most important static variables. Moreover, attention weight demonstrates that IHTF can automatically learn the seasonality from time series. Taken together, this framework can serve as a reliable travel demand forecasting component in the transportation planning process that allows modeling the travel demand continuously instead of by snapshot.

Spatio-Temporal Neural Network for Channel Prediction in Massive MIMO-OFDM Systems

In massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems, a challenging problem is how to predict channel state information (CSI) (i.e., channel prediction) accurately in mobility scenarios. However, a practical obstacle is caused by CSI non-stationary and nonlinear dynamics in temporal domain. In this paper, we propose a spatio-temporal neural network (STNN) to achieve better performance by carefully taking into account the spatio-temporal characteristics of CSI. Specifically, STNN uses its encoder and decoder modules to capture the spatial correlation and temporal dependence of CSI. Further, the differencing-attention module is designed to deal with the non-stationary and nonlinear temporal dynamics and realize adaptive feature refinement for more accurate multi-step prediction. Additionally, an advanced training scheme is adopted to reduce the discrepancy between STNN training and testing. Evaluated on a realistic channel model with enhanced mobility and spherical waves, experimental results show that STNN can effectively improve the accuracy of prediction and perform well with respect to different signal to noise ratios (SNRs). Visualization and testing for unit root illustrate STNN is able to learn CSI time-varying patterns by alleviating series non-stationarity.

Diurnal Nonlinear Recurrence Metrics of Skin Temperature and Their Association with Metabolic Hormones in Contrasting Climate Settings: A Randomized Cross-Over Trial

The urban overheating phenomenon in Mediterranean cities is a societal challenge with vast implications for the protection of public health. An additional analysis of the pilot TEMP randomized 2 × 2 cross-over trial was set up, using wearable sensor-based skin temperature measurements (n = 14). The study objectives were to: (i) assess the recurrence patterns of skin temperature measurements in individuals spending time in two climatologically contrasting settings (urban versus mountainous), and (ii) evaluate the association between the diurnal nonlinear recurrence quantification analysis (RQA) metrics and metabolic hormone levels. The intervention was a short-term stay (5-7 days) in a mountainous, climate-cooler setting (range 600-900 m altitude), which is about a 1 h drive from the main urban centres of Cyprus. The RQA analysis showed a blunting phenomenon on the nonlinear temporal dynamics of skin temperature time series observed in the urban setting. Compared with the mountainous setting, a more stable (and thus less adaptive) profile of skin temperature dynamics in the urban setting appeared, being less deterministic and with a smaller degree of complexity. No significant (p > 0.05) associations were observed between the leptin or cortisol and any of the skin temperature dynamical descriptors. However, there were marginal associations between the adiponectin and laminarity (beta = 0.24, 95%CI: -0.02, 0.50, p = 0.07) and with determinism (beta = 0.23, 95%CI: -0.037, 0.50, p = 0.09). We found dysregulations in skin temperature temporal dynamics of the study population while residing in the urban setting when compared with the cooler mountainous setting; these dysregulations took the form of reduced cycle duration and complexity, while skin temperature dynamics became less responsive to perturbations and less regular in magnitude. More research is needed to better understand heat stress temporal dynamics and their influence on human health. Trial registration: This trial is registered with ClinicalTrials.gov; number: NCT03625817.

Acoustic nonlinearities in a quasi 1-D duct with arbitrary mean properties and mean flow

Nonlinear temporal dynamics of acoustic oscillations in a quasi one-dimensional (1-D) duct are investigated using both numerical and analytical methods. The spatiotemporal nonlinear wave equation is derived for pressure oscillations in a quasi 1-D duct with axially varying cross-section and spatially inhomogeneous mean properties such as the velocity, temperature, density and pressure. Using the finite element method with quadratic interpolation functions, the linear Helmholtz equation is solved for the modal shapes and frequencies. With the modal shape as the weighting function, the standard Galerkin method is applied to transform the spatiotemporal wave equation into a second-order nonlinear ordinary differential equation (ODE) governing the time evolution of modal amplitudes. The limit-cycle amplitude and frequency of pressure oscillations are quantified analytically using the Lindstedt–Poincaré perturbation method. Furthermore, to capture the transient evolution to the limit cycle, the method of averaging is applied to the nonlinear temporal ODE for the modal amplitude. From the Lindstedt–Poincaré method, it is seen that a limit cycle exists when the linear damping coefficient μ in the nonlinear ODE is of the opposite sign as the quantity S that is a function of the coefficients of the quadratic and cubic terms in the ODE. For a given S, limit cycle is created or destroyed as μ changes sign, a scenario referred to as the “Hopf bifurcation.” The phase portraits and limit-cycle amplitudes obtained from numerical solution are in excellent agreement with those derived from the analytical techniques.

A novel low-order spatiotemporal modeling method for nonlinear distributed parameter systems

Most distributed parameter systems (DPSs) are unknown, including unknown parameter, boundary and even structure, and have a strongly nonlinear spatiotemporal nature. In order to achieve desirable modeling accuracy, the models from the commonly used DPS modeling methods often have a high order, which makes them difficultly used for prediction and control. Here, a novel low-order spatiotemporal least squares support vector machine (LS-SVM) method is proposed for modeling unknown and nonlinear DPSs. Generally, the information of a certain sensor may be represented by information of its neighboring sensors due to the spatial correlation between them. Making use of this feature, a kernel-space based spatial correlation analysis method is developed for deleting redundant spatial kernel functions, from which a low-order model can be achieved and it is without loss of any spatial information. On this basis, a LS-SVM model is constructed to represent the nonlinear temporal dynamics. Integration of the without-redundant spatial kernel functions and the LS-SVM temporal model, a low-order spatiotemporal model is created to reconstruct the spatiotemporal dynamics of the nonlinear DPSs. Additional analysis and proof show that: (1) the proposed method has the same modeling performance with the without-order-reduction spatiotemporal modeling method; and (2) it has better modeling performance than the model with the same order achieved by the without-order-reduction one. Using case studies, the effectiveness of the proposed method and its superior modeling ability compared to several common methods are demonstrated.

A long short-term recurrent spatial-temporal fusion for myoelectric pattern recognition

Current state-of-the-art myoelectric interfaces employ traditional pattern recognition (PR) algorithms to decode the Electromyogram (EMG) signals into hand movements for controlling artificial limbs. Recently, deep learning (DL) models have also been exploited for EMG feature learning/extraction. Models like Convolutional Neural Networks (CNN), which capture the spatial correlations, and Long Short-Term Memory (LSTM), which capture the non-linear temporal dynamics of EMG time-series data, have been shown to outperform traditional EMG PR systems. Nevertheless, the large number of model parameters, long training times, and large amounts of data required to train these DL models remain limiting factors that may hinder their translation into clinically viable prostheses. Consequently, rather than applying DL directly, this paper leverages concepts derived from these models to build upon our proposed concept of a Fusion of Time Domain Descriptors (FTDD). The FTDD are augmented with Range Spatial Filtering (RSF) to capture the spatial correlations and combined into an LSTM-style framework. This process, denoted as Recurrent Spatial-Temporal Fusion (RSTF), can be applied in combination with any traditional feature extraction method to exploit temporal and spatial correlations, with the potential for bi-directional applications. The advantages of the proposed RSTF method include (1) the memory concept, capturing long- and short-term spatial and temporal dependencies of the EMG signals, (2) significantly improved performance outperforming other state-of-the-art models and (3) the simplicity and the fairly low computational costs for feature extraction. Results are bench-marked against several feature extraction methods, proving the power of the RSTF using data from 82 subjects from five EMG databases with varying recording characteristics. The proposed method significantly outperforms all other methods tested for EMG pattern recognition, including a deep LSTM and other CNN methods previously reported in the literature and at a fracture of the computational cost. On the most challenging dataset, improvements of as much as 15% were found.

Neuromorphic Implementation of a Continuous Attractor Neural Network With Various Synaptic Dynamics

A continuous attractor neural network (CANN) configured with various synaptic dynamics can implement many brain cognitive functions. Corresponding neuromorphic implementation can be beneficial to carry out these cognitive computations in real-time. Herein, we present a neuromorphic implementation of the CANN of spiking neurons on the field-programmable gate array (FPGA), in which the synaptic strength of local excitation and global inhibition can be configured to achieve winner-take-all (WTA) competition. In contrast to previously reported neuromorphic CANN, in addition to fast-linear synapses, recurrent connections can also be implemented with slow-nonlinear synapses. This endows the proposed CANN on the FPGA with the capability of performing neural computations that require slow and nonlinear temporal dynamics, such as decision making and working memory. Circuit simulations on the hardware reproduced gradually ramping neural activities observed in decision-making experiments and multiple sustained activities observed during the delay in working memory experiments, especially the fade-out and merging of activity bumps in the latter task. Theoretical analysis illuminated the underlying mechanisms of decision making and working memory on the FPGA. The unstable two-bump steady state of the CANN is responsible for the two-alternative decision making, similar to the saddle-node structure in the reduced two-variable decision model. Meanwhile, the stable uniformly distributed N-bump steady states account for the multiple-item working memory, similar to the multistability in previous mean-field models. Furthermore, the asymmetrical N-bump unstable steady states exhibit attractor dynamics underlying the fade-out and merging of activity bumps. The consistency between simulations on the hardware and the theoretical analysis demonstrated that the neuromorphic CANN is endowed with attractor dynamics relating to slow and nonlinear neural computations and has the potential to implement sophisticated cognitive functions by configuring various synaptic dynamics. This implementation shows promise for integrating the cognitive platform due to its characteristics of various dynamics and flexible configurations.

A Spatiotemporal Neural Network Modeling Method for Nonlinear Distributed Parameter Systems

Neural network (NN) has been widely used in the field of modeling of lumped parameter systems. However, an NN approach cannot be used to model complex nonlinear distributed parameter systems (DPSs) because it does not account for this type of system's relationship with space. In this article, we propose a novel spatiotemporal NN (SNN) method to model nonlinear DPSs, which considers not only nonlinear dynamics regarding time, but also a nonlinear relationship with space. A temporal NN model was first constructed to represent the nonlinear temporal dynamics of each sensor's position. A spatial distribution function was then developed to represent the nonlinear relationship between spatial points. This strategy results in inherent consideration of any spatial dynamics. Finally, by integrating both the temporal NN model and the spatial distribution function, a novel SNN model was created to represent the spatiotemporal dynamics of the nonlinear DPSs. A two-step solving approach was further developed to learn the model. Additional analysis and proof of concept showed the effectiveness of this proposed method. This proposed method is different from traditional data-driven modeling methods in that it uses full information from all sensors and does not require model reduction technology. Case studies not only demonstrate the effectiveness of this proposed method, but also its superior modeling performance as compared with several commonly used methods.

STMAG: A spatial-temporal mixed attention graph-based convolution model for multi-data flow safety prediction

Spatiotemporal safety forecasting has various applications in the neuroscience, climate and transportation domains. It is challenging due to (1) the complex spatial dependency on networks, (2) non-linear temporal dynamics with changing conditions and (3) the inherent difficulty of long-term forecasting. To address these challenges, a safety prediction model called the Spatial-Temporal Mixed Attention Graph-based Convolution model (STMAG) is proposed. Specifically, STMAG captures spatial dependency using graph convolutional networks (GCN), and temporal dependency using the sequence-to-sequence (Seq2Seq) architecture with the mixed attention mechanisms. A case study on the implementation of this model in traffic safety prediction is given as an example. Traffic safety forecasting is one canonical example of such a learning task, which is also a crucial problem to improving transportation and public safety. A number of detailed features (such as vehicle type, braking state, whether changing lanes or not) and exogenous variables (such as weather, time and road condition) are extracted from our big datasets. Finally, we conduct extensive experiments to evaluate the STMAG framework on real-world large-scale road network traffic datasets. Extensive experiments on our dataset show that the STMAG framework makes reasonably accurate predictions and significantly improves the prediction accuracy over baseline approaches.

Classification of time-domain waveforms using a speckle-based optical reservoir computer.

Reservoir computing is a recurrent machine learning framework that expands the dimensionality of a problem by mapping an input signal into a higher-dimension reservoir space that can capture and predict features of complex, non-linear temporal dynamics. Here, we report on a bulk electro-optical demonstration of a reservoir computer using speckles generated by propagating a laser beam modulated with a spatial light modulator through a multimode waveguide. We demonstrate that the hardware can successfully perform a multivariate audio classification task performed using the Japanese vowel speakers public data set. We perform full wave optical calculations of this architecture implemented in a chip-scale platform using an SiO2 waveguide and demonstrate that it performs as well as a fully numerical implementation of reservoir computing. As all the optical components used in the experiment can be fabricated using a commercial photonic integrated circuit foundry, our result demonstrates a framework for building a scalable, chip-scale, reservoir computer capable of performing optical signal processing.

Parallel CNN based big data visualization for traffic monitoring

In a real-time application such as traffic monitoring, it is required to process the enormous amount of data. Traffic prediction is essential for intelligent transportation systems (ITSs), traffic management authorities, and travelers. Traffic prediction has become a challenging task due to various non-linear temporal dynamics at different locations, complicated underlying spatial dependencies, and more extended step forecasting. To accommodate these instances, efficient visualization and data mining techniques are required to predict and analyze the massive amount of traffic big data. This paper presents a deep learning-based parallel convolutional neural network (Parallel-CNN) methodology to predict the traffic conditions of a specific region. The methodology of deep learning contains multiple processing layers and performs various computational strategies, which is used to learn representations of data with multilevel abstraction. The data has captured from the department of transportation; thus, the size of data is vast, and it can be analyzed to get the behavior of the traffic condition. The purpose of this paper is to monitor traffic behavior, which enables the user to make decisions to build the traffic-free cities. Experimental results show that the proposed methodology outperforms other existing methods such as KNN, CNN, and FIMT-DD.

A Novel Spatiotemporal Fuzzy Method for Modeling of Complex Distributed Parameter Processes

Fuzzy modeling has been widely used to model lumped parameter systems. However, it cannot be used to model complex distributed parameter systems (DPS) due to its inability to handle spatial dynamics. In this paper, we propose a novel spatiotemporal fuzzy method for the modeling of complex nonlinear DPSs. A spatial fuzzy model is first constructed to represent the nonlinear spatial dynamics. This process ensures that the space information is inherently considered in the spatiotemporal fuzzy model. A fuzzy model is then used to represent the nonlinear temporal dynamics. These two fuzzy models are further integrated to construct a spatiotemporal fuzzy model, which allows for the reconstruction of the DPS. Additionally, it can improve the modeling robustness even in the presence of noise due to the robust ability of fuzzy modeling. Performance analyses and experimental validations further show that the proposed method can effectively model complex nonlinear DPSs and has the better modeling ability than several commonly used methods.

An Adaptive Scale Sea Surface Temperature Predicting Method Based on Deep Learning With Attention Mechanism

Sea surface temperature (SST) prediction plays an important role in ocean-related fields. It is challenging due to the nonlinear temporal dynamics with changing complex factors and the inherent difficulties in long-scale predictions. Conventional models often lack efficient information extraction and cannot meet the requirements of long-scale predictions. Therefore, the gate recurrent unit (GRU) encoder-decoder with SST codes and dynamic influence link (DIL), GRU encoder-decoder (GED), which considered both the static and dynamic influence, is proposed in this letter. Each SST code, capturing the static information more effectively, was computed by all hidden states of the encoder and was individually associated with each predicted SST. The DIL, capturing the dynamic influence, connected the SST code with the early predicted future SST for solving the long-scale dependence problem. GED was tested on the Bohai Sea SST data sets and South China Sea SST data sets and compared with full-connected long-short term memory (FC-LSTM) and support vector regression. The results demonstrated that GED outperformed others on different prediction scales and different prediction terms (daily, weekly, and monthly), especially in terms of long-scale and long-term predictions. In addition, attention relationships between historical and future SSTs were further explored, and there was a meaningful finding that each future daily mean SST of Bohai Sea most strongly correlated with the past 27th to 29th historical values.

Modified Empirical Eigenfunctions and Its Applications for Model Reduction of Nonlinear Spatiotemporal Systems

Model reduction can greatly reduce complexity and difficulty of control design for spatiotemporal systems (STS) in engineering applications. Empirical eigenfunctions (EEFs) are widely used for the model reduction of spatiotemporal systems, however, truncation of higher modes may describe the behaviours of nonlinear spatiotemporal systems inaccurately. In this paper, modified EEFs are proposed and applied to model reduction of nonlinear spatiotemporal systems. Modified EEFs are obtained via modifying the weights matrix in the method of snapshots, which can be rewritten as linear combinations of initial EEFs. The coefficient matrix for combinations is computed according to the nonlinear temporal dynamics of STSs. Thus, the effects of higher modes are considered into modified EEFs with less computational requirements. The reduced model can give a more accurate description for behaviours of the system. The performance of the proposed method is further proved theoretically, and a numerical example demonstrates the effectiveness of the proposed method.

Nonlinear temporal dynamics of cerebral small vessel disease: The RUN DMC study.

Objective:To investigate the temporal dynamics of cerebral small vessel disease (SVD) by 3 consecutive assessments over a period of 9 years, distinguishing progression from regression.Methods:Changes in SVD markers of 276 participants of the Radboud University Nijmegen Diffusion Tensor and Magnetic Resonance Imaging Cohort (RUN DMC) cohort were assessed at 3 time points over 9 years. We assessed white matter hyperintensities (WMH) volume by semiautomatic segmentation and rated lacunes and microbleeds manually. We categorized baseline WMH severity as mild, moderate, or severe according to the modified Fazekas scale. We performed mixed-effects regression analysis including a quadratic term for increasing age.Results:Mean WMH progression over 9 years was 4.7 mL (0.54 mL/y; interquartile range 0.95–5.5 mL), 20.3% of patients had incident lacunes (2.3%/y), and 18.9% had incident microbleeds (2.2%/y). WMH volume declined in 9.4% of the participants during the first follow-up interval, but only for 1 participant (0.4%) throughout the whole follow-up. Lacunes disappeared in 3.6% and microbleeds in 5.7% of the participants. WMH progression accelerated over time: including a quadratic term for increasing age during follow-up significantly improved the model (p < 0.001). SVD progression was predominantly seen in participants with moderate to severe WMH at baseline compared to those with mild WMH (odds ratio [OR] 35.5, 95% confidence interval [CI] 15.8–80.0, p < 0.001 for WMH progression; OR 5.7, 95% CI 2.8–11.2, p < 0.001 for incident lacunes; and OR 2.9, 95% CI 1.4–5.9, p = 0.003 for incident microbleeds).Conclusions:SVD progression is nonlinear, accelerating over time, and a highly dynamic process, with progression interrupted by reduction in some, in a population that on average shows progression.