Multiscale Framework Research Articles

Collaborative multiscale water resources planning in England

ABSTRACT Practitioners in water resources planning in England are navigating new multiscale planning structures. A National Framework introduced in 2020 embeds strategic cooperation across a privatized industry to meet higher resilience standards. This study presents a critical analysis of the National Framework to identify feasible solutions to navigate England’s water crisis. Findings are based on engagement with practitioners identifying successes, challenges, and lessons learned throughout 2020–2024. Recommendations include establishing a national coordination office as part of an explicit multiscale framework. Over time, the framework can continue to be built upon for a more informed transition to adaptive, collaborative, integrated planning.

Multi-scale Perception Enhancement of Structural Patch Decomposition and Fusion for low light imaging

Low light imaging usually exhibits defects such as low contrast, low signal-to-noise ratio, low image quality and severe color distortion. Enhancing images taken in such scenes is efficient and rewarding for image restoration and computer vision tasks under demanding imaging conditions. Existing low light image enhancement(LLIE) algorithms rarely take the consistency of image into account, showing insufficiently realistic restoration results. To solve these problem, we propose a LLIE method based on Multi-scale Perception Enhancement of Structural Patch Decomposition and Fusion (MPESPDF-LLIE) to restore images captured in a low light scene. In this model, each image patch is firstly decomposed into four components: perception gain, average intensity, signal strength and signal structure. Next the enhancement model produces the global perception gain and the original enhanced image patches by the inverted dehazing strategy. Based on the original enhanced image patches, an efficient way is used to enhance the signal strength and signal structure in patches. Then a brightness compensation is adopted to improve average intensity. Finally the four components are fused and aggregated to the final image in a multi-scale framework. Experimental results demonstrate that MPESPDF-LLIE is advantageous and effective in preserving detail information and maintaining image consistency, thus MPESPDF-LLIE compensates for the shortcomings of low-light imaging and improves image quality. The source code is available at: https://github.com/LYor61/MPESPDF-LLIE.

Tucker Decomposition Enhanced Dynamic Graph Convolutional Networks for Crowd Flows Prediction

Crowd flows prediction is an important problem for traffic management and public safety. Graph Convolutional Network (GCN), known for its ability to effectively capture and utilize topological information, has demonstrated significant advancements in addressing this problem. However, GCN-based models were often based on predefined crowd-flow graphs via historical movement behaviors of human beings and traffic vehicles, which ignored the abnormal changes in crowd flows. In this study, we propose a multi-scale fusion GCN-based framework with Tucker decomposition named mTDNet to enhance dynamic GCN for Crowd flows prediction. Following the paradigm of extant methods, we also employ the predefined crowd-flow graphs as a part of mTDNet to effectively capture the historical movement behaviors of crowd flows. To capture the abnormal changes, we propose a Tucker decomposition-based network with the product of the adjacency matrix of historical movement pattern graphs and an adaptive learning tensor ( \(ALT\) ) by reconstructing the crowd flows. Particularly, we utilize the Tucker decomposition scheme to decompose \(ALT\) , which enhances the dynamic learning of graph structures, allowing for effective capturing of the dynamic changes in crowd flow, including abnormal changes. Furthermore, a multi-scale three-dimensional GCN is utilized to mine and fuse the multiscale spatio-temporal information from crowd flows, to further boost the mTDNet prediction performance. Experiments conducted on two real-world datasets showed that the proposed mTDNet surpasses other crowd flow prediction methods.

Biomimetic Turing machine: A multiscale theoretical framework for the inverse design of target space curves

Biomimetic Turing machine: A multiscale theoretical framework for the inverse design of target space curves

A Geographic Multi-Scale Machine Learning Framework for Predicting Solar Irradiation on Tilted Surfaces

A Geographic Multi-Scale Machine Learning Framework for Predicting Solar Irradiation on Tilted Surfaces

Multiscale topology optimization for designing locally resonant acoustic metamaterials with specified low-frequency bandgaps

Locally resonant acoustic metamaterials (LRAMs) have significant potential to isolate low-frequency vibrations and noise, whereas designing them with specified bandgaps is challenging. Compared to the monoscale method, the multiscale method can design microstructures that form equivalent materials to act as scatterers, coatings, and matrices. This may aid in obtaining LRAMs that are sometimes difficult to achieve with the monoscale method. Therefore, a multiscale topology optimization method is presented to design LRAMs with bandgaps that meet specified frequency constraints. Since bandgap optimizations are complicated, many local minimum solutions may exist when using sensitivity-based methods. To mitigate this issue, a macro-parameter optimization stage using a genetic algorithm (GA) is added between the macro and micro optimizations in this top-down multiscale framework. As a result, the method comprises three optimization stages: macro-bandgap optimization, macro-parameter optimization, and micro-optimization. Since the macrostructures consist of multiple microstructures and the microstructures consist of multiple materials, a parameterized level-set-based multi-material topology method is adopted to obtain topologies on both scales. The effectiveness of the proposed method is demonstrated through numerical examples of two optimization problems. The first is to obtain LRAMs with the maximum bandgap width while ensuring their bandgaps encompass specified frequency ranges. The other is to obtain LRAMs with specified bandgaps. Successfully obtained LRAMs with specified bandgaps demonstrate the application prospects of this method in designing structures and devices to address issues related to vibrations and noise.

Multiscale structural optimization for prescribed deformations in the nonlinear elastic regime

In this paper, a multiscale structural optimization framework capable of efficiently designing two-scale structures with prescribed displacements in the nonlinear elastic regime is presented. In contrast to previous multiscale structural optimization frameworks, which are founded upon the assumptions of linear elasticity, the present framework is capable of efficiently operating within the nonlinear elastic regime. At the core of the present framework is a parameterized microscale geometry, which through the straightforward manipulation of the microscale parameters provides direct access to both positive and negative Poisson’s ratios. The microscale model is concurrently coupled to the macroscale model such that only the microscale parameter space traversed by the optimizer is resolved during the optimization procedure, leading to a significant reduction in the computational expense of analysis. To demonstrate the capability of this framework, three prescribed deformation profiles are targeted by three distinct optimization procedures. In all instances, the deformation profile is successfully targeted. To verify the accuracy of the optimized structures, high-fidelity single-scale simulations are performed. In each case, excellent agreement is noted between the high-fidelity simulations and the corresponding optimized macroscale displacement fields, with errors of less than 10%.

ESL-YOLO: Small Object Detection with Effective Feature Enhancement and Spatial-Context-Guided Fusion Network for Remote Sensing

Improving the detection of small objects in remote sensing is essential for its extensive use in various applications. The diminutive size of these objects, coupled with the complex backgrounds in remote sensing images, complicates the detection process. Moreover, operations like downsampling during feature extraction can cause a significant loss of spatial information for small objects, adversely affecting detection accuracy. To tackle these issues, we propose ESL-YOLO, which incorporates feature enhancement, fusion, and a local attention pyramid. This model includes: (1) an innovative plug-and-play feature enhancement module that incorporates multi-scale local contextual information to bolster detection performance for small objects; (2) a spatial-context-guided multi-scale feature fusion framework that enables effective integration of shallow features, thereby minimizing spatial information loss; and (3) a local attention pyramid module aimed at mitigating background noise while highlighting small object characteristics. Evaluations on the publicly accessible remote sensing datasets AI-TOD and DOTAv1.5 indicate that ESL-YOLO significantly surpasses other contemporary object detection frameworks. In particular, ESL-YOLO enhances mean average precision mAP by 10% and 1.1% on the AI-TOD and DOTAv1.5 datasets, respectively, compared to YOLOv8s. This model is particularly adept at small object detection in remote sensing imagery and holds significant potential for practical applications.

In-Operando Virtual Look inside the Battery: The Role of Physics-Based Models in Advancing State-of-X Diagnostics of Batteries with Phase-Separating Materials

Lithium iron phosphate (LFP)-based batteries, as well as their mixed analogues, such as lithium iron manganese phosphate batteries, are gaining importance owing to their high safety, high power density, acceptable energy density, durability, lack of resource-limiting critical metals, and especially their excellent price-performance ratio. However, these phase-separating active materials are characterized by several intriguing phenomena, as for example inherent voltage hysteresis, when subjected to finite (nearly) constant currents [1], newly reported entering into the voltage hysteresis during transient battery operation [2], memory effect [3], electrochemical oscillations [4] and chemical inductor properties [5]. Combining these effects with relatively flat open circuit potential of these materials imposes a significant challenge on detailed State-of-X diagnostics of batteries with phase separating materials, which is a challenge for advanced health and safety aware battery management. This paper tackles this challenge by applying innovative physics-based models to boost advanced State-of-X diagnostics of batteries with phase-separating active materials, hence elucidating an emerging area of model-based monitoring, diagnostics and management of such batteries. Innovative State-of-X diagnostics functionalities are made possible by the use of multi-scale simulation framework for batteries, which is scalable in terms of model complexity and thus its computational expenses. The multi-scale simulation framework is based on the state-of-the-art submodels that incorporate key aspects of electrochemical phenomena in phase-separating materials, while featuring spatial and temporal resolution [6, 7]. Starting from this advanced basis, this paper highlights coupling of the multi-scale simulation framework with parameter identification techniques and methods for assessing uniqueness of parameter identification into an innovative State-of-X diagnostics tool, which can be executed in the cloud. This innovative State-of-X diagnostics tool, thus, makes possible advanced virtual sensing of intra-cell states and determination of model parameters, which are interlinked with performance and degradation descriptors of the cells. These innovative functionalities make possible obtaining unprecedented model-based insight into intra-cell phenomena. One of the key merits of the proposed multi-scale simulation framework is also its scalability and computational efficiency, which opens perspectives to run computationally optimized version of the models on the vehicle, e.g. in the Battery Management System (BMS) or edge device, hence, making possible unprecedentedly accurate monitoring and management of batteries. In addition, connectivity with the State-of-X diagnostics tool in the cloud makes possible automated online updates of model parameters, control limiters and State-of-X descriptors between the State-of-X diagnostics tool in the cloud and the computationally optimized BMS/edge version of the model, complying with the vision of the Software Defined Vehicle (SDV). Presented results demonstrate capability of the newly proposed model-based framework to perform advanced State-of-X diagnostics focusing on three key aspects: 1. demonstrating capability of the multi-scale simulation framework to model specifics of phase-separating material, being enabler for adequate model-based State-of-X diagnostics; 2. providing methodological guidelines to efficiently execute State-of-X diagnostics; and 3. presenting SDV compatible methodology to distribute functionalities between the computationally optimized BMS/edge version of the model and the detailed State-of-X diagnostics tool in the cloud. Specific results, hence, demonstrate, how applied advanced physics-based models enable: 1. more accurate determination of Li-throughput in phase-separating materials, 2. more accurate determination of active particle fraction and potentials of the electrodes, 3. more accurate determination of intra- and inter-particle phase separated states [2], which determine chemical potential and electrode potential as well as its EIS response [5], and 4. duration of presence of phase boundaries in active particles, which are associated with material degradation. It will be summarized how such innovative chemistry-informed State-of-X diagnostics tool opens new perspectives in: 1. future digital twins for in-operando assessment of State-of-X diagnostics of battery with phase-separating active materials, 2. virtual exploration of BMS protocols, 3. innovative model-based DoE methodologies to maximize the amount of information obtained from a minimum amount of experimental data to identify State-of-X descriptors as uniquely as possible, and 4. future functionalities such as orchestration of preemptive self-healing processes. Presented methodology and results, therefore, indicate that proposed State-of-X diagnostics based on the multi-scale simulation framework pushes boundaries of State-of-X diagnostics and opens emerging area of advanced monitoring, diagnostics, and management of batteries with phase-separating materials.

A dimension-enhanced residual multi-scale attention framework for identifying anomalous waveforms of fault recorders

The continuous introduction of technologies such as distributed generation, wind power, and photovoltaic energy poses challenges to identifying abnormal waveforms in power disturbances. Due to the constant increase in abnormal features, existing waveform recognition schemes for power disturbance abnormalities cannot meet the requirements of high accuracy and reliability. In this paper, a Dimension-Enhanced Residual Multi-Scale Attention Framework for identifying power disturbance abnormal waveforms is proposed. This framework first employs the Phase Adaptive Adjustment (PAA) method to address the phase offset problem of original recording data, then uses the Gramian Angle Field method to perform dimensionality expansion on the data processed by PAA, and finally utilizes the Residual Pyramid Squeeze Attention Network (ResPSANet) for identifying power disturbance abnormal waveforms. Experiments demonstrate that the proposed approach improves the performance of power disturbance abnormal waveform recognition by 10% compared to existing schemes.

Multilevel modeling and control of dynamic systems

The underlying changes of complex dynamic systems are affected by numerous highly interdependent components with nonlinear interactions and cannot be suitably predicted by merely analyzing their individual parts. Recent technological developments (reducing the size of actuators and sensors, increasing speed and productivity) make it possible to monitor and handle systems on time, even during transient processes. In many practical applications, to effectively study rapidly evolving systems, their structure has to be examined at three levels: Micro-Scale (Short-Term), Meso-Scale (Intermediate-Term), and Macro-Scale (Long-Term). This multiscale framework provides a powerful tool for understanding and managing the intricate dynamics of complex systems. Macro-scale and micro-scale approaches are conventionally utilized in general system modeling and control theory, especially within the fields of networked control and multi-agent systems. By leveraging the meso-scale perspective, it is possible to balance detailed component analysis with overarching system behaviors, thereby enhancing the efficiency and effectiveness of operational strategies in complex systems. This paper presents and discusses a formal meso-level depiction of dynamics and control, assuming a finite number of attractors form and remain stable over time progress. Integral characteristics and dynamics of clusters are defined, simplifying control synthesis while maintaining problem formulation. A significant challenge is the model error due to changing cluster structures linked to randomized estimation and optimization algorithms valid under unknown disturbances. To demonstrate the practicality of this framework, the approach is applied to control tasks of a group of robots, leading to scalable and effective control strategies.

Adaptive Multi-Scale Bayesian Framework for MFL Inspection of Steel Wire Ropes

Magnetic flux leakage (MFL) technology is widely used in steel wire rope (SWR) inspection for non-destructive testing. However, accurate defect characterization requires advanced signal processing techniques to handle complex noise conditions and varying defect types. This paper presents a novel adaptive multi-scale Bayesian framework for MFL signal analysis in SWR inspection. Our approach integrates discrete wavelet transform with adaptive thresholding and multi-scale feature fusion, enabling simultaneous detection of minute defects and large-area corrosion. To validate our method, we implemented a four-channel MFL detection system and conducted extensive experiments on both simulated and real-world datasets. Compared with state-of-the-art methods, including long short-term memory (LSTM), attention mechanisms, and isolation forests, our approach demonstrated significant improvements in precision, recall, and F1 score across various tolerance levels. The proposed method showed superior detection performance, with an average precision of 91%, recall of 89%, and an F1 score of 0.90 in high-noise conditions, surpassing existing techniques. Notably, our method showed superior performance in high-noise environments, reducing false positive rates while maintaining high detection sensitivity. While computational complexity in real-time processing remains a challenge, this study provides a robust solution for non-destructive testing of SWR, potentially improving inspection efficiency and defect localization accuracy. Future work will focus on optimizing algorithmic efficiency and exploring transfer learning techniques for enhanced adaptability across different non-destructive testing (NDT) domains. This research not only advances signal processing and anomaly detection technology but also contributes to enhancing safety and maintenance efficiency in critical infrastructure.

A multi-scale modeling framework for solidification cracking during welding

A multi-scale multi-physics modeling framework has been developed to predict solidification cracking susceptibility (SCS) during welding. The framework integrates a thermo-mechanical finite element model to simulate temperature and strain rate profiles during welding, a cellular automata model to simulate the solidified microstructure in the weld pool, and a granular model to calculate the pressure drop in the mushy zone. Verification was achieved by comparing the model’s predictions with welding experiments on two steels, demonstrating its capability to accurately capture the effects of process parameters, grain refinement, and alloy composition on SCS. Results indicate that increasing welding velocity, while maintaining a constant power-to-velocity ratio, extends the size of the mushy zone and increases the maximum pressure drop in the mushy zone, leading to higher SCS. Grain refinement decreases separation velocities and the permeability of liquid channels, which increases SCS, but it also raises the coalescence temperature, resulting in an overall reduction in SCS. Alloy composition impacts SCS through thermal diffusivity and segregation. Lower thermal diffusivity or stronger segregation tends to elongate the mushy zone, resulting in an increase in SCS. This framework provides a robust tool for understanding the mechanisms of solidification cracking, optimizing welding parameters to prevent its occurrence, and comparing SCS of different compositions during alloy design.

Hierarchical deformation and anisotropic behavior of (α+β) Ti alloys: A microstructure-informed multiscale constitutive model study

In this study, the hierarchical deformation and anisotropic behavior of (α+β) Ti alloys are investigated using a novel microstructure-informed multiscale constitutive model. State-of-the-art crystal plasticity finite element (CPFE) models, due to their emphasis on a single length scale, are inadequate for capturing the complex hierarchical behavior of additively manufactured (AM) (α+β) Ti alloys, which are characterized by columnar grains and lamellar subgrain features at distinct length scales. To overcome this limitation, a decoupled multiscale framework was developed, integrating representative volume elements (RVEs) for both the columnar grain structure at the higher length scale and the lamellar subgrain microstructure at the lower length scale, with equal emphasis on each. The material behaviors at these scales were modeled using an anisotropic classical plasticity model and a mechanism-based CPFE model, respectively. The framework was experimentally validated for Directed Energy Deposition (DED) manufactured Ti-6Al-4V. It was then used to investigate microscopic stress/strain fields, deformation localizations at grain and subgrain levels, and stress partitioning among neighboring grains. From the insights gained a new theory of anisotropy for AM (α+β) Ti alloys is proposed.

MMS-EF: A Multi-Scale Modular Extraction Framework for Enhancing Deep Learning Models in Remote Sensing

The analysis of land cover using deep learning techniques plays a pivotal role in understanding land use dynamics, which is crucial for land management, urban planning, and cartography. However, due to the complexity of remote sensing images, deep learning models face practical challenges in the preprocessing stage, such as incomplete extraction of large-scale geographic features, loss of fine details, and misalignment issues in image stitching. To address these issues, this paper introduces the Multi-Scale Modular Extraction Framework (MMS-EF) specifically designed to enhance deep learning models in remote sensing applications. The framework incorporates three key components: (1) a multiscale overlapping segmentation module that captures comprehensive geographical information through multi-channel and multiscale processing, ensuring the integrity of large-scale features; (2) a multiscale feature fusion module that integrates local and global features, facilitating seamless image stitching and improving classification accuracy; and (3) a detail enhancement module that refines the extraction of small-scale features, enriching the semantic information of the imagery. Extensive experiments were conducted across various deep learning models, and the framework was validated on two public datasets. The results demonstrate that the proposed approach effectively mitigates the limitations of traditional preprocessing methods, significantly improving feature extraction accuracy and exhibiting strong adaptability across different datasets.

A shared multi-scale lightweight convolution generative network for few-shot multivariate time series forecasting

Time series forecasting is an important time series data mining technique. Among them, multivariate time series (MTS) forecasting has received extensive attention in many fields. However, many existing MTS forecasting models usually rely on a large amount of labeled data for model training, and data collection and labeling are difficult in real systems. The insufficient amount of data makes it difficult for the model to fully learn the intrinsic patterns and features of the data, which not only increases the prediction error, but also makes it hard to obtain satisfactory prediction results. To address this challenge, we propose a shared multi-scale lightweight convolution generative (SMLCG) network for few-shot multivariate time series forecasting by using samples generation strategy. The overall goal is to design a shared multi-scale feature generation prediction framework that generates data highly similar to the original sample and enriches the training sample to improve prediction accuracy. Specifically, the MTS is divided into different scales, and the multi-scale feature fusion module is utilized to capture and fuse the MTS information in different spatial dimensions to eliminate the heterogeneity among the data. Then, the key information in the multi-scale features is captured by a lightweight convolution generative network, and the feature weights are dynamically assigned to explore the change information. In addition, a spatio-temporal memory module is designed based on the parameter sharing strategy to capture the spatio-temporal dynamic relationship of sequences by learning the common knowledge in multi-scale features, thus improving the robustness and generalization ability. Through comprehensive experiments on four publicly available datasets and comparisons with other reported models, it is demonstrated that the SMLCG model can efficiently generate approximate samples in the few-shot case and provide excellent prediction results. The architecture of SMLCG serves as a valuable reference for practical solutions to address the few-shot problem in multivariate time series.

Geometric flow control in lateral flow assays: Macroscopic two-phase modeling

Lateral flow assays (LFAs) are widely employed in a diverse range of applications, including clinical diagnostics, pharmaceutical research, forensics, biotechnology, agriculture, food safety, and environmental analysis. A pivotal component of LFAs is the porous polymeric membrane, which facilitates the capillary-driven movement of fluids, known as “imbibition,” in which a wetting fluid displaces a non-wetting fluid within the pore space of the membrane. This study presents a multi-scale modeling framework designed to investigate the imbibition process within LFAs. The framework integrates microscopic membrane characteristics into a macroscopic two-phase flow model, allowing the simulation of imbibition in membranes with different micro-scale properties and macro-scale profiles. The validity of the model was established through comparative analysis with documented case studies, a macro-scale single-phase flow model, and experimental observations, demonstrating its accuracy in simulating the imbibition process. The study also examines imbibition in various geometric configurations, including bifurcated (Y-shaped) and multi-branch geometries commonly found in multiplexed LFAs. The influence of geometric features such as length ratio, width ratio, branching angle, bifurcation point location, and asymmetry on fluid transport is investigated. Results indicate that membranes with larger branching angles exhibit slower imbibition. In addition, the influence of membrane type on macroscopic flow patterns is evaluated, showing that membranes with lower permeability require longer imbibition times. The insights gained from this research support a data-driven strategy for manipulating wetting behavior within LFAs. This approach can be leveraged to optimize the performance of LFAs and increase their effectiveness in various applications.

MST-m6A: A Novel Multi-Scale Transformer-based Framework for Accurate Prediction of m6A Modification Sites Across Diverse Cellular Contexts

N6-methyladenosine (m6A) modification, a prevalent epigenetic mark in eukaryotic cells, is crucial in regulating gene expression and RNA metabolism. Accurately identifying m6A modification sites is essential for understanding their functions within biological processes and the intricate mechanisms that regulate them. Recent advances in high-throughput sequencing technologies have enabled the generation of extensive datasets characterizing m6A modification sites at single-nucleotide resolution, leading to the development of computational methods for identifying m6A RNA modification sites. However, most current methods focus on specific cell lines, limiting their generalizability and practical application across diverse biological contexts. To address the limitation, we propose MST-m6A, a novel approach for identifying m6A modification sites with higher accuracy across various cell lines and tissues. MST-m6A utilizes a multi-scale transformer-based architecture, employing dual k-mer tokenization to capture rich feature representations and global contextual information from RNA sequences at multiple levels of granularity. These representations are then effectively combined using a channel fusion mechanism and further processed by a convolutional neural network to enhance prediction accuracy. Rigorous validation demonstrates that MST-m6A significantly outperforms conventional machine learning models, deep learning models, and state-of-the-art predictors. We anticipate that the high precision and cross-cell-type adaptability of MST-m6A will provide valuable insights into m6A biology and facilitate advancements in related fields. The proposed approach is available at https://github.com/cbbl-skku-org/MST-m6A/ for prediction and reproducibility purposes.

Exploring multi-scale forgery clues for stereo super-resolution image forgery localization

Existing forgery image localization methods have achieved impressive performance on monocular images but struggle to maintain comparable performance on stereo super-resolution (SR) images. The stereo image SR process usually introduces additional noise, i.e., reconstruction artifacts, which interferes with the extraction of forgery clues and thus undermines the localization performance. To mitigate this issue, we present a multi-scale attention framework named SSR-IFL for stereo SR image forgery localization, which explores multi-scale forgery clues in stereo SR images to minimize disturbances caused by reconstruction artifacts. Specifically, the novel framework integrates two significant components: the multi-scale feature extraction (MSFE) network to thoroughly mine forgery clues against the inference of reconstruction artifacts, and the bidirectional progressive feature fusion (BPFF) network to effectively reason the learned forgery clues and obtain robust forgery feature representation. Under the MSFE network, the multi-dilated self-attention (MDSA) block makes full use of multi-resolution pixel correlation to adapt to changes in pixel correlation distributions induced by the stereo SR reconstruction process, thus extracting more precise multi-scale forgery clues. The BPFF network introduces a bidirectional feature fusion strategy to fuse multi-scale forgery clues, effectively eliminating redundant noise such as reconstruction artifacts and enhancing the robustness of forgery feature representation. Experimental results on public image datasets demonstrate that our method can achieve not only competitive performance on stereo SR images but also on monocular images.

A Multiscale Framework for Capturing Oscillation Dynamics of Autonomous Vehicles in Data-Driven Car-Following Models

A Multiscale Framework for Capturing Oscillation Dynamics of Autonomous Vehicles in Data-Driven Car-Following Models