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Jiachen Li

Jiachen Li contributes to research discovery and scholarly infrastructure.

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Published work

21 published item(s)

preprint2026arXiv

Digital Twin AI: Opportunities and Challenges from Large Language Models to World Models

Digital twins, as precise digital representations of physical systems, have evolved from passive simulation tools into intelligent and autonomous entities through the integration of artificial intelligence technologies. This paper presents a unified four-stage framework that systematically characterizes AI integration across the digital twin lifecycle, spanning modeling, mirroring, intervention, and autonomous management. By synthesizing existing technologies and practices, we distill a unified four-stage framework that systematically characterizes how AI methodologies are embedded across the digital twin lifecycle: (1) modeling the physical twin through physics-based and physics-informed AI approaches, (2) mirroring the physical system into a digital twin with real-time synchronization, (3) intervening in the physical twin through predictive modeling, anomaly detection, and optimization strategies, and (4) achieving autonomous management through large language models, foundation models, and intelligent agents. We analyze the synergy between physics-based modeling and data-driven learning, highlighting the shift from traditional numerical solvers to physics-informed and foundation models for physical systems. Furthermore, we examine how generative AI technologies, including large language models and generative world models, transform digital twins into proactive and self-improving cognitive systems capable of reasoning, communication, and creative scenario generation. Through a cross-domain review spanning eleven application domains, including healthcare, aerospace, smart manufacturing, robotics, and smart cities, we identify common challenges related to scalability, explainability, and trustworthiness, and outline directions for responsible AI-driven digital twin systems.

preprint2026arXiv

EvoNav: Evolutionary Reward Function Design for Robot Navigation with Large Language Models

Robot navigation is a crucial task with applications to social robots in dynamic human environments. While Reinforcement Learning (RL) has shown great promise for this problem, the policy quality is highly sensitive to the specification of reward functions. Hand-crafted rewards require substantial domain expertise and embed inductive biases that are difficult to audit or adapt, limiting their effectiveness and leading to suboptimal performance. In this paper, we propose EvoNav, an evolutionary framework that automates the design of robot navigation reward functions via large language models (LLMs). To overcome prohibitively costly policy training, EvoNav evaluates each candidate proposal from the LLM via a progressive three-stage warm-up-boost procedure. EvoNav advances from analytical proxies with low-cost surrogates, such as small datasets and analytic rules, to lightweight rollouts and, finally, to full policy training, enabling computationally efficient exploration under effective feedback. Experiment results show that EvoNav produces more effective navigation policies than manually designed RL rewards and state-of-the-art reward design methods.

preprint2026arXiv

PD-4DGS:Progressive Decomposition of 4D Gaussian Splatting for Bandwidth-Adaptive Dynamic Scene Streaming

4D Gaussian Splatting (4DGS) enables high-quality dynamic novel view synthesis, yet current models remain monolithic bitstreams that clients must download in full before any frame can be rendered, causing black-screen waits of tens to hundreds of seconds on mobile bandwidth and leaving 4DGS incompatible with modern adaptive-bitrate delivery. Progressive 3DGS compression alleviates this for static scenes, but it acts only on spatial anchors and cannot partition the temporal deformation networks that dominate dynamic-scene size. We present PD-4DGS, the first framework for progressive compression and on-demand transmission of 4DGS. Hierarchical Deformation Decomposition (HDD) externalises the coarse-to-fine motion hierarchy already latent in 4DGS into three independently transmittable layers -- a static scaffold, a global deformation, and a local refinement -- so that any prefix of the bitstream is already renderable, turning a single training run into a scalable, DASH/HLS-compatible bitstream. A Gaussian-entropy attribute rate-distortion loss together with a temporal mask consistency regulariser shrink the base layer while suppressing low-bitrate flicker; a capacity-weighted rollout schedule, gated online by a learnt activation rate rho, then prevents deformation-network under-training without any per-scene hyperparameter. On the Dycheck iPhone benchmark, PD-4DGS cuts the streamed bitstream by >60% at matched rendering fidelity and reduces first-frame latency from 73--930 s to ~1.7 s on a 2 Mbps link, uniquely enabling true on-demand progressive streaming for 4DGS.

preprint2026arXiv

Priority-Aware Multi-Robot Coverage Path Planning

Multi-robot systems are widely used for coverage tasks that require efficient coordination across large environments. In Multi-Robot Coverage Path Planning (MCPP), the objective is typically to minimize the makespan by generating non-overlapping paths for full-area coverage. However, most existing methods assume uniform importance across regions, limiting their effectiveness in scenarios where some zones require faster attention. We introduce the Priority-Aware MCPP (PA-MCPP) problem, where a subset of the environment is designated as prioritized zones with associated weights. The goal is to minimize, in lexicographic order, the total priority-weighted latency of zone coverage and the overall makespan. To address this, we propose a scalable two-phase framework combining (1) greedy zone assignment with local search, spanning-tree-based path planning, and (2) Steiner-tree-guided residual coverage. Experiments across diverse scenarios demonstrate that our method significantly reduces priority-weighted latency compared to standard MCPP baselines, while maintaining competitive makespan. Sensitivity analyses further show that the method scales well with the number of robots and that zone coverage behavior can be effectively controlled by adjusting priority weights.

preprint2026arXiv

Prototypical Contrastive Learning-based CLIP Fine-tuning for Object Re-identification

This work aims to adapt large-scale pre-trained vision-language models, such as contrastive language-image pretraining (CLIP), to enhance the performance of object reidentification (Re-ID) across various supervision settings. Although prompt learning has enabled a recent work named CLIP-ReID to achieve promising performance, the underlying mechanisms and the necessity of prompt learning remain unclear due to the absence of semantic labels in ReID tasks. In this work, we first analyze the role prompt learning in CLIP-ReID and identify its limitations. Based on our investigations, we propose a simple yet effective approach to adapt CLIP for supervised object Re-ID. Our approach directly fine-tunes the image encoder of CLIP using a prototypical contrastive learning (PCL) loss, eliminating the need for prompt learning. Experimental results on both person and vehicle Re-ID datasets demonstrate the competitiveness of our method compared to CLIP-ReID. Furthermore, we extend our PCL-based CLIP fine-tuning approach to unsupervised scenarios, where we achieve state-of-the art performance. Code is available at https://github.com/RikoLi/PCL-CLIP.

preprint2024arXiv

Disentangled Neural Relational Inference for Interpretable Motion Prediction

Effective interaction modeling and behavior prediction of dynamic agents play a significant role in interactive motion planning for autonomous robots. Although existing methods have improved prediction accuracy, few research efforts have been devoted to enhancing prediction model interpretability and out-of-distribution (OOD) generalizability. This work addresses these two challenging aspects by designing a variational auto-encoder framework that integrates graph-based representations and time-sequence models to efficiently capture spatio-temporal relations between interactive agents and predict their dynamics. Our model infers dynamic interaction graphs in a latent space augmented with interpretable edge features that characterize the interactions. Moreover, we aim to enhance model interpretability and performance in OOD scenarios by disentangling the latent space of edge features, thereby strengthening model versatility and robustness. We validate our approach through extensive experiments on both simulated and real-world datasets. The results show superior performance compared to existing methods in modeling spatio-temporal relations, motion prediction, and identifying time-invariant latent features.

preprint2022arXiv

BCOT: A Markerless High-Precision 3D Object Tracking Benchmark

Template-based 3D object tracking still lacks a high-precision benchmark of real scenes due to the difficulty of annotating the accurate 3D poses of real moving video objects without using markers. In this paper, we present a multi-view approach to estimate the accurate 3D poses of real moving objects, and then use binocular data to construct a new benchmark for monocular textureless 3D object tracking. The proposed method requires no markers, and the cameras only need to be synchronous, relatively fixed as cross-view and calibrated. Based on our object-centered model, we jointly optimize the object pose by minimizing shape re-projection constraints in all views, which greatly improves the accuracy compared with the single-view approach, and is even more accurate than the depth-based method. Our new benchmark dataset contains 20 textureless objects, 22 scenes, 404 video sequences and 126K images captured in real scenes. The annotation error is guaranteed to be less than 2mm, according to both theoretical analysis and validation experiments. We re-evaluate the state-of-the-art 3D object tracking methods with our dataset, reporting their performance ranking in real scenes. Our BCOT benchmark and code can be found at https://ar3dv.github.io/BCOT-Benchmark/.

preprint2022arXiv

Combining Localized Orbital Scaling Correction and Bethe-Salpeter Equation for Accurate Excitation Energies

We applied localized orbital scaling correction (LOSC) in Bethe-Salpeter equation (BSE) to predict accurate excitation energies for molecules. LOSC systematically eliminates the delocalization error in the density functional approximation and is capable of approximating quasiparticle (QP) energies with accuracy similar or better than the $GW$ Green's function approach and with much less computational cost. The QP energies from LOSC instead of commonly used $G_{0}W_{0}$ and ev$GW$ are directly used in BSE. We show that the BSE/LOSC approach greatly outperforms the commonly used BSE/$G_{0}W_{0}$ approach for predicting excitations with different characters. For the calculations for Truhlar-Gagliardi test set containing valence, charge transfer (CT) and Rydberg excitations, BSE/LOSC with the Tamm-Dancoff approximation provides a comparable accuracy to time-dependent density functional theory (TDDFT) and BSE/ev$GW$. For the calculations of Stein CT test set and Rydberg excitations of atoms, BSE/LOSC considerably outperforms both BSE/$G_{0}W_{0}$ and TDDFT approaches with a reduced starting point dependence. BSE/LOSC is thus a promising and efficient approach to calculate excitation energies for molecular systems.

preprint2022arXiv

ConvNeXt-backbone HoVerNet for nuclei segmentation and classification

This manuscript gives a brief description of the algorithm used to participate in CoNIC Challenge 2022. After the baseline was made available, we follow the method in it and replace the ResNet baseline with ConvNeXt one. Moreover, we propose to first convert RGB space to Haematoxylin-Eosin-DAB(HED) space, then use Haematoxylin composition of origin image to smooth semantic one hot label. Afterwards, nuclei distribution of train and valid set are explored to select the best fold split for training model for final test phase submission. Results on validation set shows that even with channel of each stage smaller in number, HoVerNet with ConvNeXt-tiny backbone still improves the mPQ+ by 0.04 and multi r2 by 0.0144

preprint2022arXiv

Escaping the Big Data Paradigm with Compact Transformers

With the rise of Transformers as the standard for language processing, and their advancements in computer vision, there has been a corresponding growth in parameter size and amounts of training data. Many have come to believe that because of this, transformers are not suitable for small sets of data. This trend leads to concerns such as: limited availability of data in certain scientific domains and the exclusion of those with limited resource from research in the field. In this paper, we aim to present an approach for small-scale learning by introducing Compact Transformers. We show for the first time that with the right size, convolutional tokenization, transformers can avoid overfitting and outperform state-of-the-art CNNs on small datasets. Our models are flexible in terms of model size, and can have as little as 0.28M parameters while achieving competitive results. Our best model can reach 98% accuracy when training from scratch on CIFAR-10 with only 3.7M parameters, which is a significant improvement in data-efficiency over previous Transformer based models being over 10x smaller than other transformers and is 15% the size of ResNet50 while achieving similar performance. CCT also outperforms many modern CNN based approaches, and even some recent NAS-based approaches. Additionally, we obtain a new SOTA result on Flowers-102 with 99.76% top-1 accuracy, and improve upon the existing baseline on ImageNet (82.71% accuracy with 29% as many parameters as ViT), as well as NLP tasks. Our simple and compact design for transformers makes them more feasible to study for those with limited computing resources and/or dealing with small datasets, while extending existing research efforts in data efficient transformers. Our code and pre-trained models are publicly available at https://github.com/SHI-Labs/Compact-Transformers.

preprint2022arXiv

EvolveHypergraph: Group-Aware Dynamic Relational Reasoning for Trajectory Prediction

While the modeling of pair-wise relations has been widely studied in multi-agent interacting systems, its ability to capture higher-level and larger-scale group-wise activities is limited. In this paper, we propose a group-aware relational reasoning approach (named EvolveHypergraph) with explicit inference of the underlying dynamically evolving relational structures, and we demonstrate its effectiveness for multi-agent trajectory prediction. In addition to the edges between a pair of nodes (i.e., agents), we propose to infer hyperedges that adaptively connect multiple nodes to enable group-aware relational reasoning in an unsupervised manner without fixing the number of hyperedges. The proposed approach infers the dynamically evolving relation graphs and hypergraphs over time to capture the evolution of relations, which are used by the trajectory predictor to obtain future states. Moreover, we propose to regularize the smoothness of the relation evolution and the sparsity of the inferred graphs or hypergraphs, which effectively improves training stability and enhances the explainability of inferred relations. The proposed approach is validated on both synthetic crowd simulations and multiple real-world benchmark datasets. Our approach infers explainable, reasonable group-aware relations and achieves state-of-the-art performance in long-term prediction.

preprint2022arXiv

Grouptron: Dynamic Multi-Scale Graph Convolutional Networks for Group-Aware Dense Crowd Trajectory Forecasting

Accurate, long-term forecasting of pedestrian trajectories in highly dynamic and interactive scenes is a long-standing challenge. Recent advances in using data-driven approaches have achieved significant improvements in terms of prediction accuracy. However, the lack of group-aware analysis has limited the performance of forecasting models. This is especially nonnegligible in highly crowded scenes, where pedestrians are moving in groups and the interactions between groups are extremely complex and dynamic. In this paper, we present Grouptron, a multi-scale dynamic forecasting framework that leverages pedestrian group detection and utilizes individual-level, group-level and scene-level information for better understanding and representation of the scenes. Our approach employs spatio-temporal clustering algorithms to identify pedestrian groups, creates spatio-temporal graphs at the individual, group, and scene levels. It then uses graph neural networks to encode dynamics at different scales and aggregate the embeddings for trajectory prediction. We conducted extensive comparisons and ablation experiments to demonstrate the effectiveness of our approach. Our method achieves 9.3% decrease in final displacement error (FDE) compared with state-of-the-art methods on ETH/UCY benchmark datasets, and 16.1% decrease in FDE in more crowded scenes where extensive human group interactions are more frequently present.

preprint2022arXiv

High-Capacity Rechargeable $Li/Cl_2$ Batteries with Graphite Positive Electrodes

Developing new types of high-capacity and high-energy density rechargeable battery is important to future generations of consumer electronics, electric vehicles, and mass energy storage applications. Recently we reported ~ 3.5 V sodium/chlorine $(Na/Cl_2)$ and lithium/chlorine $(Li/Cl_2)$ batteries with up to 1200 mAh $g^{-1}$ reversible capacity, using either a Na or Li metal as the negative electrode, an amorphous carbon nanosphere (aCNS) as the positive electrode, and aluminum chloride $(AlCl_3)$ dissolved in thionyl chloride $(SOCl_2)$ with fluoride-based additives as the electrolyte. The high surface area and large pore volume of aCNS in the positive electrode facilitated NaCl or LiCl deposition and trapping of $Cl_2$ for reversible $NaCl/Cl_2$ or $LiCl/Cl_2$ redox reactions and battery discharge/charge cycling. Here we report an initially low surface area/porosity graphite (DGr) material as the positive electrode in a $Li/Cl_2$ battery, attaining high battery performance after activation in carbon dioxide $(CO_2)$ at 1000 °C (DGr_ac) with the first discharge capacity ~ 1910 mAh $g^{-1}$ and a cycling capacity up to 1200 mAh $g^{-1}$. Ex situ Raman spectroscopy and X-ray diffraction (XRD) revealed the evolution of graphite over battery cycling, including intercalation/de-intercalation and exfoliation that generated sufficient pores for hosting $LiCl/Cl_2$ redox. This work opens up widely available, low-cost graphitic materials for high-capacity alkali metal/$Cl_2$ batteries. Lastly, we employed mass spectrometry to probe the $Cl_2$ trapped in the graphitic positive electrode, shedding light into the $Li/Cl_2$ battery operation.

preprint2022arXiv

Important Object Identification with Semi-Supervised Learning for Autonomous Driving

Accurate identification of important objects in the scene is a prerequisite for safe and high-quality decision making and motion planning of intelligent agents (e.g., autonomous vehicles) that navigate in complex and dynamic environments. Most existing approaches attempt to employ attention mechanisms to learn importance weights associated with each object indirectly via various tasks (e.g., trajectory prediction), which do not enforce direct supervision on the importance estimation. In contrast, we tackle this task in an explicit way and formulate it as a binary classification ("important" or "unimportant") problem. We propose a novel approach for important object identification in egocentric driving scenarios with relational reasoning on the objects in the scene. Besides, since human annotations are limited and expensive to obtain, we present a semi-supervised learning pipeline to enable the model to learn from unlimited unlabeled data. Moreover, we propose to leverage the auxiliary tasks of ego vehicle behavior prediction to further improve the accuracy of importance estimation. The proposed approach is evaluated on a public egocentric driving dataset (H3D) collected in complex traffic scenarios. A detailed ablative study is conducted to demonstrate the effectiveness of each model component and the training strategy. Our approach also outperforms rule-based baselines by a large margin.

preprint2022arXiv

Multireference Density Functional Theory for Describing Ground and Excited States with Renormalized Singles

We applied renormalized singles (RS) in the multireference density functional theory (DFT) to calculate accurate energies of ground and excited states. The multireference DFT approach determines the total energy of the $N$-electron system as the sum of the ($N-2$)-electron energy from a density functional approximation (DFA) and the two-electron addition energies from the particle-particle Tamm-Dancoff approximation (ppTDA), naturally including multireference description. The ppTDA@RS-DFA approach uses the RS Hamiltonian capturing all singles contributions in calculating two-electron addition energies, and its total energy is optimized with the optimized effective potential method. It significantly improves the original ppTDA@DFA. For ground states, ppTDA@RS-DFA properly describes dissociation curves tested and the double bond rotation of ethylene. For excited states, ppTDA@RS-DFA provides accurate excitation energies and largely eliminates the DFA dependence. ppTDA@RS-DFA thus provides an efficient multireference approach to systems with static correlation.

preprint2022arXiv

OneFormer: One Transformer to Rule Universal Image Segmentation

Universal Image Segmentation is not a new concept. Past attempts to unify image segmentation in the last decades include scene parsing, panoptic segmentation, and, more recently, new panoptic architectures. However, such panoptic architectures do not truly unify image segmentation because they need to be trained individually on the semantic, instance, or panoptic segmentation to achieve the best performance. Ideally, a truly universal framework should be trained only once and achieve SOTA performance across all three image segmentation tasks. To that end, we propose OneFormer, a universal image segmentation framework that unifies segmentation with a multi-task train-once design. We first propose a task-conditioned joint training strategy that enables training on ground truths of each domain (semantic, instance, and panoptic segmentation) within a single multi-task training process. Secondly, we introduce a task token to condition our model on the task at hand, making our model task-dynamic to support multi-task training and inference. Thirdly, we propose using a query-text contrastive loss during training to establish better inter-task and inter-class distinctions. Notably, our single OneFormer model outperforms specialized Mask2Former models across all three segmentation tasks on ADE20k, CityScapes, and COCO, despite the latter being trained on each of the three tasks individually with three times the resources. With new ConvNeXt and DiNAT backbones, we observe even more performance improvement. We believe OneFormer is a significant step towards making image segmentation more universal and accessible. To support further research, we open-source our code and models at https://github.com/SHI-Labs/OneFormer

preprint2022arXiv

SeMask: Semantically Masked Transformers for Semantic Segmentation

Finetuning a pretrained backbone in the encoder part of an image transformer network has been the traditional approach for the semantic segmentation task. However, such an approach leaves out the semantic context that an image provides during the encoding stage. This paper argues that incorporating semantic information of the image into pretrained hierarchical transformer-based backbones while finetuning improves the performance considerably. To achieve this, we propose SeMask, a simple and effective framework that incorporates semantic information into the encoder with the help of a semantic attention operation. In addition, we use a lightweight semantic decoder during training to provide supervision to the intermediate semantic prior maps at every stage. Our experiments demonstrate that incorporating semantic priors enhances the performance of the established hierarchical encoders with a slight increase in the number of FLOPs. We provide empirical proof by integrating SeMask into Swin Transformer and Mix Transformer backbones as our encoder paired with different decoders. Our framework achieves a new state-of-the-art of 58.25% mIoU on the ADE20K dataset and improvements of over 3% in the mIoU metric on the Cityscapes dataset. The code and checkpoints are publicly available at https://github.com/Picsart-AI-Research/SeMask-Segmentation .

preprint2022arXiv

Symbolic Expression Transformer: A Computer Vision Approach for Symbolic Regression

Symbolic Regression (SR) is a type of regression analysis to automatically find the mathematical expression that best fits the data. Currently, SR still basically relies on various searching strategies so that a sample-specific model is required to be optimized for every expression, which significantly limits the model's generalization and efficiency. Inspired by the fact that human beings can infer a mathematical expression based on the curve of it, we propose Symbolic Expression Transformer (SET), a sample-agnostic model from the perspective of computer vision for SR. Specifically, the collected data is represented as images and an image caption model is employed for translating images to symbolic expressions. A large-scale dataset without overlap between training and testing sets in the image domain is released. Our results demonstrate the effectiveness of SET and suggest the promising direction of image-based model for solving the challenging SR problem.

preprint2020arXiv

SkyNet: a Hardware-Efficient Method for Object Detection and Tracking on Embedded Systems

Object detection and tracking are challenging tasks for resource-constrained embedded systems. While these tasks are among the most compute-intensive tasks from the artificial intelligence domain, they are only allowed to use limited computation and memory resources on embedded devices. In the meanwhile, such resource-constrained implementations are often required to satisfy additional demanding requirements such as real-time response, high-throughput performance, and reliable inference accuracy. To overcome these challenges, we propose SkyNet, a hardware-efficient neural network to deliver the state-of-the-art detection accuracy and speed for embedded systems. Instead of following the common top-down flow for compact DNN (Deep Neural Network) design, SkyNet provides a bottom-up DNN design approach with comprehensive understanding of the hardware constraints at the very beginning to deliver hardware-efficient DNNs. The effectiveness of SkyNet is demonstrated by winning the competitive System Design Contest for low power object detection in the 56th IEEE/ACM Design Automation Conference (DAC-SDC), where our SkyNet significantly outperforms all other 100+ competitors: it delivers 0.731 Intersection over Union (IoU) and 67.33 frames per second (FPS) on a TX2 embedded GPU; and 0.716 IoU and 25.05 FPS on an Ultra96 embedded FPGA. The evaluation of SkyNet is also extended to GOT-10K, a recent large-scale high-diversity benchmark for generic object tracking in the wild. For state-of-the-art object trackers SiamRPN++ and SiamMask, where ResNet-50 is employed as the backbone, implementations using our SkyNet as the backbone DNN are 1.60X and 1.73X faster with better or similar accuracy when running on a 1080Ti GPU, and 37.20X smaller in terms of parameter size for significantly better memory and storage footprint.

preprint2020arXiv

Social-WaGDAT: Interaction-aware Trajectory Prediction via Wasserstein Graph Double-Attention Network

Effective understanding of the environment and accurate trajectory prediction of surrounding dynamic obstacles are indispensable for intelligent mobile systems (like autonomous vehicles and social robots) to achieve safe and high-quality planning when they navigate in highly interactive and crowded scenarios. Due to the existence of frequent interactions and uncertainty in the scene evolution, it is desired for the prediction system to enable relational reasoning on different entities and provide a distribution of future trajectories for each agent. In this paper, we propose a generic generative neural system (called Social-WaGDAT) for multi-agent trajectory prediction, which makes a step forward to explicit interaction modeling by incorporating relational inductive biases with a dynamic graph representation and leverages both trajectory and scene context information. We also employ an efficient kinematic constraint layer applied to vehicle trajectory prediction which not only ensures physical feasibility but also enhances model performance. The proposed system is evaluated on three public benchmark datasets for trajectory prediction, where the agents cover pedestrians, cyclists and on-road vehicles. The experimental results demonstrate that our model achieves better performance than various baseline approaches in terms of prediction accuracy.

preprint2019arXiv

Generic Tracking and Probabilistic Prediction Framework and Its Application in Autonomous Driving

Accurately tracking and predicting behaviors of surrounding objects are key prerequisites for intelligent systems such as autonomous vehicles to achieve safe and high-quality decision making and motion planning. However, there still remain challenges for multi-target tracking due to object number fluctuation and occlusion. To overcome these challenges, we propose a constrained mixture sequential Monte Carlo (CMSMC) method in which a mixture representation is incorporated in the estimated posterior distribution to maintain multi-modality. Multiple targets can be tracked simultaneously within a unified framework without explicit data association between observations and tracking targets. The framework can incorporate an arbitrary prediction model as the implicit proposal distribution of the CMSMC method. An example in this paper is a learning-based model for hierarchical time-series prediction, which consists of a behavior recognition module and a state evolution module. Both modules in the proposed model are generic and flexible so as to be applied to a class of time-series prediction problems where behaviors can be separated into different levels. Finally, the proposed framework is applied to a numerical case study as well as a task of on-road vehicle tracking, behavior recognition, and prediction in highway scenarios. Instead of only focusing on forecasting trajectory of a single entity, we jointly predict continuous motions for interactive entities simultaneously. The proposed approaches are evaluated from multiple aspects, which demonstrate great potential for intelligent vehicular systems and traffic surveillance systems.