Pith. sign in

REVIEW 4 major objections 6 minor 101 references

Towards Physics-informed Diffusion for Anomaly Detection in Trajectories

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Physics-informed diffusion detects spoofed trajectories by enforcing motion laws.

desk verdict A sensible physics-informed diffusion architecture, but the evaluation is circular: the synthetic anomalies are built from the exact kinematic violations the model penalizes, so the spoofing claim is not yet supported. read the letter →

arxiv 2506.06999 v2 pith:MWKSDSAG submitted 2025-06-08 cs.LG cs.AIcs.CVstat.ML

Arun Sharma , Mingzhou Yang , Majid Farhadloo , Subhankar Ghosh , Bharat Jayaprakash , Shashi Shekhar This is my paper
classification cs.LGcs.AIcs.CVstat.ML
keywords anomalydetectionGPSspoofingtrajectoryminingdiffusionprobabilisticmodelkinematicbicyclephysics-informedmachinelearningspatiotemporalattentionreconstructionerror
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that a diffusion-based generative model for trajectories can be made a much sharper detector of GPS-spoofing-style anomalies by teaching it the physics of motion. The authors add kinematic bicycle-model constraints to the denoising objective, so reconstructed trajectories are forced to obey relationships among position, heading, speed, and curvature. Anomalies are then scored by reconstruction error: physically impossible moves cannot be faithfully reconstructed and exceed a user-set threshold. On urban and maritime datasets with injected sudden speed changes, bearing jumps, and acceleration spikes, the method reports accuracy and F1 scores around 0.97–0.99, beating previous trajectory-anomaly detectors, and it also produces the lowest trajectory-generation errors. The societal hook is that spoofed vessel tracks are used to conceal sanctions-evading oil transfers and illegal fishing.

What carries the argument

The load-bearing mechanism is the physics-informed regularization loss built on the kinematic bicycle model (KBM), a three-degree-of-freedom model that assumes zero slip and low speed and relates position, heading, speed, and curvature by dx/dt = v cos(ψ), dy/dt = v sin(ψ), dψ/dt = vκ, and dv/dt = a. The paper penalizes the squared deviations from these equations in the decoder output (Eq. 21) and adds this to the diffusion variational lower bound and reconstruction loss. This is what turns the diffusion model from a purely statistical denoiser into one that cannot reproduce physically impossible motion; anomaly detection is then the reconstruction error ‖x0 − x̂0‖ exceeding a user threshold λ. A context-informed encoder with spatial and temporal attention adds neighbor trajectories as conditioning, capturing the signal that nearby objects are moving normally.

What would settle it

Feed Pi-DPM a recorded legitimate trajectory that is time-shifted or replayed at different speeds but still obeys the bicycle model; if such replayed tracks are not flagged because their reconstruction error stays below λ, the claim that physics-informed reconstruction detects deception-based GPS spoofing is refuted.

Watch

Extended reading notes

Core claim

The central discovery is that integrating the kinematic bicycle model into a denoising diffusion probabilistic model improves both anomaly detection and trajectory generation. During the reverse denoising process, the decoder is conditioned on neighbor trajectories through a context-informed encoder, and a physics loss penalizes deviations from the KBM differential equations, so the model cannot reproduce physically impossible motion. The paper reports that on three real-world datasets (Geolife, MarineCadastre, Danish Maritime Authority), the full model achieves accuracy and F1 scores of 0.97–0.99 at 5% injected anomalies, outperforming the strongest baseline by several points, and ablations confirm both components matter: removing the KBM drops F1 from 0.98 to 0.94 on Geolife, while removing the context encoder gives 0.96. In trajectory generation, RMSE on Geolife drops from 247.18 for a VAE baseline and 211.50 for a diffusion baseline to 143.33, with similar gains on the maritime datasets.

Load-bearing premise

The detecting power comes from assuming that the spoofing and attack trajectories injected in the evaluation—abrupt speed changes, sudden bearing jumps, and acceleration spikes—violate the kinematic bicycle model's assumptions of zero slip, low speed, and negligible inertia, so real attacks of that form will be caught; if real spoofing instead replays physically plausible motion or involves dynamics outside the bicycle model, the advantage may vanish.

Editorial extensions

If this is right

  • If the claim holds, spoofed trajectories can be flagged without labeled attack data, because anomalies are defined by physical infeasibility rather than by matching a known attack pattern.
  • The same physics-regularized diffusion backbone doubles as a higher-fidelity trajectory generator, useful for synthetic data and simulation.
  • The method transfers across maritime regions with as little as 5% target-domain data, suggesting it can be adapted quickly when new AIS coverage areas come online.
  • Across threshold values λ from 0.2 to 1.0, the model stays above the baselines, so an operator can trade recall against precision without losing the comparative advantage.
  • Ablations show the gains are additive: physics alone without the context encoder and context alone without physics both underperform the combination.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: the evaluation injects anomalies that are tailor-made to violate KBM assumptions (sudden bearing shifts greater than 90 degrees, speed jumps around ±50%), so the reported advantage is an upper bound for attacks of that specific form; replay attacks that rebroadcast physically legitimate tracks may evade detection.
  • Editorial inference: the physics loss is model-agnostic, so grafting the same KBM regularization onto a VAE or GAN generator would test whether the gain comes from the physics prior itself rather than from the diffusion backbone.
  • Editorial inference: the bicycle model assumes low speed, zero slip, and negligible inertia, so extending to four-wheel or six-degree-of-freedom models, which the paper lists as future work, would be needed for high-speed vessels or aircraft with different turning dynamics.
  • Editorial inference: the threshold λ is user-set, so a practical deployment would calibrate λ per region from normal-traffic reconstruction-error percentiles instead of a fixed global value.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The manuscript proposes Pi-DPM, a diffusion probabilistic model for trajectory anomaly detection that augments a transformer-based encoder-decoder with kinematic bicycle model (KBM) constraints. The training objective combines a variational lower bound, a reconstruction loss, and a physics loss penalizing deviations from KBM dynamics. Anomaly detection is performed by thresholding the reconstruction error between the input and denoised trajectories. The method is evaluated on Geolife, MarineCadastre, and Danish Maritime Authority data against anomaly detection and trajectory generation baselines, with additional ablations, threshold sensitivity, and transfer-learning experiments. The paper reports that Pi-DPM achieves higher accuracy and F1 for anomaly detection and lower RMSE/MAE/MAPE for trajectory generation than the compared baselines.

Significance. If the central claims held, the paper would make a useful contribution: combining a physics-informed regularizer with a diffusion backbone for trajectory anomaly detection is timely, and the proposed architecture is plausible. The public implementation and the breadth of the experimental comparison are strengths. However, the main empirical claim is currently not established because the synthetic anomalies used for evaluation are generated from exactly the kinematic violations penalized by the physics loss, and because several reported numbers are internally inconsistent. With a non-aligned anomaly benchmark and corrected computations, the contribution could be valuable.

major comments (4)
  1. [Sections 3.3, 4.1, and 6] The anomaly detection evaluation is circular with respect to the proposed physics prior. Section 4.1 injects anomalies as abrupt speed changes, bearing discontinuities, acceleration spikes, high-jerk events, and temporal resampling that changes speed by roughly ±50%, while Eq. 21 penalizes exactly the corresponding KBM violations: (dŷ/dt − v̂ cos ψ̂)^2, (dŷ/dt − v̂ sin ψ̂)^2, (dθ̂/dt − v̂κ̂)^2, and (dv̂/dt − â)^2. The gains in Tables 3, 5, and 6 therefore demonstrate that Pi-DPM detects kinematic-violation anomalies, not that it detects GPS spoofing. The record-and-replay spoofing scenario highlighted in Section 6 is a kinematically consistent replay of a legitimate route, so the assertion that such replays violate physical motion constraints needs evidence or a formal argument. I recommend evaluating on real spoofing incidents or on kinematically consistent synthetic anomalies in addition to the current kinematic-violation anomalies.
  2. [Table 4 and Appendix C] Table 4 reports MAE values greater than RMSE for nearly every method and dataset, which is impossible because RMSE = sqrt(mean(e^2)) ≥ mean(|e|) = MAE for any error vector. Examples include Geolife VAE (RMSE 247.18, MAE 333.30) and DMA DiffTraj (RMSE 215.21, MAE 364.66). This indicates a metric computation error, and since RQ5's claim of lower trajectory generation error rests on this table, the generation experiments must be recomputed and the corrected numbers reported. The text also calls the third metric 'Mean Average Precision Error (MAPE)' while Eq. 28 defines mean absolute percentage error; the acronym and definition need to be aligned.
  3. [Eq. 20] The reverse sampling update in Eq. 20 is not consistent with the DDPM update derived in Eqs. 9–10 and is not a standard DDIM update either. Canonical DDPM sampling is x_{t−1} = (1/sqrt(α_t))(x_t − ((1−α_t)/sqrt(1−ᾱ_t)) εθ(x_t,t)) + σ_t z, whereas Eq. 20 multiplies by sqrt(α_{t−1}), uses coefficient sqrt(1−α_t) on εθ, and adds an extra εθ term with coefficient sqrt(1−α_{t−1}−σ_t^2). If Eq. 20 is what was implemented, the model is not the DDPM described in the paper; if it is a typo, it must be corrected because the reverse sampler is load-bearing for the reconstruction-error anomaly score.
  4. [Eq. 22] The reconstruction loss LRec in Eq. 22 is not well defined: it sums over diffusion steps t=1..T the squared deviation between (x̂_t, ŷ_t) and (x_t, y_t), but x̂_t is never defined, and the reverse process outputs x_{t−1}, not x̂_t. Since LRec is part of the total training objective in Eq. 23, the manuscript should state explicitly how the reconstructed trajectory is formed during training and how the loss is computed. This is needed to make the training procedure reproducible.
minor comments (6)
  1. [Section 3.2] The text says 'After obtaining spatial information from Eq. (8)' but the spatial attention output is given in Eq. (11); the cross-reference should be corrected.
  2. [Section 7] The conclusion refers to 'Pi-CDPM' while the model is named Pi-DPM throughout the paper.
  3. [Appendix C and Appendix D] The definitions of Density Error, Trip Error, and Length Error are duplicated (Eq. 24 and Eq. 32) with identical text; one copy should be removed.
  4. [Table 2] The hyperparameter table lists Diffusion Steps as 1000 with a reference range of 200–500; the relationship between the chosen value and the range should be clarified.
  5. [Section 4.1 and Appendix E] The dataset statistics are inconsistent: Section 4.1 reports 132,135 coastal vessel trajectories for the Danish Maritime dataset, while Appendix E says the dataset includes over 1.5 million trajectories; these numbers should be reconciled.
  6. [Appendix A] The baseline is called 'DeepTA' in the appendix but 'DeepTEA' in the main text and reference [30]; the naming should be unified.

Circularity Check

1 steps flagged · score 6.0 of 10

Reported detection gains reduce to the anomaly generator matching the physics loss; score 6 reflects this partial evaluation circularity, while the method itself is otherwise self-contained.

  1. self definitional [Section 4.1 (Synthetic Data Generation); Eq. 21 (Physics-based Regularization); Section 3.4 (Reconstruction-based Regularization)]
    "Given the scarcity of annotated anomalous trajectory data across all three datasets, we synthetically injected context-aware anomalies using first- and second-order kinematic derivatives, such as abrupt speed changes, bearing discontinuities, acceleration spikes, and high-jerk events. ... In this paper, we focused on temporal distortions by reducing the time interval between consecutive points, which consequently induced perturbations in the computed speed (typically within a ±50% range)."

    Eq. 21 penalizes exactly the kinematic-bicycle constraints (d\hat x/dt − \hat v cos \hat ψ)^2, (d\hat y/dt − \hat v sin \hat ψ)^2, (d\hat θ/dt − \hat v\hat κ)^2, and (d\hat v/dt − \hat a)^2. The injected anomalies are abrupt speed changes, bearing discontinuities, acceleration spikes, and temporal resampling that changes speed by roughly ±50% — i.e., violations of precisely the quantities LPhy penalizes. Anomaly detection is then performed by reconstruction error EΔ=||x0−\hat x0||^2 after denoising with LPhy, which pulls reconstructions toward KBM-consistent motion. Hence the labeled anomalies are, by construction, high-LPhy examples and therefore high-reconstruction-error examples; the detector is measuring the label generator's own perturbation rule.

full rationale

The core circularity is confined to the experimental construction: the anomaly labels are generated from the same speed, bearing, acceleration, and jerk deviations that the physics regularizer of Eq. 21 is designed to penalize. Because detection uses reconstruction error after physics-regularized denoising, the separation between normal and anomalous trajectories is substantially engineered by the evaluation setup rather than discovered from real spoofing data. This is not full circularity: the diffusion reconstruction and KBM regularization are genuine algorithmic components, and the trajectory-generation results (Table 4, Table 7) are evaluated against real-data distributions and are not circular. No load-bearing self-citation or imported uniqueness theorem appears; the KBM is cited to Polack et al. rather than to the authors' own prior work, and self-citations such as [64]–[67] are related-work references rather than premises of the derivation. One additional risk, noted but not counted as a circular step, is that Section 6 asserts 'record and replay based anomalies that mimic historical trajectories but violate physical motion constraints' without evidence, while Section 1 limits the model to a simple 3-DoF KBM and excludes complex physics; a replayed historical trajectory is generally KBM-consistent, so the motivating spoofing scenario is not covered by the evaluation. Weighted together, the detection claim is partially circular because the benchmark's ground truth and the model's inductive bias are two implementations of the same constraint set.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim depends on user-chosen hyperparameters, lambda, w, gamma, and the diffusion schedule, which are either tuned or unreported, and on physical assumptions, KBM validity and curvature estimation, that are stated but not validated. No new entities are introduced. The threshold lambda is arguably the most consequential free parameter because it is the decision boundary for the entire anomaly detection task.

free parameters (5)
  • Reconstruction threshold lambda = Not reported; varied 0.2 to 1.0; best at 1.0
    User-defined decision boundary for classifying anomalies; no principled selection, tuned via sensitivity analysis in Section 4.4.
  • Physics loss weights w1-w4 = Not reported
    Weights in Eq. 21 balancing KBM derivative residuals; values are not given, preventing reproduction.
  • Total loss weights gamma1-gamma3 = Not reported
    Weights in Eq. 23 combining VLB, reconstruction, and physics losses; values not given.
  • Diffusion schedule and sampling hyperparameters = T=1000, beta1=1e-4, betaT=0.02, guidance scale 2.5, skip steps 4
    Chosen from stated reference ranges in Table 2, not optimized; these affect the reconstruction quality and detection results.
  • Curvature kappa in KBM physics loss = Estimated from data, method unspecified
    KBM control input in Eq. 13 and physics loss Eq. 21; no estimation method described.
assumptions (5)
  • standard math Gaussian forward diffusion with a fixed linear schedule yields a valid reverse process for trajectory reconstruction (Eqs. 1-3, 20).
    This is the standard DDPM framework (Ho et al., 2020), assumed without re-derivation; Eq. 20 deviates from the canonical DDPM update in ways that are not explained.
  • domain assumption The kinematic bicycle model with zero slip, negligible inertia, and low-speed operation describes physically plausible vehicle and vessel motion (Eqs. 12-13).
    Section 3.3 explicitly lists these assumptions; they are reasonable for low-speed cars but questionable for maritime vessels and high-speed urban traffic, and no validation that KBM holds on the datasets is provided.
  • ad hoc to paper Anomalous trajectories of interest manifest as violations of KBM kinematic constraints and will produce higher reconstruction error under a physics-regularized diffusion model.
    This is the core modeling assumption; it is engineered into the evaluation because the synthetic anomalies in Section 4.1 are generated by changing speed and bearing, which directly violate Eq. 21.
  • domain assumption The reconstruction threshold lambda separates normal from anomalous trajectories, and its value can be set by the user.
    lambda is part of the problem statement in Section 2.2; no principled method to set it is given, and the sensitivity analysis shows performance depends strongly on it.
  • domain assumption Curvature kappa can be estimated from trajectory data to serve as the KBM control input.
    Section 3.3 says kappa replaces wheelbase and steering angle because datasets lack them, but the estimation procedure for kappa is not described.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Towards Physics-informed Diffusion for Anomaly Detection in Trajectories." pith.science (2026). https://pith.science/paper/MWKSDSAG

@misc{pith2026250606999,
  author       = {Pith},
  title        = {Pith review of: Towards Physics-informed Diffusion for Anomaly Detection in Trajectories},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MWKSDSAG}},
  note         = {Machine review of arXiv:2506.06999}
}
read the original abstract

Given trajectory data, a domain-specific study area, and a user-defined threshold, we aim to find anomalous trajectories indicative of possible GPS spoofing (e.g., fake trajectory). The problem is societally important to curb illegal activities in international waters, such as unauthorized fishing and illicit oil transfers. The problem is challenging due to advances in AI generated in deep fakes generation (e.g., additive noise, fake trajectories) and lack of adequate amount of labeled samples for ground-truth verification. Recent literature shows promising results for anomalous trajectory detection using generative models despite data sparsity. However, they do not consider fine-scale spatiotemporal dependencies and prior physical knowledge, resulting in higher false-positive rates. To address these limitations, we propose a physics-informed diffusion model that integrates kinematic constraints to identify trajectories that do not adhere to physical laws. Experimental results on real-world datasets in the maritime and urban domains show that the proposed framework results in higher prediction accuracy and lower estimation error rate for anomaly detection and trajectory generation methods, respectively. Our implementation is available at https://github.com/arunshar/Physics-Informed-Diffusion-Probabilistic-Model.

Figures

Figures reproduced from arXiv: 2506.06999 by the authors.

Figure 1
Figure 1. An illustration example of problem statement where trajectories [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. A case study of an oil tanker Cathay Phoenix whose bearing distribution (right) is [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Limitations of Related Work Scope: This paper focuses on a simple kinematic model with 3 degrees-of-freedom. The model excludes complex physics due to dataset limitations. The model is applied to maritime and road networks, using Gaussian noise [34] for the denoising process. Organization: The rest of the paper is organized as follows. Section 2 introduces key concepts and formally defines the problem. 3 describes t… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Forward and reverse diffusion processes A forward process progressively introduces (q) Gaussian noise to x0 over T iterations [34] as described by: q(x1:T | x0) = Y T t=1 q(xt | xt−1) , (1) q(xt | xt−1) = N (xt | √ αt xt−1,(1 − αt)I) , (2) Here, the hyperparameters α1:…
Figure 5
Figure 5. Figure 5: Side-by-side training (left) and inference (right) procedures for the diffusion model. A reverse process (pθ) is the reverse of a forward diffusion process in that it begins with a completely noisy state, xT ∼ N (0, I). The model then incrementally refines the trajecto…
Figure 6
Figure 6. Figure 6: Physics-informed Diffusion Model (Pi-DPM) Architecture [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: shows three trajectories T1, T2, and T3, where trajectory T2 exhibits significantly different mobility behavior compared to T1 and T3 in terms of angular deviation and physical parameters such as speed resulting in a higher reconstruction error (λ) in red, as indicated…
Figure 8
Figure 8. Figure 8: Context-informed Encoder Spatial attention uses a sliding window at time t, where the target object’s trajectory features form the query Q, and its neighbors contribute keys K and values V . Attention weights, which are computed via softmax-scaled dot products of Q and…
Figure 9
Figure 9. Figure 9: Proposed Encoder-Decoder Model 3.3 Physics-informed Decoder Data-driven models capture complex patterns but often lack physical constraints, limiting robustness in noisy or unseen scenarios. To address this, we integrate the kinematic bicycle model (KBM) [59], a 3-DoF …
Figure 10
Figure 10. Figure 10: shows the kinematic bicycle model for a given constanct velocity v, [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 11
Figure 11. Figure 11: Kinematic Bicycle Model (KBM) datasets without high-speed maneuvers. The KBM models vehicle state is defined by z = [x, y, ψ] ⊤, and its input is defined by u = [v, δ], where (x, y) is the position, ψ is the heading, and v is the velocity. Substituting x = v cos(ψ), y…
Figure 12
Figure 12. Figure 12: Experiment Design 4.1 Experimental Design Dataset: We evaluated our Pi-DPM data model from three real-world datasets spanning diverse spatial and temporal domains, namely: (1) Geolife [93], (2) MarineCadastre [5], and (3) Dan￾ish Maritime Authority [2]. These datasets…
Figure 13
Figure 13. Figure 13: Effect of increases in the λ threshold (a) Transfer Learning in Maritime Domain (b) Transfer Learning across Domains [PITH_FULL_IMAGE:figures/full_fig_p015_13.png]
Figure 14
Figure 14. Figure 14: Illustrations of transfer learning scenarios. [PITH_FULL_IMAGE:figures/full_fig_p015_14.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

101 extracted references · 71 canonical work pages

  1. [1]

    Mark Alber, Adrian Buganza Tepole, William R Cannon, Suvranu De, Salvador Dura-Bernal, Krishna Garikipati, George Karniadakis, William W Lytton, Paris Perdikaris, Linda Petzold, et al. 2019. Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences.NPJ digital me...

    2019

  2. [2]

    Danish Maritime Authority. 2024. Danish Maritime Authority. https://www.dma.dk/ safety-at-sea/navigational-information/download-data

    2024

  3. [3]

    MF Aycin and RF Benekohal. 1999. Comparison of car-following models for simulation. Transportation research record1678, 1 (1999), 116–127

    1999

  4. [4]

    Petko Bakalov, Marios Hadjieleftheriou, Eamonn Keogh, and Vassilis J Tsotras. 2005. Effi- cient trajectory joins using symbolic representations. InProceedings of the 6th international conference on Mobile data management. 86–93

    2005

  5. [5]

    BOEM and NOAA. 2020. MarineCadastre.https://marinecadastre.gov/ais/

    2020

  6. [6]

    Chu Cao and Mo Li. 2021. Generating mobility trajectories with retained data utility. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining. 2610–2620

    2021

  7. [7]

    Chandola, A

    V . Chandola, A. Banerjee, and V . Kumar. 2009. Anomaly detection: A survey.ACM computing surveys (CSUR)41, 3 (2009), 1–58

    2009

  8. [8]

    Yanchuan Chang, Jianzhong Qi, Yuxuan Liang, and Egemen Tanin. 2023. Contrastive trajectory similarity learning with dual-feature attention. In2023 IEEE 39th International conference on data engineering (ICDE). IEEE, 2933–2945

    2023

Show all 101 references
  1. [9]

    Chao Chen, Daqing Zhang, Pablo Samuel Castro, Nan Li, Lin Sun, Shijian Li, and Zonghui Wang. 2013. iBOAT: Isolation-based online anomalous trajectory detection.IEEE Transactions on Intelligent Transportation Systems14, 2 (2013), 806–818

    2013

  2. [10]

    Lei Chen, M Tamer Özsu, and Vincent Oria. 2005. Robust and fast similarity search for moving object trajectories. InProceedings of the 2005 ACM SIGMOD international conference on Management of data. 491–502

    2005

  3. [11]

    Yun Chen and Jignesh M Patel. 2009. Design and evaluation of trajectory join algorithms. In Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems. 266–275. 17

    2009

  4. [12]

    Seongjin Choi, Jiwon Kim, and Hwasoo Yeo. 2021. TrajGAIL: Generating urban vehicle trajectories using generative adversarial imitation learning.Transportation Research Part C: Emerging Technologies128 (2021), 103091

    2021

  5. [13]

    Bangchao Deng, Xin Jing, Tianyue Yang, Bingqing Qu, Dingqi Yang, and Philippe Cudre- Mauroux. 2025. Revisiting Synthetic Human Trajectories: Imitative Generation and Benchmarks Beyond Datasaurus.arXiv:2409.13790(2025), 201–212

    2025 arXiv

  6. [14]

    Somayeh Dodge, Robert Weibel, and Anna-Katharina Lautenschütz. 2008. Towards a taxonomy of movement patterns.Information visualization7, 3-4 (2008), 240–252

    2008

  7. [15]

    Yuntao Du, Yujia Hu, Zhikun Zhang, Ziquan Fang, Lu Chen, Baihua Zheng, and Yunjun Gao

  8. [16]

    J H Faghmous and Vipin Kumar. 2014. A big data guide to understanding climate change: Case for theory-guided data science.Big data2, 3 (2014), 155–163

    2014

  9. [17]

    Majid Farhadloo, Carl Molnar, Gaoxiang Luo, Yan Li, Shashi Shekhar, Rachel L Maus, Svetomir Markovic, Alexey Leontovich, and Raymond Moore. 2022. SAMCNet: towards a spatially explainable AI approach for classifying MxIF oncology data. InProceedings of the 28th ACM SIGKDD confe...

    2022

  10. [18]

    Majid Farhadloo, Arun Sharma, Jayant Gupta, Alexey Leontovich, Svetomir N Markovic, and Shashi Shekhar. 2024. Towards spatially-lucid ai classification in non-euclidean space: An application for mxif oncology data. InProceedings of the 2024 SIAM International Conference on Dat...

    2024

  11. [19]

    Majid Farhadloo, Arun Sharma, Alexey Leontovich, Svetomir N Markovic, and Shashi Shekhar

  12. [20]

    Majid Farhadloo, Arun Sharma, Shashi Shekhar, and Svetomir Markovic. 2024. Spatial com- puting opportunities in biomedical decision support: The atlas-ehr vision.ACM Transactions on Spatial Algorithms and Systems10, 3 (2024), 1–36

    2024

  13. [21]

    Martin Fellendorf and Peter V ortisch. 2010. Microscopic traffic flow simulator VISSIM. Fundamentals of traffic simulation(2010), 63–93

    2010

  14. [22]

    Jie Feng, Zeyu Yang, Fengli Xu, Haisu Yu, Mudan Wang, and Yong Li. 2020. Learning to simulate human mobility. InProceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining. 3426–3433

    2020

  15. [23]

    Qiang Gao, Xiaohan Wang, Chaoran Liu, Goce Trajcevski, Li Huang, and Fan Zhou. 2023. Open anomalous trajectory recognition via probabilistic metric learning. InIJCAI. International Joint Conferences on Artificial Intelligence Organization

    2023

  16. [24]

    Subhankar Ghosh, Jayant Gupta, Arun Sharma, Shuai An, and Shashi Shekhar. 2022. To- wards geographically robust statistically significant regional colocation pattern detection. In Proceedings of the 5th ACM SIGSPATIAL International Workshop on GeoSpatial Simulation. 11–20

    2022

  17. [25]

    Subhankar Ghosh, Arun Sharma, Jayant Gupta, Aneesh Subramanian, and Shashi Shekhar. 2024. Towards Kriging-informed Conditional Diffusion for Regional Sea-Level Data Downscaling: A Summary of Results. InProceedings of the 32nd ACM International Conference on Advances in Geograp...

    2024

  18. [26]

    Agapius Bou Ghosn, Philip Polack, and Arnaud de La Fortelle. 2022. Learning-based Observer Evaluated on the Kinematic Bicycle Model. In2022 10th International Conference on Systems and Control (ICSC). IEEE, 423–428

    2022

  19. [27]

    Gillespie

    Thomas D. Gillespie. 1992.Fundamentals of Vehicle Dynamics. Society of Automotive Engineers, Inc.https://doi.org/10.4271/R-114 18

    1992 doi

  20. [28]

    Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. 2014. Generative adversarial nets. InAdvances in Neural Information Processing Systems. 2672–2680

    2014

  21. [29]

    Jayant Gupta and Arun Sharma. 2022. Mining taxonomy-aware colocations: a summary of results. InProceedings of the 30th International Conference on Advances in Geographic Information Systems. 1–11

    2022

  22. [30]

    Xiaolin Han, Reynold Cheng, Chenhao Ma, and Tobias Grubenmann. 2022. DeepTEA: Effective and efficient online time-dependent trajectory outlier detection.Proceedings of the VLDB Endowment15, 7 (2022), 1493–1505

    2022

  23. [31]

    Nils Henke, Shimon Wonsak, Prasenjit Mitra, Michael Nolting, and Nicolas Tempelmeier

  24. [32]

    Alex Hern. 2020. Berlin artist uses 99 phones to trick Google into traffic jam alert.The Guardian3 (2020)

    2020

  25. [33]

    Jonathan Ho and Stefano Ermon. 2016. Generative adversarial imitation learning. InAdvances in Neural Information Processing Systems. 4565–4573

    2016

  26. [34]

    In Pacific-Asia Conference on Knowledge Discovery and Data Mining

    Condtraj-gan: Conditional sequential gan for generating synthetic vehicle trajectories. In Pacific-Asia Conference on Knowledge Discovery and Data Mining. Springer, 79–91

  27. [35]

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. 2020. Denoising diffusion probabilistic models. Advances in neural information processing systems33 (2020), 6840–6851

    2020

  28. [36]

    Wenjun Jiang, Wayne Xin Zhao, Jingyuan Wang, and Jiawei Jiang. 2023. Continuous trajectory generation based on two-stage GAN. InProceedings of the AAAI Conference on Artificial Intelligence, V ol. 37. 4374–4382

    2023

  29. [37]

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. 2020. Denoising diffusion probabilistic models. In Advances in Neural Information Processing Systems, V ol. 33. 6840–6851

    2020

  30. [38]

    Daniel Krajzewicz, Jakob Erdmann, Michael Behrisch, and Laura Bieker. 2012. Recent development and applications of SUMO-Simulation of Urban MObility.International journal on advances in systems and measurements5, 3&4 (2012)

    2012

  31. [39]

    K Vimal Kumar, Divakar Yadav, and Arun Sharma. 2015. Graph based technique for hindi text summarization. InInformation Systems Design and Intelligent Applications: Proceedings of Second International Conference INDIA 2015, Volume 1. Springer, 301–310

    2015

  32. [40]

    Wei Ping-Jiaji Huang Kexin Zhao Kong, Zhifeng and Bryan Catanzaro. 2021. DiffWave: A Versatile Diffusion Model for Audio Synthesis. InInternational Conference on Learning Representations.https://openreview.net/forum?id=a-xFK8Ymz5J

    2021

  33. [41]

    Shuzhe Li, Wei Chen, Bingqi Yan, Zhen Li, Shunzhi Zhu, and Yanwei Yu. 2023. Self-supervised contrastive representation learning for large-scale trajectories.Future Generation Computer Systems148 (2023), 357–366

    2023

  34. [42]

    Siyu Li, Toan Tran, Haowen Lin, John Krumm, Cyrus Shahabi, Lingyi Zhao, Khurram Shafique, and Li Xiong. 2024. Geo-Llama: Leveraging LLMs for Human Mobility Trajectory Generation with Spatiotemporal Constraints.arXiv preprint arXiv:2408.13918(2024)

    2024 arXiv

  35. [43]

    Chaoneng Li, Guanwen Feng, Yunan Li, Ruyi Liu, Qiguang Miao, and Liang Chang. 2024. Difftad: Denoising diffusion probabilistic models for vehicle trajectory anomaly detection. Knowledge-Based Systems286 (2024), 111387

    2024

  36. [44]

    Yan Li, Majid Farhadloo, Santhoshi Krishnan, Yiqun Xie, Timothy L Frankel, Shashi Shekhar, and Arvind Rao. 2022. CSCD: towards spatially resolving the heterogeneous landscape of MxIF oncology data. InProceedings of the 10th ACM SIGSPATIAL International Workshop on Analytics fo...

    2022

  37. [45]

    Yan Li, Mingzhou Yang, Matthew Eagon, Majid Farhadloo, Yiqun Xie, William F Northrop, and Shashi Shekhar. 2023. Eco-pinn: A physics-informed neural network for eco-toll estimation. InProceedings of the 2023 SIAM International Conference on Data Mining (SDM). SIAM, 838–846

    2023

  38. [46]

    Wenbin Li, Di Yao, Chang Gong, Xiaokai Chu, Quanliang Jing, Xiaolei Zhou, Yuxuan Zhang, Yunxia Fan, and Jingping Bi. 2024. Causaltad: Causal implicit generative model for debiased online trajectory anomaly detection. In2024 IEEE 40th International Conference on Data Engineerin...

    2024

  39. [47]

    Rake& Agrawal King-lp Lin and HSSK Shim. 1995. Fast similarity search in the presence of noise, scaling, and translation in time-series databases. InProceeding of the 21th International Conference on Very Large Data Bases. Citeseer, 490–501

    1995

  40. [48]

    Yan Lin, Huaiyu Wan, Jilin Hu, Shengnan Guo, Bin Yang, Youfang Lin, and Christian S Jensen

  41. [49]

    Chumeng Liang, Zherui Huang, Yicheng Liu, Zhanyu Liu, Guanjie Zheng, Hanyuan Shi, Kan Wu, Yuhao Du, Fuliang Li, and Zhenhui Jessie Li. 2023. Cblab: Supporting the training of large-scale traffic control policies with scalable traffic simulation. InProceedings of the 29th ACM S...

    2023

  42. [50]

    Yiding Liu, Kaiqi Zhao, Gao Cong, and Zhifeng Bao. 2020. Online anomalous trajectory detection with deep generative sequence modeling. In2020 IEEE 36th International Conference on Data Engineering (ICDE). IEEE, 949–960

    2020

  43. [51]

    Huandong Wang-Tong Li Lisi Huang Kun Wang Qiong Wu Guangyu Li Yanping Liang Li Yu Long, Qingyue and Yong Li. 2023. Practical Synthetic Human Trajectories Generation Based on Variational Point Processes. InProceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and...

    2023

  44. [52]

    Origin-destination travel time oracle for map-based services.Proceedings of the ACM on Management of Data1, 3 (2023), 1–27

    2023

  45. [53]

    Xi Liu, Hanzhou Chen, and Clio Andris. 2018. trajGANs: Using generative adversarial networks for geo-privacy protection of trajectory data (Vision paper). InLocation privacy and security workshop. 1–7

    2018

  46. [54]

    Jonathan Kabala Mbuya, Dieter Pfoser, and Antonios Anastasopoulos. 2024. Trajectory Anomaly Detection with Language Models. InProceedings of the 32nd ACM International Conference on Advances in Geographic Information Systems. 208–219

    2024

  47. [55]

    Sandro Meloni, Nicola Perra, Alex Arenas, Sergio Gómez, Yamir Moreno, and Alessandro Vespignani. 2011. Modeling human mobility responses to the large-scale spreading of infectious diseases.Scientific reports1, 1 (2011), 62

    2011

  48. [56]

    Massimiliano Luca, Gianni Barlacchi, Bruno Lepri, and Luca Pappalardo. 2021. A survey on deep learning for human mobility.ACM Computing Surveys (CSUR)55, 1 (2021), 1–44

    2021

  49. [57]

    Gengchen Mai, Weiming Huang, Jin Sun, Suhang Song, Deepak Mishra, Ninghao Liu, Song Gao, Tianming Liu, Gao Cong, Yingjie Hu, Chris Cundy, Ziyuan Li, Rui Zhu, and Ni Lao. 2024. On the Opportunities and Challenges of Foundation Models for GeoAI (Vision Paper).ACM Trans. Spatial ...

    2024 doi

  50. [58]

    Philip Polack, Florent Altché, Brigitte d’Andréa Novel, and Arnaud de La Fortelle. 2017. The kinematic bicycle model: A consistent model for planning feasible trajectories for autonomous vehicles?. In2017 IEEE intelligent vehicles symposium (IV). IEEE, 812–818

    2017

  51. [59]

    Philip Polack, Florent Altché, Brigitte d’Andréa Novel, and Arnaud de La Fortelle. 2018. Guaranteeing consistency in a motion planning and control architecture using a kinematic bicycle model. In2018 Annual American Control Conference (ACC). IEEE, 3981–3987

    2018

  52. [60]

    Kun Ouyang, Reza Shokri, David S Rosenblum, and Wenzhuo Yang. 2018. A non-parametric generative model for human trajectories.. InIJCAI, V ol. 18. 3812–3817

    2018

  53. [61]

    Dieter Pfoser and Yannis Theodoridis. 2003. Generating semantics-based trajectories of moving objects.Computers, Environment and Urban Systems27, 3 (2003), 243–263

    2003

  54. [62]

    Arun Sharma, Majid Farhadloo, Yan Li, Jayant Gupta, Aditya Kulkarni, and Shashi Shekhar

  55. [63]

    Arun Sharma, Majid Farhadloo, Mingzhou Yang, Ruolei Zeng, Subhankar Ghosh, and Shashi Shekhar. 2025. Spatial Distribution-Shift Aware Knowledge-Guided Machine Learning.arXiv preprint arXiv:2502.14840(2025)

    2025 arXiv

  56. [64]

    2011.Vehicle Dynamics and Control

    Rajesh Rajamani. 2011.Vehicle Dynamics and Control. Springer. https://doi.org/10. 1007/978-1-4614-1433-9 20

    2011

  57. [65]

    Jinmeng Rao, Song Gao, Yuhao Kang, and Qunying Huang. 2020. LSTM-TrajGAN: A deep learning approach to trajectory privacy protection.arXiv preprint arXiv:2006.10521(2020)

    2020 arXiv

  58. [66]

    Arun Sharma, Zhe Jiang, and Shashi Shekhar. 2022. Spatiotemporal data mining: A survey. arXiv preprint arXiv:2206.12753(2022)

    2022 arXiv

  59. [67]

    Arun Sharma, Xun Tang, Jayant Gupta, Majid Farhadloo, and Shashi Shekhar. 2020. Analyzing trajectory gaps for possible rendezvous: A summary of results. In11th International Conference on Geographic Information Science (GIScience 2021)-Part I (2020). Schloss Dagstuhl–Leibniz- ...

    2020

  60. [68]

    Arun Sharma, Syed Mohammed Arshad Zaidi, Varun Chandola, Melissa R Allen, and Budhen- dra L Bhaduri. 2018. WebGIobe-A cloud-based geospatial analysis framework for interacting with climate data. InProceedings of the 7th ACM SIGSPATIAL International Workshop on Analytics for Bi...

    2018

  61. [69]

    Arun Sharma, Subhankar Ghosh, and Shashi Shekhar. 2024. Physics-based abnormal trajectory gap detection.ACM Transactions on Intelligent Systems and Technology15, 5 (2024), 1–31

    2024

  62. [70]

    Arun Sharma, Jayant Gupta, and Shashi Shekhar. 2022. Abnormal trajectory-gap detection: A summary (short paper). In15th International Conference on Spatial Information Theory (COSIT 2022). Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 26–1

    2022

  63. [71]

    Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli. 2015. Deep unsupervised learning using nonequilibrium thermodynamics. InInternational conference on machine learning. PMLR, 2256–2265

    2015

  64. [72]

    Yang Song and Stefano Ermon. 2019. Generative modeling by estimating gradients of the data distribution. InAdvances in Neural Information Processing Systems. 11895–11907

    2019

  65. [73]

    Chris Stanford, Suman Adari, Xishun Liao, Yueshuai He, Qinhua Jiang, Chenchen Kuai, Jiaqi Ma, Emmanuel Tung, Yinlong Qian, Lingyi Zhao, et al. 2024. NUMOSIM: A Synthetic Mobility Dataset with Anomaly Detection Benchmarks. InProceedings of the 1st ACM SIGSPATIAL International W...

    2024

  66. [74]

    Shashi Shekhar, Majid Farhadloo, Arun Sharma, Mingzhou Yang, Bharat Jayaprakash, and William Northrop. 2025. Towards Physics-Guided Foundation Models. InAAAI 2025 Bridge on Knowledge-guided Machine Learning

    2025

  67. [75]

    Filippo Simini, Gianni Barlacchi, Massimilano Luca, and Luca Pappalardo. 2021. A deep gravity model for mobility flows generation.Nature communications12, 1 (2021), 6576

    2021

  68. [76]

    Pawan Kumar Upadhyay, Arun Sharma, et al. 2018. A Novel Approach of Intuitive K-means Clustering for Renal Calculi Detection in Ultrasound Images.International Journal on Electrical Engineering & Informatics10, 1 (2018)

    2018

  69. [77]

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. 2017. Attention is all you need.Advances in neural information processing systems30 (2017). 21

    2017

  70. [78]

    Chenhao Wang, Lisi Chen, Shuo Shang, Christian S Jensen, and Panos Kalnis. 2024. Multi- Scale Detection of Anomalous Spatio-Temporal Trajectories in Evolving Trajectory Datasets. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2980–2990

    2024

  71. [79]

    Christiaan Triebert, Blacki Migliozzi, Alexander Cardia, Muyi Xiao, and David Botti. 2023. Fake Signals and American Insurance: How a Dark Fleet Moves Russian Oil.International New York Times(2023), NA–NA

    2023

  72. [80]

    Pawan Kumar Upadhyay, Satish Chandra, and Arun Sharma. 2016. A novel approach of adaptive thresholding for image segmentation on GPU. In2016 Fourth International Conference on Parallel, Distributed and Grid Computing (PDGC). IEEE, 652–655

    2016

  73. [81]

    Yong Wang, Guoliang Li, Kaiyu Li, and Haitao Yuan. 2022. A deep generative model for trajectory modeling and utilization.Proceedings of the VLDB Endowment16, 4 (2022), 973– 985

    2022

  74. [82]

    Yu Wang, Tongya Zheng, Shunyu Liu, Zunlei Feng, Kaixuan Chen, Yunzhi Hao, and Mingli Song. 2024. Spatiotemporal-augmented graph neural networks for human mobility simulation. IEEE Transactions on Knowledge and Data Engineering(2024)

    2024

  75. [83]

    Jared Willard, Xiaowei Jia, Shaoming Xu, Michael Steinbach, and Vipin Kumar. 2022. Inte- grating scientific knowledge with machine learning for engineering and environmental systems. Comput. Surveys55, 4 (2022), 1–37

    2022

  76. [84]

    Huandong Wang, Changzheng Gao, Yuchen Wu, Depeng Jin, Lina Yao, and Yong Li. 2023. PateGail: a privacy-preserving mobility trajectory generator with imitation learning. InProceed- ings of the AAAI Conference on Artificial Intelligence, V ol. 37. AAAI Press, Washington, DC, USA...

    2023

  77. [85]

    Xingrui Wang, Xinyu Liu, Ziteng Lu, and Hanfang Yang. 2021. Large scale GPS trajectory generation using map based on two stage GAN.Journal of Data Science19, 1 (2021), 126–141

    2021

  78. [86]

    Mingzhou Yang, Ruolei Zeng, Arun Sharma, Shunichi Sawamura, William F Northrop, and Shashi Shekhar. 2024. Towards Pareto-optimality with Multi-level Bi-objective Routing: A Summary of Results. InProceedings of the 17th ACM SIGSPATIAL International Workshop on Computational Tra...

    2024

  79. [87]

    Byoung-Kee Yi, Hosagrahar V Jagadish, and Christos Faloutsos. 1998. Efficient retrieval of similar time sequences under time warping. InProceedings 14th International Conference on Data Engineering. IEEE, IEEE, 201–208

    1998

  80. [88]

    Yuan Yuan, Jingtao Ding, Huandong Wang, Depeng Jin, and Yong Li. 2022. Activity trajectory generation via modeling spatiotemporal dynamics. InProceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 4752–4762

    2022

  81. [89]

    Tianqi Xia, Xuan Song, Zipei Fan, Hiroshi Kanasugi, QuanJun Chen, Renhe Jiang, and Ryosuke Shibasaki. 2018. Deeprailway: a deep learning system for forecasting railway traffic. In2018 IEEE Conference on Multimedia Information Processing and Retrieval (MIPR). IEEE, 51–56

    2018

  82. [90]

    Hao Xue, Flora Salim, Yongli Ren, and Nuria Oliver. 2021. MobTCast: Leveraging auxil- iary trajectory forecasting for human mobility prediction.Advances in Neural Information Processing Systems34 (2021), 30380–30391

    2021

  83. [91]

    Huichu Zhang, Siyuan Feng, Chang Liu, Yaoyao Ding, Yichen Zhu, Zihan Zhou, Weinan Zhang, Yong Yu, Haiming Jin, and Zhenhui Li. 2019. Cityflow: A multi-agent reinforcement learning environment for large scale city traffic scenario. InThe world wide web conference. 3620–3624

    2019

  84. [92]

    Jing Zhang, Qihan Huang, Yirui Huang, Qian Ding, and Pei-Wei Tsai. 2023. DP-TrajGAN: A privacy-aware trajectory generation model with differential privacy.Future Generation Computer Systems142 (2023), 25–40

    2023

  85. [93]

    Xing Xie Zheng, Yu and Wei-Ying Ma. 2010. GeoLife: A collaborative social networking service among user, location and trajectory.IEEE Data Eng. Bull.33, 2 (2010), 32–39. 22

    2010

  86. [94]

    Paul A Zandbergen. 2014. Ensuring confidentiality of geocoded health data: Assessing ge- ographic masking strategies for individual-level data.Advances in medicine2014, 1 (2014), 567049

    2014

  87. [95]

    Daqing Zhang, Nan Li, Zhi-Hua Zhou, Chao Chen, Lin Sun, and Shijian Li. 2011. iBAT: detecting anomalous taxi trajectories from GPS traces. InProceedings of the 13th international conference on Ubiquitous computing. 99–108

    2011

  88. [96]

    Yuanshao Zhu, James Jianqiao Yu, Xiangyu Zhao, Qidong Liu, Yongchao Ye, Wei Chen, Zijian Zhang, Xuetao Wei, and Yuxuan Liang. 2024. Controltraj: Controllable trajectory generation with topology-constrained diffusion model. InProceedings of the 30th ACM SIGKDD Conference on Kno...

    2024

  89. [99]

    Yu Zheng. 2015. Trajectory data mining: an overview.ACM Transactions on Intelligent Systems and Technology (TIST)6, 3 (2015), 1–41

    2015

  90. [100]

    Yuanshao Zhu, Yongchao Ye, Shiyao Zhang, Xiangyu Zhao, and James Yu. 2023. Difftraj: Generating gps trajectory with diffusion probabilistic model.Advances in Neural Information Processing Systems36 (2023), 65168–65188

    2023

  91. [2022]

    Understanding covid-19 effects on mobility: A community-engaged approach.AGILE: GIScience Series3 (2022), 14

    2022

  92. [2023]

    Ldptrace: Locally differentially private trajectory synthesis.Proceedings of the VLDB Endowment16, 8 (2023), 1897–1909

    2023

  93. [2025]

    InProceedings of the 2025 SIAM International Conference on Data Mining (SDM)

    Spatially-Delineated Domain-Adapted AI Classification: An Application for Oncology Data. InProceedings of the 2025 SIAM International Conference on Data Mining (SDM). SIAM, 487–496

    2025

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.