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arxiv: 2501.17653 · v3 · submitted 2025-01-29 · 💻 cs.LG · cs.CE· eess.SP

Drivetrain simulation using variational autoencoders

Pallavi Sharma , Jorge-Humberto Urrea-Quintero , Bogdan Bogdan , Adrian-Dumitru Ciotec , Laura Vasilie , Henning Wessels , Matteo Skull This is my paper

Pith reviewed 2026-05-23 04:27 UTC · model grok-4.3

classification 💻 cs.LG cs.CEeess.SP
keywords variational autoencodersdrivetrain simulationjerk signalselectric vehiclesgenerative modelstorque demanddata augmentationvehicle development
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The pith

Variational autoencoders generate realistic jerk signals for electric SUV drivetrains from torque demand using data from only two variants.

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

The paper proposes variational autoencoders to predict jerk signals from torque demand when real-world drivetrain datasets are limited. It trains unconditional and conditional VAEs on experimental data from two fully electric SUV variants that differ in torque and drivetrain setups. The models use their learned latent space to synthesize signals that recombine characteristics across multiple scenarios. Performance matches or exceeds physics-based and hybrid baselines while avoiding the need for detailed system parametrization. This would cut reliance on time-intensive experiments and manual modeling, supporting faster data augmentation and scenario exploration in vehicle development.

Core claim

Both unconditional and conditional VAEs synthesize jerk signals that capture characteristics from multiple drivetrain scenarios by leveraging the learned latent space, with effectiveness confirmed by comparison to baseline physics-based and hybrid models without requiring detailed system parametrization.

What carries the argument

The learned latent space of the variational autoencoder, which recombines training characteristics from two SUV variants to generate outputs for torque inputs and scenarios not seen during training.

If this is right

  • Unconditional VAEs generate realistic jerk signals without any prior system knowledge.
  • Conditional VAEs produce jerk signals tailored to specific torque inputs.
  • The method reduces dependence on costly real-world experiments and extensive manual modeling.
  • Generative models can integrate into drivetrain simulation pipelines for data augmentation.
  • This enables efficient exploration of complex operational scenarios and streamlines validation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same latent-space approach could apply to predicting other vehicle signals such as vibration or noise beyond jerk.
  • Recombination in the latent space might support generation for vehicle configurations outside the two training variants.
  • Hybrid systems pairing VAEs with partial physics models could improve robustness for edge cases.
  • Trained models could be tested for use in real-time onboard simulation during vehicle operation.

Load-bearing premise

The latent space learned from data of only two SUV variants is sufficient to capture and recombine characteristics across multiple drivetrain scenarios and torque inputs not seen in training.

What would settle it

Apply the trained VAE to measured jerk data from a third SUV variant with a different torque configuration and check whether prediction error stays comparable to the original variants; significantly higher error would falsify the claim.

Figures

Figures reproduced from arXiv: 2501.17653 by Adrian-Dumitru Ciotec, Bogdan Bogdan, Henning Wessels, Jorge-Humberto Urrea-Quintero, Laura Vasilie, Matteo Skull, Pallavi Sharma.

Figure 1
Figure 1. Figure 1: shows the distribution of the experimental jerk signals, that is, torque values 𝑀 against the electric machine speed 𝑣 at which the jerk signal (represented by a point) was collected. The torque is within the interval 𝑀 ∈ [−250, 1000] Nm, and the electric machine speed 𝑣 ∈ [0, 14000] rpm. The signals were recorded for a duration of 20 seconds. Upon recording the data, the signal is divided into short time-… view at source ↗
Figure 2
Figure 2. Figure 2: illustrates that 320 jerk signals (around 51%) lie in the ideal region, fulfilling the 𝑝-value criteria for the ADF test. Hence, these 320 jerk signals can be called stationary in time and converted into spectrograms to be used as input to the VAE model. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ADF test p-value 0 50 100 150 200 250 300 count p-value < 0.05 [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Signal transformation: a Jerk signal and b spectrogram obtained from STFT. is a consequence of time-frequency analysis and does not indicate a misalignment in data representation. Spectrograms characterization: We analyze the characteristics of the spectrograms to understand challenges for VAE training by assessing the distribution of pixel values and Signal-to-Noise Ratio (SNR). The pixel values, which re… view at source ↗
Figure 4
Figure 4. Figure 4: exemplarily illustrates the performance of the unconditional VAE for a specific jerk signal. Figure 4a compares the original and generated jerk signals in the time domain, showing strong align￾ment, indicating good reconstruction capability. In Figure 4b, the original spectrogram is displayed, while Figure 4c shows the generated spectrogram of the VAE, which closely resembles the original. Figure 4d depict… view at source ↗
Figure 5
Figure 5. Figure 5: displays 10,000 realizations of jerk signals. These signals are generated by first encoding the original jerk signal (red) to obtain its latent distribution 𝑞𝝓 (z|xoriginal), then repeatedly sampling z from this distribution using the reparameterization trick (Equation 3.19), and finally decoding these latent samples. The phase for all signals is estimated using the Griffin-Lim algorithm. The close alignme… view at source ↗
Figure 6
Figure 6. Figure 6: Latent space interpretation and labeling: Clusters are observed for a the two different vehicle types and b seven torque ranges [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Unconditional VAE: New jerk signals generation by sampling from the labeled latent space. a Normalized generated spectrograms, b generated jerk signals in the time domain, and c frequency spectrum of each jerk signal. The shaded areas highlight important frequency bands (0-2 Hz and 8-12 Hz). Note: the colorbar displayed in the top subfigure applies to all spectrograms. spectrograms. The unconditional VAE a… view at source ↗
Figure 8
Figure 8. Figure 8: CVAE: New jerk signals generation by sampling from the latent space given a desired torque demand as condition. a Generated spectrograms, b generated jerk signals in the time domain, and c frequency spectrum of each jerk signal. The shaded areas highlight important frequency bands (0-2 Hz and 8-12 Hz). Note: the colorbar displayed in the top subfigure applies to all spectrograms. observed. This can be attr… view at source ↗
read the original abstract

This work proposes variational autoencoders (VAEs) to predict a vehicle's jerk signals from torque demand in the context of limited real-world drivetrain datasets. We implement both unconditional and conditional VAEs, trained on experimental data from two variants of a fully electric SUV with differing torque and drivetrain configurations. The VAEs synthesize jerk signals that capture characteristics from multiple drivetrain scenarios by leveraging the learned latent space. A performance comparison with baseline physics-based and hybrid models confirms the effectiveness of the VAEs, without requiring detailed system parametrization. Unconditional VAEs generate realistic jerk signals without prior system knowledge, while conditional VAEs enable the generation of signals tailored to specific torque inputs. This approach reduces the dependence on costly and time-intensive real-world experiments and extensive manual modeling. The results support the integration of generative models such as VAEs into drivetrain simulation pipelines, both for data augmentation and for efficient exploration of complex operational scenarios, with the potential to streamline validation and accelerate vehicle development.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper proposes unconditional and conditional variational autoencoders (VAEs) to generate vehicle jerk signals from torque demand inputs, trained on experimental data from two electric SUV variants with differing drivetrain and torque configurations. It claims that the learned latent space enables synthesis of signals capturing multiple unseen drivetrain scenarios, and that quantitative comparisons against physics-based and hybrid baseline models demonstrate effectiveness without requiring detailed system parametrization. The approach is positioned as reducing reliance on costly real-world testing and manual modeling for data augmentation and scenario exploration in drivetrain simulation.

Significance. If the central claims hold after clarification of the evaluation protocol, the work would demonstrate a practical application of generative models to engineering simulation with limited data, offering a potential alternative to physics-based modeling that avoids extensive parametrization. The use of both unconditional and conditional VAEs for tailored signal generation is a reasonable technical choice for the domain. However, the current presentation provides no basis to assess whether the reported superiority is meaningful or generalizes as claimed.

major comments (3)
  1. [Abstract] Abstract: the statement that 'a performance comparison with baseline physics-based and hybrid models confirms the effectiveness of the VAEs' supplies no quantitative metrics (e.g., MSE, MAE, or distributional distances), error bars, data-split details, or statistical tests. This renders the central effectiveness claim uninspectable and load-bearing for the contribution.
  2. [Experimental setup] Experimental setup (implicit in §3–4): training occurs exclusively on data from two SUV variants; the manuscript does not state whether held-out evaluation samples are drawn from the same two variants (interpolation) or from truly novel drivetrain hardware/torque regimes outside the observed distribution. Without this clarification the recombination claim in the abstract and introduction cannot be evaluated.
  3. [Results] Results: no tables or figures report numerical performance values against the baselines, preventing assessment of whether any advantage is statistically significant or practically relevant.
minor comments (1)
  1. [Methods] Notation for the conditional VAE input (torque demand) should be defined consistently with the unconditional case to avoid ambiguity in the methods description.

Simulated Author's Rebuttal

3 responses · 0 unresolved

Thank you for the constructive feedback. We address each major comment below and will incorporate clarifications and additions into the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that 'a performance comparison with baseline physics-based and hybrid models confirms the effectiveness of the VAEs' supplies no quantitative metrics (e.g., MSE, MAE, or distributional distances), error bars, data-split details, or statistical tests. This renders the central effectiveness claim uninspectable and load-bearing for the contribution.

    Authors: We agree that the abstract should include quantitative support for the effectiveness claim. In the revised version, we will add specific metrics such as MSE and MAE (with error bars) from the VAE versus baseline comparisons to make the claim inspectable. revision: yes

  2. Referee: [Experimental setup] Experimental setup (implicit in §3–4): training occurs exclusively on data from two SUV variants; the manuscript does not state whether held-out evaluation samples are drawn from the same two variants (interpolation) or from truly novel drivetrain hardware/torque regimes outside the observed distribution. Without this clarification the recombination claim in the abstract and introduction cannot be evaluated.

    Authors: We will explicitly clarify in §3–4 that held-out samples are drawn from the same two SUV variants (interpolation within the observed distribution). The recombination claim refers to synthesizing signals for multiple torque inputs and drivetrain characteristics within these two configurations via the latent space. revision: yes

  3. Referee: [Results] Results: no tables or figures report numerical performance values against the baselines, preventing assessment of whether any advantage is statistically significant or practically relevant.

    Authors: We will add a dedicated table in the results section reporting numerical metrics (MSE, MAE, and any distributional distances) for the unconditional/conditional VAEs against the physics-based and hybrid baselines, along with error bars and data-split details to allow assessment of significance and relevance. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical training and external baseline comparison are self-contained

full rationale

The paper trains unconditional and conditional VAEs on held-out experimental jerk/torque data from two SUV variants, then reports performance against independent physics-based and hybrid models. No equation, latent recombination step, or claim reduces by construction to a fitted input or self-citation chain; the central effectiveness claim rests on external benchmark comparison rather than internal redefinition. This is the normal non-circular outcome for a data-driven modeling paper.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on the standard VAE modeling assumption that jerk signals arise from a low-dimensional latent distribution plus the empirical claim that two vehicle variants suffice to span relevant drivetrain variation.

free parameters (1)
  • VAE latent dimension and beta weighting
    Chosen during training to balance reconstruction and regularization; typical free hyperparameters in VAE fitting.
axioms (1)
  • domain assumption Jerk time series can be usefully represented as samples from a learned latent Gaussian distribution
    Core modeling choice that enables the generative claim.

pith-pipeline@v0.9.0 · 5724 in / 1082 out tokens · 31182 ms · 2026-05-23T04:27:07.358052+00:00 · methodology

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Reference graph

Works this paper leans on

59 extracted references · 59 canonical work pages · 1 internal anchor

  1. [1]

    Advanced estimation techniques for vehicle system dynamic state: A survey

    Xianjian Jin, Guodong Yin, and Nan Chen. Advanced estimation techniques for vehicle system dynamic state: A survey. Sensors, 19(19):4289, 2019

    work page 2019

  2. [2]

    High performance electric vehicle powertrain modeling, simulation and validation.Energies, 14(5):1493, 2021

    Feyijimi Adegbohun, Annette Von Jouanne, Ben Phillips, Emmanuel Agamloh, and Alex Yokochi. High performance electric vehicle powertrain modeling, simulation and validation.Energies, 14(5):1493, 2021

    work page 2021

  3. [3]

    Zhiguo Zhao, Haijun Chen, Jie Yang, Xiaowei Wu, and Zhuoping Yu. Estimation of the vehicle speed in the driving mode for a hybrid electric car based on an unscented Kalman filter.Proceedings of the Institution of Mechanical Engineers, Part D: Journal of automobile engineering, 229(4):437–456, 2015

    work page 2015

  4. [4]

    Prediction of electric vehicle driving range and performance characteristics: A review on analytical modeling strategies with its influential factors and improvisation techniques

    Azhaganathan Gurusamy, Bragadeshwaran Ashok, and Byron Mason. Prediction of electric vehicle driving range and performance characteristics: A review on analytical modeling strategies with its influential factors and improvisation techniques. IEEE Access, 11:131521–131548, 2023

    work page 2023

  5. [5]

    InInternational Conference on Machine Learning, pages 10222–10248

    StathiFotiadis,MarioLinoValencia,ShunlongHu,StefGarasto,ChrisDCantwell,andAnilAnthonyBharath.Disentangled generative models for robust prediction of system dynamics. InInternational Conference on Machine Learning, pages 10222–10248. PMLR, 2023

    work page 2023

  6. [6]

    Generative learning for nonlinear dynamics.Nature Reviews Physics, 6(3):194–206, 2024

    William Gilpin. Generative learning for nonlinear dynamics.Nature Reviews Physics, 6(3):194–206, 2024

    work page 2024

  7. [7]

    Rave:Avariationalautoencoderforfastandhigh-qualityneuralaudiosynthesis

    AntoineCaillonandPhilippeEsling. Rave:Avariationalautoencoderforfastandhigh-qualityneuralaudiosynthesis. arXiv preprint arXiv:2111.05011, 2021

    work page arXiv 2021

  8. [8]

    Asemi-supervisedautoencoderframeworkforjointgeneration and classification of breathing.Computer Methods and Programs in Biomedicine, 209:106312, 2021

    OscarPastor-Serrano,DannyLathouwers,andZoltánPerkó. Asemi-supervisedautoencoderframeworkforjointgeneration and classification of breathing.Computer Methods and Programs in Biomedicine, 209:106312, 2021

    work page 2021

  9. [9]

    Auto-Encoding Variational Bayes

    Diederik P Kingma. Auto-encoding variational bayes.arXiv preprint arXiv:1312.6114, 2013

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  10. [10]

    Conditional variational autoencoder for learned image reconstruction

    Chen Zhang, Riccardo Barbano, and Bangti Jin. Conditional variational autoencoder for learned image reconstruction. Computation, 9(11):114, 2021

    work page 2021

  11. [11]

    Variationalautoencoderwithoptimizing Gaussian mixture model priors.IEEE Access, 8:43992–44005, 2020

    ChunshengGuo,JialuoZhou,HuahuaChen,NaYing,JianwuZhang,andDiZhou. Variationalautoencoderwithoptimizing Gaussian mixture model priors.IEEE Access, 8:43992–44005, 2020

    work page 2020

  12. [12]

    Machine learning of Kondo physics using variational autoencoders and symbolic regression.Physical Review B, 104(23): 235111, 2021

    Cole Miles, Matthew R Carbone, Erica J Sturm, Deyu Lu, Andreas Weichselbaum, Kipton Barros, and Robert M Konik. Machine learning of Kondo physics using variational autoencoders and symbolic regression.Physical Review B, 104(23): 235111, 2021

    work page 2021

  13. [13]

    Latent space interpretation and visualisation for understanding the decisions of con- volutional variational autoencoders trained with EEG topographic maps

    Taufique Ahmed and Luca Longo. Latent space interpretation and visualisation for understanding the decisions of con- volutional variational autoencoders trained with EEG topographic maps. InxAI (Late-breaking Work, Demos, Doctoral Consortium), pages 65–70, 2023

    work page 2023

  14. [14]

    Sabatina Criscuolo, Andrea Apicella, Roberto Prevete, and Luca Longo. Interpreting the latent space of a convolutional variational autoencoder for semi-automated eye blink artefact detection in EEG signals.Computer Standards & Interfaces, 92:103897, 2025

    work page 2025

  15. [15]

    Drivability optimization by reducing oscillation of electric vehicle drivetrains.World Electric Vehicle Journal, 11(4):68, 2020

    Andreas Koch, Ludwig Schulz, Gabrielius Jakstas, and Jens Falkenstein. Drivability optimization by reducing oscillation of electric vehicle drivetrains.World Electric Vehicle Journal, 11(4):68, 2020

    work page 2020

  16. [16]

    Anti-jerk controllers for automotive applications: A review.Annual Reviews in Control, 50:174–189, 2020

    Alessandro Scamarcio, Patrick Gruber, Stefano De Pinto, and Aldo Sorniotti. Anti-jerk controllers for automotive applications: A review.Annual Reviews in Control, 50:174–189, 2020. ISSN 1367-5788. 28 Pallavi et al

    work page 2020

  17. [17]

    Comparison of anti-jerk controllers for electric vehicles with on-board motors.IEEE Transactions on Vehicular Technology, 69(10):10681–10699, 2020

    Alessandro Scamarcio, Mathias Metzler, Patrick Gruber, Stefano De Pinto, and Aldo Sorniotti. Comparison of anti-jerk controllers for electric vehicles with on-board motors.IEEE Transactions on Vehicular Technology, 69(10):10681–10699, 2020

    work page 2020

  18. [18]

    Methods for virtual validation of automotive powertrain systems in terms of vehicle drivability—a systematic literature review.IEEE Access, 11:27043–27065, 2023

    Henrik Schmidt, Kay Büttner, and Günther Prokop. Methods for virtual validation of automotive powertrain systems in terms of vehicle drivability—a systematic literature review.IEEE Access, 11:27043–27065, 2023

    work page 2023

  19. [19]

    Torsional finite elements and nonlinear numerical modelling in vehicle powertrain dynamics

    AR Crowther and N Zhang. Torsional finite elements and nonlinear numerical modelling in vehicle powertrain dynamics. Journal of Sound and Vibration, 284(3-5):825–849, 2005

    work page 2005

  20. [20]

    Jerk analysisofapower-splithybridelectricvehiclebasedonadata-drivenvehicledynamicsmodel

    Xiaohua Zeng, Haoyong Cui, Dafeng Song, Nannan Yang, Tong Liu, Huiyong Chen, Yinshu Wang, and Yulong Lei. Jerk analysisofapower-splithybridelectricvehiclebasedonadata-drivenvehicledynamicsmodel. Energies,11(6):1537,2018

    work page 2018

  21. [21]

    Data-driven vehicle modeling of longitudinal dynamics based on a multibody model and deep neural networks.Measurement, 180:109541, 2021

    Yongjun Pan, Xiaobo Nie, Zhixiong Li, and Shuitao Gu. Data-driven vehicle modeling of longitudinal dynamics based on a multibody model and deep neural networks.Measurement, 180:109541, 2021

    work page 2021

  22. [22]

    Longitudinal vehicle dynamics: A comparison of physical and data-driven models under large-scale real-world driving conditions.IEEE Access, 8:73714–73729, 2020

    Sebastian S James, Sean R Anderson, and Mauro Da Lio. Longitudinal vehicle dynamics: A comparison of physical and data-driven models under large-scale real-world driving conditions.IEEE Access, 8:73714–73729, 2020

    work page 2020

  23. [23]

    and Lal Priya P.S

    Lekshmi S. and Lal Priya P.S. Mathematical modeling of electric vehicles - a survey.Control Engineering Practice, 92: 104138, 2019. ISSN 0967-0661

    work page 2019

  24. [24]

    Transient system model for the analysis of structural dynamic interactions of electric drivetrains.Energies, 14(4), 2021

    Marius Franck, Jan Philipp Rickwärtz, Daniel Butterweck, Martin Nell, and Kay Hameyer. Transient system model for the analysis of structural dynamic interactions of electric drivetrains.Energies, 14(4), 2021. ISSN 1996-1073

    work page 2021

  25. [25]

    Integrated design of the torsion beam electric driving axle.Journal of Vibroengineering, pages 537–549, jan 2022

    Peicheng Shi, Kangji Liu, and Kehang Shi. Integrated design of the torsion beam electric driving axle.Journal of Vibroengineering, pages 537–549, jan 2022

    work page 2022

  26. [26]

    Modeling and simulation of the complete electric power train of a hybrid electric vehicle

    Prathviraj Shetty and S Dawnee. Modeling and simulation of the complete electric power train of a hybrid electric vehicle. In2014AnnualInternationalConferenceonEmergingResearchAreas:Magnetics,MachinesandDrives ,pages1–5.IEEE, 2014

    work page 2014

  27. [27]

    McDonald

    D. McDonald. Electric vehicle drive simulation with Matlab/Simulink. InProceedings of the 2012 North-Central Section Conference, pages 1–24, 2012

    work page 2012

  28. [28]

    K. L. Butler, M. Ehsani, and P. Kamath. A Matlab-based modeling and simulation package for electric and hybrid electric vehicle design.IEEE Transactions on Vehicular Technology, 48(6):1770–1778, 1999

    work page 1999

  29. [29]

    R. Zhao, W. Deng, Y. Wang, K. Huang, B. Zheng, and J. Ding. An improved data-driven method for steering feedback torque of driving simulator.IEEE/ASME Transactions on Mechatronics, 28(5):2953–2963, Oct. 2023

    work page 2023

  30. [30]

    In2022 4th International Conference on Frontiers Technology of Information and Computer (ICFTIC), pages 511–514, 2022

    GuohangLi,MiaohuaHuang,RuifengWang,andWenyuanZheng.SOHestimationofpowerbatterybasedontherealvehicle multi-feature and LightGBM algorithm. In2022 4th International Conference on Frontiers Technology of Information and Computer (ICFTIC), pages 511–514, 2022

    work page 2022

  31. [31]

    Litao Zhou, Yang Zhao, Da Li, and Zhenpo Wang. State-of-health estimation for lifepo4 battery system on real-world electric vehicles considering aging stage.IEEE Transactions on Transportation Electrification, 8(2):1724–1733, 2022

    work page 2022

  32. [32]

    Data-augmentedpredictivedeepneuralnetwork:Enhancingtheextrapolation capabilities of non-intrusive surrogate models.arXiv preprint arXiv:2410.13376, 2024

    ShuwenSun,LihongFeng,andPeterBenner. Data-augmentedpredictivedeepneuralnetwork:Enhancingtheextrapolation capabilities of non-intrusive surrogate models.arXiv preprint arXiv:2410.13376, 2024

    work page arXiv 2024

  33. [33]

    Raissi, P

    M. Raissi, P. Perdikaris, and G.E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.Journal of Computational Physics, 378: 686–707, 2019. ISSN 0021-9991

    work page 2019

  34. [34]

    Learning nonlinear operators in latentspacesforreal-timepredictionsofcomplexdynamicsinphysicalsystems

    Katiana Kontolati, Somdatta Goswami, George Em Karniadakis, and Michael D Shields. Learning nonlinear operators in latentspacesforreal-timepredictionsofcomplexdynamicsinphysicalsystems. NatureCommunications,15(1):5101,2024

    work page 2024

  35. [35]

    State-space models are accurate and efficient neural operators for dynamical systems.arXiv preprint arXiv:2409.03231, 2024

    Zheyuan Hu, Nazanin Ahmadi Daryakenari, Qianli Shen, Kenji Kawaguchi, and George Em Karniadakis. State-space models are accurate and efficient neural operators for dynamical systems.arXiv preprint arXiv:2409.03231, 2024

    work page arXiv 2024

  36. [36]

    Hybrid physics-based and data-driven models for smart manufacturing: Modelling, simulation, and explainability.Journal of Manufacturing Systems, 63:381–391, 2022

    Jinjiang Wang, Yilin Li, Robert X Gao, and Fengli Zhang. Hybrid physics-based and data-driven models for smart manufacturing: Modelling, simulation, and explainability.Journal of Manufacturing Systems, 63:381–391, 2022

    work page 2022

  37. [37]

    Physics- basedanddata-drivenhybridmodelinginmanufacturing:areview

    SathishKasilingam,RuoyuYang,ShubhenduKumarSingh,MojtabaAFarahani,RahulRai,andThorstenWuest. Physics- basedanddata-drivenhybridmodelinginmanufacturing:areview. Production&ManufacturingResearch ,12(1):2305358, 2024

    work page 2024

  38. [38]

    Hybrid modeling of first-principles and machine learning: A step-by-step tutorial review for practical implementation.Computers & Chemical Engineering, page 108926, 2024

    Parth Shah, Silabrata Pahari, Raj Bhavsar, and Joseph Sang-Il Kwon. Hybrid modeling of first-principles and machine learning: A step-by-step tutorial review for practical implementation.Computers & Chemical Engineering, page 108926, 2024

    work page 2024

  39. [39]

    AI-basedmethodologyforthecalibrationofanti-jerkcontrolonelectricdrives

    M.Skull,M.Bach,T.Roulet,andM.Hauss. AI-basedmethodologyforthecalibrationofanti-jerkcontrolonelectricdrives. ATZ - Automobiltechnische Zeitschrift, April 2024

    work page 2024

  40. [40]

    Griffin and J

    D. Griffin and J. Lim. Signal estimation from modified short-time Fourier transform.IEEE Transactions on Acoustics, Speech, and Signal Processing, 32(2):236–243, April 1984

    work page 1984

  41. [41]

    Pearson Education India, 1999

    Alan V Oppenheim.Discrete-time signal processing. Pearson Education India, 1999

    work page 1999

  42. [42]

    Pytorch: An imperative style, high-performance deep learning library.Advances in neural information processing systems, 32, 2019

    Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library.Advances in neural information processing systems, 32, 2019

    work page 2019

  43. [43]

    A comprehensive survey and analysis of generative models in machine learning.Computer Science Review, 38:100285, 2020

    GM Harshvardhan, Mahendra Kumar Gourisaria, Manjusha Pandey, and Siddharth Swarup Rautaray. A comprehensive survey and analysis of generative models in machine learning.Computer Science Review, 38:100285, 2020

    work page 2020

  44. [44]

    Tutorial on variational autoencoders.arXiv preprint arXiv:1606.05908, 2016

    Carl Doersch. Tutorial on variational autoencoders.arXiv preprint arXiv:1606.05908, 2016. Pallavi et al. 29

    work page arXiv 2016

  45. [45]

    Kingma and Max Welling

    Diederik P. Kingma and Max Welling. An introduction to variational autoencoders.Foundations and Trends® in Machine Learning, 12(4):307–392, 2019. ISSN 1935-8245

    work page 2019

  46. [46]

    R. Mushtaq. Augmented Dickey Fuller test.SSRN, 2011

    work page 2011

  47. [47]

    Kokoszka and G

    P. Kokoszka and G. Young. KPSS test for functional time series.Statistics, 50(5):957–973, 2016

    work page 2016

  48. [48]

    Statsmodels: econometric and statistical modeling with python.SciPy, 7(1), 2010

    Skipper Seabold and Josef Perktold. Statsmodels: econometric and statistical modeling with python.SciPy, 7(1), 2010

    work page 2010

  49. [49]

    Theoretical foundations of t-SNE for visualizing high-dimensional clustered data.Journal of Machine Learning Research, 23(301):1–54, 2022

    T Tony Cai and Rong Ma. Theoretical foundations of t-SNE for visualizing high-dimensional clustered data.Journal of Machine Learning Research, 23(301):1–54, 2022

    work page 2022

  50. [50]

    Visualizing data using t-SNE.Journal of machine learning research, 9(11), 2008

    Laurens Van der Maaten and Geoffrey Hinton. Visualizing data using t-SNE.Journal of machine learning research, 9(11), 2008

    work page 2008

  51. [51]

    Neighbourhood component analysis.Adv

    Sam Roweis, Geoffrey Hinton, and Ruslan Salakhutdinov. Neighbourhood component analysis.Adv. Neural Inf. Process. Syst.(NIPS), 17(513-520):4, 2004

    work page 2004

  52. [52]

    Vanderplas, A

    F.Pedregosa,G.Varoquaux,A.Gramfort,V.Michel,B.Thirion,O.Grisel,M.Blondel,P.Prettenhofer,R.Weiss,V.Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12:2825–2830, 2011

    work page 2011

  53. [53]

    Modelling framework for artificial hybrid dynamical systems

    Stefanie Winkler, Andreas Körner, and Felix Breitenecker. Modelling framework for artificial hybrid dynamical systems. Nonlinear Analysis: Hybrid Systems, 42:101072, 2021. ISSN 1751-570X

    work page 2021

  54. [54]

    Jiang, Senwei Liang, and Haizhao Yang

    John Harlim, Shixiao W. Jiang, Senwei Liang, and Haizhao Yang. Machine learning for prediction with missing dynamics. Journal of Computational Physics, 428:109922, 2021. ISSN 0021-9991

    work page 2021

  55. [55]

    Lindemann, D

    Matthias Kötter, B. Lindemann, D. Bergmann, M. Ehrly, T. Jung, M. Nijs, S. Thewes, T. Körfer, S. Trampert, T. Drecq, and P. Gautier. Powertrain calibration based on x-in-theloop: Virtualization in the vehicle development process. In18. Internationales Stuttgarter Symposium, pages 1187–1201, Wiesbaden, 2018. Springer Fachmedien Wiesbaden

    work page 2018

  56. [56]

    U-net: Convolutional networks for biomedical image segmentation

    Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. Medical Image Computing and Computer-Assisted Intervention (MICCAI), 2015

    work page 2015

  57. [57]

    Wave-U-Net: A multi-scale neural network for end-to-end audio source separation

    Daniel Stoller, Sebastian Ewert, and Simon Dixon. Wave-U-Net: A multi-scale neural network for end-to-end audio source separation. InProceedings of the 19th ISMIR Conference, 2018

    work page 2018

  58. [58]

    Aconvnetforthe2020s

    ZhuangLiu,HanziMao,Chao-YuanWu,ChristophFeichtenhofer,TrevorDarrell,andSainingXie. Aconvnetforthe2020s. In2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022

    work page 2022

  59. [59]

    Mobilenetv2: Inverted residuals and linear bottlenecks

    Mark Sandler, Andrew Howard, Menglong Zhu, Andrey Zhmoginov, and Liang-Chieh Chen. Mobilenetv2: Inverted residuals and linear bottlenecks. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 4510–4520, 2018

    work page 2018