pith. sign in

arxiv: 2605.24860 · v1 · pith:OZAZPCG5new · submitted 2026-05-24 · 📡 eess.SY · cs.AI· cs.ET· cs.LG· cs.RO· cs.SY

DBPnet: Damper Characteristics-Based Bayesian Physics-Informed Neural Network for Wheel Load Estimation

Tianyi Wang , Tianyi Zeng , Zimo Zeng , Feiyang Zhang , Yujin Wang , Xiangyu Li , Yiming Xu , Sikai Chen
show 3 more authors
Junfeng Jiao Christian Claudel Xinbo Chen
This is my paper

Pith reviewed 2026-06-30 00:11 UTC · model grok-4.3

classification 📡 eess.SY cs.AIcs.ETcs.LGcs.ROcs.SY
keywords wheel load estimationphysics-informed neural networkBayesian inferencedamper characteristicssuspension modelingvehicle dynamicsstate estimationADAS
0
0 comments X

The pith

DBPnet estimates vehicle wheel loads more accurately by combining suspension geometry modeling with Bayesian inference and a damper characteristics embedding in a physics-informed neural network.

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

The paper aims to solve the problem of robust wheel load estimation needed for advanced driver assistance systems, which suffer from complex nonlinear suspension dynamics and sensor noise. It first builds a suspension linkage-level model that captures instantaneous nonlinear behavior from the suspension's geometric structure. Bayesian inference is layered into the neural network to manage uncertainty, a physics-informed loss keeps outputs consistent with physical laws, and a damper-inspired embedding module injects temporal signal features into every network layer. High-fidelity simulations and real-vehicle tests show DBPnet produces lower root-mean-square error and maximum error than baseline estimators. If this holds, chassis control and safety functions in vehicles gain more reliable inputs without depending on fixed physical equations alone.

Core claim

DBPnet integrates suspension linkage-level modeling to build a nonlinear dynamic model, applies Bayesian inference for noise robustness, uses a physics-informed loss for physical consistency, and adds a damper characteristics-inspired embedding module to feed temporal features into each PINN layer, yielding lower RMSE and MaxError than baselines across simulations and real experiments.

What carries the argument

The damper characteristics-inspired embedding module, which extracts temporal variation features from input signals and feeds them into every layer of the Bayesian PINN while the suspension linkage-level model supplies the geometric nonlinear dynamics.

If this is right

  • Wheel load estimates become consistent with both measured data and fundamental physical principles even under noise.
  • The Bayesian treatment allows the network to quantify uncertainty in chassis states rather than outputting point estimates only.
  • ADAS actuator functions receive more reliable wheel load signals for stability and safety control.
  • The embedding approach avoids locking the network to a single fixed physical model while still guiding it with observations.

Where Pith is reading between the lines

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

  • The same embedding and Bayesian structure might transfer to estimating other nonlinear vehicle states such as tire slip or body roll.
  • Online retraining on streaming sensor data could turn the model into an adaptive estimator for changing road or load conditions.
  • Similar physics-informed Bayesian networks could address state estimation in other mechanical systems that combine geometry-driven nonlinearity with noisy measurements.

Load-bearing premise

The suspension linkage-level modeling accurately constructs a nonlinear instantaneous dynamic model by explicitly considering the complex geometric structure of the suspension.

What would settle it

DBPnet producing higher RMSE or MaxError than at least one baseline method when both are evaluated on the identical set of high-fidelity simulation runs or the same real-world vehicle experiment data.

Figures

Figures reproduced from arXiv: 2605.24860 by Christian Claudel, Feiyang Zhang, Junfeng Jiao, Sikai Chen, Tianyi Wang, Tianyi Zeng, Xiangyu Li, Xinbo Chen, Yiming Xu, Yujin Wang, Zimo Zeng.

Figure 1
Figure 1. Figure 1: Overview of the proposed DBPnet framework: Sensor data vector xt is input into the Bayesian neural network (BNN), while xt and xt−1 form the input to the damper characteristic-based physics conditioning (DPC) module together, which embeds physics information into the weight parameters of the BNN. ture model uncertainty. While traditional Bayesian inference methods require informative prior knowledge about … view at source ↗
Figure 2
Figure 2. Figure 2: Revolute-sphere-sphere-revolute (RSSR) structure model. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Front suspension model for wheel load estimation: Two-degree-of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Structure of the proposed damper characteristic-based physics condi [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Overview of the experiments: In the simulation, the required input data are directly obtained by software and 10 types of vehicle and 4 types of testing [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Design and deployment of several critical sensors are as follows: [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Results of simulation: We select an urban driving scenario from the [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Real-world test of “figure-8” circuit: This is a standard race track with an inner diameter of 15.25m, an outer diameter of 21.25 m, a distance of 18.25 m between the centers of the circles, and a track width of 3 m. Race cars are required to drive two clockwise laps and then two counterclockwise laps within the track, and finally exit the track [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Results of real-world experiments: The top-left pair of graphs illustrate the distributions of front-left and front-right wheel loads; the bottom-left [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Real-world test of “asymmetric ellipse” circuit: This circuit includes high-speed corners, low-speed corners, long straightaway, and a slalom section, [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Results of real-world experiments: The top-left pair of graphs illustrate the distributions of front-left and front-right wheel loads; the bottom-left two [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
read the original abstract

Advanced driver assistance systems (ADAS) play an important role in modern automotive intelligence, significantly enhancing vehicle safety and stability. The performance of ADAS critically relies on accurate and reliable vehicle state estimation, particularly from vehicle dynamic sensors. Among these signals, wheel load is a key variable for chassis control and safety-critical functions, yet it remains difficult to estimate robustly due to complex suspension geometry, nonlinear dynamics, and measurement noise. To address this issue, we propose DBPnet, a Bayesian physics-informed neural network (PINN) with a physics-aware embedding module inspired by damper characteristics. First, this paper presents a suspension linkage-level modeling (SLLM) approach that constructs a nonlinear instantaneous dynamic model by explicitly considering the complex geometric structure of the suspension. Building upon SLLM, Bayesian inference is integrated into the PINN to effectively cope with noise and uncertainty in the vehicle chassis system, thereby improving the model's robustness. Then, a physics-informed loss function is employed to ensure consistency with fundamental physical principles, while the damper characteristics-inspired embedding module extracts temporal variation features of input signals and incorporates them into each layer of the PINN, ensuring that physical observations guide the neural network without being constrained by fixed physical models. Extensive evaluations on high-fidelity simulations and real-world experiments demonstrate that our DBPnet consistently achieves lower RMSE and MaxError than baseline methods. These results highlight the potential of our DBPnet to advance wheel load estimation and contribute to the development of more reliable ADAS actuator functions.

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 / 2 minor

Summary. The paper proposes DBPnet, a Bayesian physics-informed neural network (PINN) for wheel load estimation that incorporates a damper characteristics-inspired embedding module. It introduces a suspension linkage-level modeling (SLLM) approach to construct a nonlinear instantaneous dynamic model from explicit suspension geometry, integrates Bayesian inference to handle noise and uncertainty, employs a physics-informed loss for physical consistency, and claims that extensive evaluations on high-fidelity simulations and real-world experiments show consistently lower RMSE and MaxError than baseline methods.

Significance. If the SLLM produces an accurate nonlinear model and the physics-informed components demonstrably enforce the claimed physical principles beyond data-driven fitting, the approach could advance robust wheel load estimation for ADAS chassis control. The combination of Bayesian handling of uncertainty with a domain-inspired embedding module represents a targeted extension of PINNs to vehicle dynamics; however, the absence of explicit validation for the load-bearing SLLM assumption limits the assessed significance.

major comments (3)
  1. [SLLM description (abstract and §3)] The central performance claim (lower RMSE and MaxError on simulations and real experiments) is load-bearing on the accuracy of the SLLM nonlinear instantaneous dynamic model. The manuscript provides no explicit kinematic equations, derivation steps, or validation of SLLM outputs against multibody dynamics ground truth or sensitivity analysis, leaving open the possibility that reported gains arise from the embedding module or network capacity alone.
  2. [Abstract and evaluation sections] No quantitative results, tables, error bars, or statistical tests are supplied to support the abstract's assertion of lower RMSE and MaxError relative to baselines; the physics-informed loss is described at a high level without verification that it enforces the SLLM-derived principles rather than reducing to a data-fit term.
  3. [Bayesian inference integration] The Bayesian component is stated to cope with noise via priors, yet the manuscript does not report the specific priors, hyperparameter values, or posterior diagnostics, making it impossible to assess whether uncertainty quantification contributes to the claimed robustness or merely adds free parameters.
minor comments (2)
  1. [Method description] Notation for the damper characteristics-inspired embedding module should be defined with explicit input/output dimensions and layer integration equations for reproducibility.
  2. [Abstract] The abstract would benefit from a brief statement of the number of simulation scenarios and real-vehicle test conditions to contextualize the 'extensive evaluations'.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below, indicating where revisions will be made to improve clarity and rigor.

read point-by-point responses

  1. Referee: [SLLM description (abstract and §3)] The central performance claim (lower RMSE and MaxError on simulations and real experiments) is load-bearing on the accuracy of the SLLM nonlinear instantaneous dynamic model. The manuscript provides no explicit kinematic equations, derivation steps, or validation of SLLM outputs against multibody dynamics ground truth or sensitivity analysis, leaving open the possibility that reported gains arise from the embedding module or network capacity alone.

    Authors: We agree that explicit details are required to support the central claims. Although §3 outlines the SLLM approach, the manuscript does not include the full set of kinematic equations or validation. In the revised version we will insert the complete kinematic equations derived from suspension geometry, the step-by-step derivation, and direct comparisons of SLLM outputs against multibody-dynamics ground truth together with a sensitivity analysis. revision: yes

  2. Referee: [Abstract and evaluation sections] No quantitative results, tables, error bars, or statistical tests are supplied to support the abstract's assertion of lower RMSE and MaxError relative to baselines; the physics-informed loss is described at a high level without verification that it enforces the SLLM-derived principles rather than reducing to a data-fit term.

    Authors: The evaluation sections present comparative results through figures, yet we acknowledge the absence of tabulated values, error bars, and statistical tests. We will add tables listing RMSE and MaxError (with standard deviations from repeated trials), error bars, and appropriate statistical tests. We will also include an ablation study or diagnostic analysis demonstrating that the physics-informed loss enforces the SLLM-derived principles beyond pure data fitting. revision: yes

  3. Referee: [Bayesian inference integration] The Bayesian component is stated to cope with noise via priors, yet the manuscript does not report the specific priors, hyperparameter values, or posterior diagnostics, making it impossible to assess whether uncertainty quantification contributes to the claimed robustness or merely adds free parameters.

    Authors: We will expand the Bayesian-inference section to report the exact prior distributions, all hyperparameter values, and posterior diagnostics (e.g., convergence metrics or uncertainty quantification results) so that readers can evaluate the contribution of the Bayesian component. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation relies on explicit geometric modeling and standard PINN components without reduction to inputs

full rationale

The paper's chain begins with SLLM as an explicit construction of the nonlinear dynamic model from suspension geometry (abstract), followed by integration of Bayesian inference, a physics-informed loss, and a damper-characteristics embedding module into the PINN. No equations or steps are quoted that reduce any prediction or result to a fitted parameter by construction, nor are self-citations used to justify uniqueness or import an ansatz. Performance claims rest on external evaluations against baselines on simulations and real experiments, which are independent of the modeling steps. This is the common case of a self-contained method description.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

Only the abstract is available, preventing exhaustive extraction of free parameters, axioms, or invented entities. The description implies reliance on standard vehicle-dynamics assumptions and the introduction of one new module.

free parameters (1)
  • Bayesian priors or hyperparameters
    Required for the Bayesian inference component to handle noise and uncertainty, but no specific values or fitting procedure are stated.
axioms (1)
  • domain assumption Suspension linkage geometry produces a nonlinear instantaneous dynamic model that can be explicitly constructed (SLLM).
    Invoked when the abstract states that SLLM 'constructs a nonlinear instantaneous dynamic model by explicitly considering the complex geometric structure of the suspension.'
invented entities (1)
  • Damper characteristics-inspired embedding module no independent evidence
    purpose: Extracts temporal variation features of input signals and incorporates them into each layer of the PINN so that physical observations guide the network without fixed physical models.
    New module introduced in the abstract to embed damper behavior; no independent evidence outside the paper is provided.

pith-pipeline@v0.9.1-grok · 5852 in / 1484 out tokens · 41150 ms · 2026-06-30T00:11:40.057168+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

57 extracted references · 4 canonical work pages · 1 internal anchor

  1. [1]

    Wheel load estimation and anti-roll bar control using suspension analysis with neural network,

    T. Zeng, T. Wang, L. Yu, Z. Liu, H. Chen, and X. Chen, “Wheel load estimation and anti-roll bar control using suspension analysis with neural network,” inIFToMM World Congress on Mechanism and Machine Science. Springer, 2023, pp. 332–342

    2023

  2. [2]

    Analysis and design of suspension state observer for wheel load estimation,

    T. Zeng, Z. Liu, C. He, Z. Zeng, H. Chen, F. Zhang, K. Fu, and X. Chen, “Analysis and design of suspension state observer for wheel load estimation,” SAE Technical Paper, Tech. Rep., 2024

    2024

  3. [3]

    Kalman and extended kalman filters: Concept, derivation and properties,

    M. I. Ribeiro, “Kalman and extended kalman filters: Concept, derivation and properties,”Institute for Systems and Robotics, vol. 43, no. 46, pp. 3736–3741, 2004

    2004

  4. [4]

    The ensemble kalman filter: a signal processing perspective,

    M. Roth, G. Hendeby, C. Fritsche, and F. Gustafsson, “The ensemble kalman filter: a signal processing perspective,”EURASIP Journal on Advances in Signal Processing, vol. 2017, no. 1, p. 56, 2017

    2017

  5. [5]

    Ftekfnet: Hybridizing physical and data-driven estimation algorithms for vehicle state,

    Y . Wang, F. Hu, C. Tian, P. Li, H. Huang, G. Yin, and C. Huang, “Ftekfnet: Hybridizing physical and data-driven estimation algorithms for vehicle state,”IEEE Transactions on Intelligent Vehicles, vol. 9, no. 11, pp. 7301–7311, 2024

    2024

  6. [6]

    Physics-informed neural network for model prediction and dynamics parameter identification of collaborative robot joints,

    X. Yang, Y . Du, L. Li, Z. Zhou, and X. Zhang, “Physics-informed neural network for model prediction and dynamics parameter identification of collaborative robot joints,”IEEE Robotics and Automation Letters, vol. 8, no. 12, pp. 8462–8469, 2023

    2023

  7. [7]

    Vehicle state estimation combining physics-informed neural network and unscented kalman filtering on manifolds,

    C. Tan, Y . Cai, H. Wang, X. Sun, and L. Chen, “Vehicle state estimation combining physics-informed neural network and unscented kalman filtering on manifolds,”Sensors, vol. 23, no. 15, p. 6665, 2023

    2023

  8. [8]

    Hlcg: A hierarchical lane-changing gaming decision model for heterogeneous traffic flow on two-lane highways,

    T. Wang, C. He, H. Li, Y . Li, Y . Xu, Y . Wang, and J. Jiao, “Hlcg: A hierarchical lane-changing gaming decision model for heterogeneous traffic flow on two-lane highways,”Transportation Research Record, vol. 2679, no. 10, pp. 449–469, 2025

    2025

  9. [9]

    On the estimation rate of bayesian pinn for inverse problems,

    Y . Sun, D. Mukherjee, and Y . Atchad ´e, “On the estimation rate of bayesian pinn for inverse problems,”arXiv preprint arXiv:2406.14808v1, 2024

    work page arXiv 2024

  10. [10]

    Deep operator networks for bayesian parameter estimation in pdes,

    A. Raj, S. Bun, K. Srinivasa, C. E. Gudumotou, and A. Sarshar, “Deep operator networks for bayesian parameter estimation in pdes,”Computer Physics Communications, p. 109853, 2025

    2025

  11. [11]

    Physics-guided deep learning for dynamical systems: A survey,

    R. Wang and R. Yu, “Physics-guided deep learning for dynamical systems: A survey,”ACM Computing Surveys, vol. 58, no. 5, pp. 1– 31, 2025

    2025

  12. [12]

    Film: Visual reasoning with a general conditioning layer,

    E. Perez, F. Strub, H. De Vries, V . Dumoulin, and A. Courville, “Film: Visual reasoning with a general conditioning layer,” inProceedings of the AAAI Conference on Artificial Intelligence, vol. 32, no. 1, 2018. JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021 13

    2018

  13. [13]

    Physics-informed neural networks for pde problems: A comprehensive review,

    K. Luo, J. Zhao, Y . Wang, J. Li, J. Wen, J. Liang, H. Soekmadji, and S. Liao, “Physics-informed neural networks for pde problems: A comprehensive review,”Artificial Intelligence Review, vol. 58, no. 10, p. 323, 2025

    2025

  14. [14]

    Bayesian neural networks,

    I. Kononenko, “Bayesian neural networks,”Biological Cybernetics, vol. 61, no. 5, pp. 361–370, 1989

    1989

  15. [15]

    A bayesian approach for parameter estimation with uncertainty for dynamic power systems,

    N. Petra, C. G. Petra, Z. Zhang, E. M. Constantinescu, and M. Anitescu, “A bayesian approach for parameter estimation with uncertainty for dynamic power systems,”IEEE Transactions on Power Systems, vol. 32, no. 4, pp. 2735–2745, 2017

    2017

  16. [16]

    A theoretically grounded application of dropout in recurrent neural networks,

    Y . Gal and Z. Ghahramani, “A theoretically grounded application of dropout in recurrent neural networks,”Advances in Neural Information Processing Systems, vol. 29, 2016

    2016

  17. [17]

    B-pinns: Bayesian physics- informed neural networks for forward and inverse pde problems with noisy data,

    L. Yang, X. Meng, and G. E. Karniadakis, “B-pinns: Bayesian physics- informed neural networks for forward and inverse pde problems with noisy data,”Journal of Computational Physics, vol. 425, p. 109913, 2021

    2021

  18. [18]

    Improvement of bayesian pinn training convergence in solving multi-scale pdes with noise,

    Y . Hou, X. Li, and J. Wu, “Improvement of bayesian pinn training convergence in solving multi-scale pdes with noise,”arXiv preprint arXiv:2408.09340, 2024

    work page arXiv 2024

  19. [19]

    A new approach to linear filtering and prediction problems,

    R. E. Kalmanet al., “A new approach to linear filtering and prediction problems,”Journal of Basic Engineering, vol. 82, no. 1, pp. 35–45, 1960

    1960

  20. [20]

    The unscented kalman filter for nonlinear estimation,

    E. A. Wan and R. Van Der Merwe, “The unscented kalman filter for nonlinear estimation,” inProceedings of the IEEE Adaptive Systems for Signal Processing, Communications, and Control Symposium. IEEE, 2000, pp. 153–158

    2000

  21. [21]

    Kfd-nerf: Rethinking dynamic nerf with kalman filter,

    Y . Zhan, Z. Li, M. Niu, Z. Zhong, S. Nobuhara, K. Nishino, and Y . Zheng, “Kfd-nerf: Rethinking dynamic nerf with kalman filter,” in European Conference on Computer Vision. Springer, 2024, pp. 1–18

    2024

  22. [22]

    An un- scented kalman filter-informed neural network for vehicle sideslip angle estimation,

    A. Bertipaglia, M. Alirezaei, R. Happee, and B. Shyrokau, “An un- scented kalman filter-informed neural network for vehicle sideslip angle estimation,”IEEE Transactions on Vehicular Technology, vol. 73, no. 9, pp. 12 731–12 746, 2024

    2024

  23. [23]

    Rkfnet: A novel neural network aided robust kalman filter,

    P. Hao, O. Karakus ¸, and A. Achim, “Rkfnet: A novel neural network aided robust kalman filter,”Signal Processing, vol. 230, p. 109856, 2025

    2025

  24. [24]

    Estimation of dynamic tire force by measurement of vehicle body responses with numerical and experimental validation,

    H. Wang, T. Nagayama, and D. Su, “Estimation of dynamic tire force by measurement of vehicle body responses with numerical and experimental validation,”Mechanical Systems and Signal Processing, vol. 123, pp. 369–385, 2019

    2019

  25. [25]

    Kalmannet: Neural network aided kalman filtering for partially known dynamics,

    G. Revach, N. Shlezinger, X. Ni, A. L. Escoriza, R. J. Van Sloun, and Y . C. Eldar, “Kalmannet: Neural network aided kalman filtering for partially known dynamics,”IEEE Transactions on Signal Processing, vol. 70, pp. 1532–1547, 2022

    2022

  26. [26]

    Latent-kalmannet: Learned kalman filtering for tracking from high-dimensional signals,

    I. Buchnik, G. Revach, D. Steger, R. J. Van Sloun, T. Routtenberg, and N. Shlezinger, “Latent-kalmannet: Learned kalman filtering for tracking from high-dimensional signals,”IEEE Transactions on Signal Processing, vol. 72, pp. 352–367, 2023

    2023

  27. [27]

    Gsp-kalmannet: Tracking graph signals via neural- aided kalman filtering,

    I. Buchnik, G. Sagi, N. Leinwand, Y . Loya, N. Shlezinger, and T. Routtenberg, “Gsp-kalmannet: Tracking graph signals via neural- aided kalman filtering,”IEEE Transactions on Signal Processing, 2024

    2024

  28. [28]

    Maml- kalmannet: A neural network-assisted kalman filter based on model- agnostic meta-learning,

    S. Chen, Y . Zheng, D. Lin, P. Cai, Y . Xiao, and S. Wang, “Maml- kalmannet: A neural network-assisted kalman filter based on model- agnostic meta-learning,”IEEE Transactions on Signal Processing, 2025

    2025

  29. [29]

    Bayesian kalmannet: quantifying uncertainty in deep learning augmented kalman filter,

    Y . Dahan, G. Revach, J. Dunik, and N. Shlezinger, “Bayesian kalmannet: quantifying uncertainty in deep learning augmented kalman filter,”IEEE Transactions on Signal Processing, 2025

    2025

  30. [30]

    Achieving high accuracy with pinns via energy natural gradient descent,

    J. M ¨uller and M. Zeinhofer, “Achieving high accuracy with pinns via energy natural gradient descent,” inProceedings of the International Conference on Machine Learning, N. Hansen, Ed. Honolulu, Hawaii, USA: PMLR, 2023, pp. 1234–1245

    2023

  31. [31]

    Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems,

    A. D. Jagtap, E. Kharazmi, and G. E. Karniadakis, “Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems,”Computer Methods in Applied Mechanics and Engineering, vol. 365, p. 113028, 2020

    2020

  32. [32]

    npinns: Nonlocal physics-informed neural networks for a parametrized nonlocal universal laplacian operator. algorithms and applications,

    G. Pang, M. D’Elia, M. Parks, and G. E. Karniadakis, “npinns: Nonlocal physics-informed neural networks for a parametrized nonlocal universal laplacian operator. algorithms and applications,”Journal of Computa- tional Physics, vol. 422, p. 109760, 2020

    2020

  33. [33]

    Adaptive Physics-Informed Neural Networks for Markov- Chain Monte Carlo,

    M. A. Nabian and H. Meidani, “Adaptive physics-informed neural net- works for markov-chain monte carlo,”arXiv preprint arXiv:2008.01604, 2020

    work page arXiv 2008

  34. [34]

    Physics-informed deep learning for traffic state estimation: A hybrid paradigm informed by second-order traffic models,

    R. Shi, Z. Mo, and X. Di, “Physics-informed deep learning for traffic state estimation: A hybrid paradigm informed by second-order traffic models,” inProceedings of the AAAI Conference on Artificial Intelli- gence, vol. 35, no. 1, 2021, pp. 540–547

    2021

  35. [35]

    A physics- informed neural network for the prediction of unmanned surface vehicle dynamics,

    P.-F. Xu, C.-B. Han, H.-X. Cheng, C. Cheng, and T. Ge, “A physics- informed neural network for the prediction of unmanned surface vehicle dynamics,”Journal of Marine Science and Engineering, vol. 10, no. 2, p. 148, 2022

    2022

  36. [36]

    Ev-pinn: A physics- informed neural network for predicting electric vehicle dynamics,

    H. Lim, J. W. Lee, J. Boyack, and J. B. Choi, “Ev-pinn: A physics- informed neural network for predicting electric vehicle dynamics,” in IEEE International Conference on Robotics and Automation. Atlanta, USA: IEEE, 2025, pp. 1–7

    2025

  37. [37]

    Adaptive construction of surrogates for the bayesian solution of inverse problems,

    J. Li and Y . M. Marzouk, “Adaptive construction of surrogates for the bayesian solution of inverse problems,”SIAM Journal on Scientific Computing, vol. 36, no. 3, pp. A1163–A1186, 2014

    2014

  38. [38]

    Quality of Uncertainty Quantification for Bayesian Neural Network Inference

    J. Yao, W. Pan, S. Ghosh, and F. Doshi-Velez, “Quality of uncertainty quantification for bayesian neural network inference,”arXiv preprint arXiv:1906.09686, 2019

    work page internal anchor Pith review Pith/arXiv arXiv 1906

  39. [39]

    Efficient bayesian physics informed neural networks for inverse problems via ensemble kalman inversion,

    A. Pensoneault and X. Zhu, “Efficient bayesian physics informed neural networks for inverse problems via ensemble kalman inversion,”Journal of Computational Physics, vol. 508, p. 113006, 2024

    2024

  40. [40]

    Bayesian physics informed neural networks for real-world nonlinear dynamical systems,

    K. Linka, A. Sch ¨afer, X. Meng, Z. Zou, G. E. Karniadakis, and E. Kuhl, “Bayesian physics informed neural networks for real-world nonlinear dynamical systems,”Computer Methods in Applied Mechanics and Engineering, vol. 402, p. 115346, 2022

    2022

  41. [41]

    Bayesian physics-informed neural networks for system identification of inverter- dominated power systems,

    S. Stock, D. Babazadeh, C. Becker, and S. Chatzivasileiadis, “Bayesian physics-informed neural networks for system identification of inverter- dominated power systems,”Electric Power Systems Research, vol. 235, no. 110860, 2024

    2024

  42. [42]

    Efficient bayesian inference using physics-informed invertible neural networks for inverse problems,

    X. Guan, X. Wang, H. Wu, Z. Yang, and P. Yu, “Efficient bayesian inference using physics-informed invertible neural networks for inverse problems,”Machine Learning: Science and Technology, vol. 5, no. 035026, 2024

    2024

  43. [43]

    Surrogate modeling for bayesian inverse problems based on physics-informed neural networks,

    Y . Li, Y . Wang, and L. Yan, “Surrogate modeling for bayesian inverse problems based on physics-informed neural networks,”Journal of Com- putational Physics, vol. 475, no. 111841, 2023

    2023

  44. [44]

    Physics-informed bayesian neural networks for solving phonon boltzmann transport equation in forward and inverse problems with sparse and noisy data,

    R. Li, J. Zhou, J.-X. Wang, and T. Luo, “Physics-informed bayesian neural networks for solving phonon boltzmann transport equation in forward and inverse problems with sparse and noisy data,”ASME Journal of Heat and Mass Transfer, vol. 147, no. 3, p. 032501, 2025

    2025

  45. [45]

    Literature review and funda- mental approaches for vehicle and tire state estimation,

    K. B. Singh, M. A. Arat, and S. Taheri, “Literature review and funda- mental approaches for vehicle and tire state estimation,”Vehicle System Dynamics, 2019

    2019

  46. [46]

    Tire normal force estimation using artificial neural networks and fuzzy classifiers: Experi- mental validation,

    A. H. Salari, H. Mirzaeinejad, and M. F. Mahani, “Tire normal force estimation using artificial neural networks and fuzzy classifiers: Experi- mental validation,”Applied Soft Computing, vol. 132, p. 109835, 2023

    2023

  47. [47]

    Multi-class optimal margin distribution ma- chine,

    T. Zhang and Z. Zhou, “Multi-class optimal margin distribution ma- chine,” inProceedings of the International Conference on Machine Learning. PMLR, 2017, pp. 4063–4071

    2017

  48. [48]

    Hy- brid state estimation combining artificial neural network and physical model,

    P. M. Sieberg, S. Blume, N. Harnack, N. Maas, and D. Schramm, “Hy- brid state estimation combining artificial neural network and physical model,” inIEEE Intelligent Transportation Systems Conference. IEEE, 2019, pp. 894–899

    2019

  49. [49]

    Challenges in training pinns: A loss landscape perspective,

    P. Rathore, W. Lei, Z. Frangella, L. Lu, and M. Udell, “Challenges in training pinns: A loss landscape perspective,” inProceedings of the International Conference on Machine Learning. Vienna, Austria: PMLR, 2024, pp. 1–13

    2024

  50. [50]

    Physics-informed machine learning,

    G. E. Karniadakiset al., “Physics-informed machine learning,”Nature Reviews Physics, vol. 3, no. 6, pp. 422–430, 2021

    2021

  51. [51]

    Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,

    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, vol. 378, pp. 686–707, 2019

    2019

  52. [52]

    A dynamic wheel load measurement system for the formula student race car,

    T. Zeng, Z. Liu, H. Chen, and X. Chen, “A dynamic wheel load measurement system for the formula student race car,” inInternational Conference on Electromechanical Control Technology and Transporta- tion, vol. 12790. SPIE, 2023, pp. 94–104

    2023

  53. [53]

    Pacejka,Tire and vehicle dynamics

    H. Pacejka,Tire and vehicle dynamics. Elsevier, 2005

    2005

  54. [54]

    Bayesian methods for neural networks: Theory and applications,

    D. J. MacKayet al., “Bayesian methods for neural networks: Theory and applications,”Course notes for Neural Networks Summer School, 1995

    1995

  55. [55]

    Weight uncertainty in neural network,

    C. Blundell, J. Cornebise, K. Kavukcuoglu, and D. Wierstra, “Weight uncertainty in neural network,” inProceedings of the International Conference on Machine Learning. PMLR, 2015, pp. 1613–1622

    2015

  56. [56]

    Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems,

    D. Zhang, L. Lu, L. Guo, and G. E. Karniadakis, “Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems,”Journal of Computational Physics, vol. 397, no. 108850, 2019

    2019

  57. [57]

    Vehicle trajectory prediction based on lstm recurrent neural networks,

    A. Ip, L. Irio, and R. Oliveira, “Vehicle trajectory prediction based on lstm recurrent neural networks,” inIEEE Vehicular Technology Conference. IEEE, 2021, pp. 1–5. JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021 14 VII. BIOGRAPHY Tianyi Wangis currently a Ph.D. student at the Department of Civil, Architectural, and Environmental Engineering, ...

    2021