Active Learning of Fractional-Order Viscoelastic Model Parameters for Realistic Haptic Rendering

arXiv:2512.00667 · eess.SY, cs.AI, cs.RO, cs.SY · Submitted 2025-11-29 · Read on arXiv

Listen

Transcript

Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: Today's paper: "Active Learning of Fractional-Order Viscoelastic Model Parameters for Realistic Haptic Rendering".

Dev: The gist: Generalized fractional-order viscoelastic models established through the proposed HiL optimization and aggregation approach possess the potential to significantly improve the simto-real transition performance of medical training simulators.

Rosa: First, who's behind it and why it matters.

Paper summary: Rosa: The core thesis here is that fractional-order models can describe time-dependent viscoelastic dynamics with few parameters because they capture memory effects naturally. But because those parameters are so coupled, finding the right values to make things feel realistic is a real challenge for medical simulators.

Dev: That's right. This paper argues that instead of trying to guess the best parameters, we should use active learning with human-in-the-loop feedback to optimize them for each individual first.

Taro: So, the initial step is letting users give qualitative feedback iteratively to dial in the parameters for a single person's simulation experience.

Rosa: Exactly. Once you have those individual mappings of what realism means, they propose a way to aggregate those results into one large perceptual map trained on all that data from all participants.

Dev: That aggregation method is key because simply averaging individual models can be misleading; it might pull the average towards the prior settings and lose information about where things are truly uncertain.

Taro: So, this aggregate approach, training a single GP model on the entire dataset, preserves that uncertainty in sparsely sampled regions while still capturing generalizable patterns across all participants.

Rosa: And from that aggregate model, they select population-level optimal parameters that are perceived as realistic by the general group. That's what makes it matter for simulators used widely.

Dev: It matters because this approach gives us a systematic means to parameterize these complex models in a way that is robust across different users, which should substantially enhance the realism of viscoelasticity renderings, such as tissue rendering.

Conclusion: Rosa: Thinking about the paper, "Active Learning of Fractional-Order Viscoelastic Model Parameters for Realistic Haptic Rendering," it’s essentially saying we can systematically figure out the fractional-order parameters needed for realistic haptic rendering using this active learning and aggregation technique.

Dev: The authors found that by optimizing parameters individually through human feedback and then aggregating those findings into a single population model, you get a set of parameters that are perceived as realistic across general populations.

Taro: So the implication is that we don't have to manually tune these complex fractional-order models one by one; we can use this learning process to find the best settings for widespread use in medical training simulators.

Rosa: That’s right. It suggests a more practical way to bridge the gap between theoretical viscoelastic models and what actually feels right when you're interacting with them haptically.

Dev: It moves the problem from just finding one perfect parameter set to developing a framework that handles the complexity of these parameters for diverse users in a scalable way.

Taro: So, for someone listening who doesn't deal with the math directly, this means we are getting a method that aims to make medical training simulators feel more accurate and reliable for everyone using them.

Sabanci University

eess.SY, cs.AI, cs.RO, cs.SY

Submitted: 2025-11-29

Updated: 2026-05-19

Comments: This work has been submitted to the IEEE Transactions on Haptics for possible publication. 14 pages, 8 figures

License: http://creativecommons.org/licenses/by-nc-nd/4.0/

Importance score: 86/100

The gist: The gist: Generalized fractional-order viscoelastic models established through the proposed HiL optimization and aggregation approach possess the potential to significantly improve the simto-real

Key concepts

Fractional-Order Models: These are mathematical models used to describe materials like biological tissues that exhibit time-dependent behavior, such as creep and stress relaxation. Unlike simpler models, they naturally capture long-term memory effects in the material's response over time.
Active Learning (HiL Optimization): This is a process where a system iteratively asks human experts for feedback on model parameters to improve the model. In this study, users provided qualitative feedback on how realistic the haptic rendering felt, allowing the system to learn which parameter settings are best for that specific user.
Perceptual Map Aggregation: This involves combining individual optimization results from many users into a single map representing what is generally perceived as realistic across a whole population. By using techniques like Bayesian Committee Machine, the study found parameters that were highly realistic for individuals while also being broadly acceptable to the group.
Viscoelasticity: This describes materials that exhibit both viscous (fluid-like) and elastic (solid-like) properties. Biological tissues are a prime example because their mechanical response changes depending on how quickly they are deformed or stressed, making them complex to simulate.

Terminology

Active Learning — 2× in this paper · explained in 6 episodes
Aggregation — 1× in this paper
Human-in-the-Loop — 1× in this paper · explained in 3 episodes

Summary

The gist: Generalized fractional-order viscoelastic models established through the proposed HiL optimization and aggregation approach possess the potential to significantly improve the simto-real transition performance of medical training simulators.

Model Background

Biological tissues possess viscoelastic material properties that are intrinsically time-dependent, making their modeling challenging Traditional integer-order springdamper networks fail to provide satisfactory approximations, as they cannot capture the memory-dependent nature of viscoelasticity. Linear fractional-order models are widely embraced as more accurate representations because they can describe sophisticated viscoelastic dynamics with fewer parameters, naturally capturing long-time memory effects. Fractional-order models are significantly less intuitive because the effects of model parameters on material behavior are harder to predict due to the frequency-dependent coupling between the fractional order and other parameters.

Proposed Methodology

The study proposes a systematic means of determining the parameters of fractional-order viscoelastic models that optimizes their perceived realism for each individual through active learning, using qualitative feedback-based human-in-the-loop (HiL) optimization. First, they demonstrate that the parameters can be effectively optimized through active learning using qualitative feedback to ensure consistently high realism ratings for each individual. Second, a rigorous method is proposed to combine HiL optimization results into an aggregate perceptual map trained on the entire dataset, and then select population-level optimal parameters from this representation that are broadly perceived as realistic across general populations.

Key Contributions

The contributions of the study can be summarized as follows:

(i) They propose an active learning framework based on sample-efficient human-in-the-loop (HiL) Bayesian optimization with qualitative perceptual feedback, where users’ feedback is collected iteratively to determine the parameters that maximize the perceived realism of viscoelasticity renderings.

(ii) Given the perceptual mappings characterized for each individual, they propose a rigorous means to combine these results so that an aggregate perceptual map trained on the entire dataset is computed, and then select population-level optimal parameters for this representation that are perceived as realistic.

(iii) They provide evidence of the effectiveness of the generalized fractional-order viscoelastic model by characterizing its perceived realism through human-subject experiments.

Model and Optimization Details

The fractional-order SLS model is defined by the force-position impedance transfer function H(s) = K0 + K1B1sα / (K1 + B1sα) where K0 and K1 denote stiffness constants, α represents the order of the fractional-order derivative, and B1 is the coefficient of the fractional-order element. The study uses a short-memory discretization method to handle practical concerns regarding infinite history by considering only a finite window length N. The discrete force–position impedance transfer function for the fractional-order SLS virtual environment model can be expressed as H(z) = K0 + K1B1 / (Tα PN i=0 ciz−i) K1 + B1 / (Tα PN i=0 ciz−i).

Validation and Aggregation

The study employs Gaussian Process (GP) models to model perceived realism, placing a GP prior on the latent function of perceived realism f(x) as f(x) ∼ GP(0, K), where K is the noiseless kernel matrix. To handle aggregation efficiently, they use the Bayesian Committee Machine (BCM) to combine individual GP models into a population-level aggregate GP model. This method respects each participant’s unique preferences while capturing patterns shared across the group. The results show that the aggregate GP posterior model estimates the population-level optimal parameter set, marked with a green dot in Figure 6(a), as given in Table I.

Conclusion and Findings

The findings indicate that the proposed HiL optimization and aggregation technique provides a systematic and practical solution for fractional-order viscoelastic model parameterization. The aggregate GP posterior model estimates the population-level optimal parameter set, marked with a green dot in Figure 6(a), as given in Table I. These parameters maximize the perceived realism score under the aggregate GP posterior model and closely match those obtained from system identification for the memory foam material. The results in Table IV indicate that the aggregate-best rendering was preferred significantly more often than the individually optimized ones. Overall, both the Model Validation and the Aggregate-Best Validation results for the memory-foam material provide strong evidence that Hypothesis H2 holds.

Future Work

Further efficiency improvements may be needed for higher-dimensional optimization tasks, as the search space grows exponentially with respect to the number of parameters. The study plans to compare models with varying numbers of parameters to assess their optimization costs and perceptual performance. The framework is expected to perform reliably when the feasible parameter range is selected to ensure users can provide consistent perceptual judgments.

References

[1] K. Salisbury, D. Brock, T. Massie, N. Swarup, and C. Zilles, “Haptic rendering: Programming touch interaction with virtual objects,” in Symposium on Interactive 3D graphics, 1995, pp. 123–130

[2] S. Park, A. L. Chien, I. D. Brown, and J. Chen, “Characterizing viscoelastic properties of human melanoma tissue using prony series,” Frontiers in Bioeng., vol 11, p 1162880, 2023

[3] B. Carmichael, H. Babahosseini, S. N. Mahmoodi, and M. Agah, “The fractional viscoelastic response of human breast tissue cells,” Physical Biology, vol 12, no 4, p 046001, 2015

[4] D. Klatt, U. Hamhaber, P. Asbach, J. Braun, and I. Sack, “Noninvasive assessment of the rheological behavior of human organs using multifrequency mr elastography: a study of brain and liver viscoelasticity,” Physics in Medicine & Biology, vol 52, no 24, p 7281, 2007

[5] B. Carmichael, H. Babahosseini, S. Mahmoodi, and M. Agah, “The fractional viscoelastic response of human breast tissue cells,” Physical Biology, vol 12, no 4, p 046001, 2015

[6] A. Bonfanti, J. L. Kaplan, G. Charras, and A. Kabla, “Fractional viscoelastic models for power-law materials,” Soft matter, vol 16, no 26, pp 6002–6020, 2020

[7] J. D. Ferry, Viscoelastic Properties of Polymers., John Wiley & Sons, 1980

[8] C. Zener, Elasticity and Anelasticity of Metals., University of Chicago Press, 1948

[9] A. Gemant, “A method of analyzing experimental results obtained from elasto-viscous bodies,” Physics, vol 7, no 8, pp 311–317, 1936

[10] R. L. Bagley and P. J. Torvik, “A generalized derivative model for an elastomer damper,” Shock and Vibration Bulletin, vol 49, pp 135–143, 1979

[11] R. Bagley and P.

Improvements for AI systems

Bold header: Active Learning for Individual Optimization

This improvement enables AI systems to determine the parameters of fractional-order viscoelastic models that optimizes the perceived realism of haptic rendering across general populations by using active learning, using qualitative feedback-based human-in-the-loop (HiL) optimization.

Bold header: Population Perceptual Map Construction

The improved system can create an aggregate perceptual map trained on the entire dataset by combining individual results via the Bayesian Committee Machine (BCM), allowing researchers to select population-level optimal parameters that are broadly perceived as realistic across general populations.

Bold header: Generalized Model Validation and Generalization

The AI can now provide evidence of the effectiveness of the generalized fractional-order viscoelastic model by characterizing its perceived realism through human-subject experiments, ensuring that models optimized for one material type, such as memory foam, are robust across viscoelastic materials with different mechanical properties.

Bold header: Robustness to Individual Model Convergence

The system can reliably determine population parameters even when individual participants’ GP models do not converge, by leveraging the BCM framework which weights individual predictions by their precision rather than requiring every model to fully converge.

Abstract

Effective medical simulators necessitate realistic haptic rendering of biological tissues that exhibit viscoelastic material properties, such as creep and stress relaxation. Fractional-order models provide an effective means of describing intrinsically time-dependent viscoelastic dynamics with few parameters, as they naturally capture memory effects. However, due to the unintuitive, frequency-dependent coupling among the order of the fractional element and other parameters, determining appropriate parameter values for fractional-order models that yield high perceived realism remains a significant challenge. In this study, we propose a systematic means of determining the parameters of fractional-order viscoelastic models that optimizes the perceived realism of haptic rendering across general populations. First, we demonstrate that the parameters of fractional-order models can be effectively optimized through active learning, using qualitative feedback-based human-in-the-loop (HiL) optimization, to ensure consistently high realism ratings for each individual. Second, we propose a rigorous method to combine HiL optimization results into an aggregate perceptual map trained on the entire dataset, and demonstrate how to select population-level optimal parameters from this representation that are broadly perceived as realistic across general populations. Finally, we provide evidence of the effectiveness of the generalized fractional-order viscoelastic model parameters for three viscoelastic materials by characterizing their perceived realism through human-subject experiments. Overall, generalized fractional-order viscoelastic models established through the proposed HiL optimization and aggregation approach possess the potential to significantly improve the sim-to-real transition performance of medical training simulators.