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

arXiv: https://arxiv.org/abs/2512.00667 · HTML: https://mlsanity.com/paper/2512.00667/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2025.

## Built on by (most cited first, 3 of 3)

- [A Koopman-Bayesian Framework for High-Fidelity, Perceptually Optimized Haptic Surgical Simulation](https://mlsanity.com/paper/2602.15834/) (2026)
- [Human-in-the-Loop Pareto Optimization: Trade-off Characterization for Assist-as-Needed Training and Performance Evaluation](https://mlsanity.com/paper/2603.23777/) (2026)
- [Haptic Rendering of Fractional-Order Viscoelasticity: Passivity and Rendering Fidelity](https://mlsanity.com/paper/2605.16389/) (2026)

## Abstract (arXiv)

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.