# Diff-MSM: Differentiable MusculoSkeletal Model for Simultaneous Identification of Human Muscle and Bone Parameters

arXiv: https://arxiv.org/abs/2508.13303 · HTML: https://mlsanity.com/paper/2508.13303/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 18 Aug 2025.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [DiffCloud: Real-to-Sim from Point Clouds with Differentiable Simulation and Rendering of Deformable Objects](https://mlsanity.com/paper/2204.03139/) (2022)
- [PyPose: A Library for Robot Learning with Physics-based Optimization](https://mlsanity.com/paper/2209.15428/) (2022)
- [A Review of Differentiable Simulators](https://mlsanity.com/paper/2407.05560/) (2024)
- [Differentiable Physics Models for Real-world Offline Model-based Reinforcement Learning](https://mlsanity.com/paper/2011.01734/) (2020)
- [Encoding Physical Constraints in Differentiable Newton-Euler Algorithm](https://mlsanity.com/paper/2001.08861/) (2020)
- [Self Model for Embodied Intelligence: Modeling Full-Body Human Musculoskeletal System and Locomotion Control with Hierarchical Low-Dimensional Representation](https://mlsanity.com/paper/2312.05473/) (2023)
- [Linear Matrix Inequalities for Physically-Consistent Inertial Parameter Identification: A Statistical Perspective on the Mass Distribution](https://mlsanity.com/paper/1701.04395/) (2017)
- [Augmenting Differentiable Simulators with Neural Networks to Close the Sim2Real Gap](https://mlsanity.com/paper/2007.06045/) (2020)
- [Identification of Fully Physical Consistent Inertial Parameters using Optimization on Manifolds](https://mlsanity.com/paper/1610.08703/) (2016)
- [Real2Sim2Real Transfer for Control of Cable-driven Robots via a Differentiable Physics Engine](https://mlsanity.com/paper/2209.06261/) (2022)

## Abstract (arXiv)

High-fidelity personalized human musculoskeletal models are crucial for simulating realistic behavior of physically coupled human-robot interactive systems and verifying their safety-critical applications in simulations before actual deployment, such as human-robot co-transportation and rehabilitation through robotic exoskeletons. Identifying subject-specific Hill-type muscle model parameters and bone dynamic parameters is essential for a personalized musculoskeletal model, but very challenging due to the difficulty of measuring the internal biomechanical variables in vivo directly, especially the joint torques. In this paper, we propose using Differentiable MusculoSkeletal Model (Diff-MSM) to simultaneously identify its muscle and bone parameters with an end-to-end automatic differentiation technique differentiating from the measurable muscle activation, through the joint torque, to the resulting observable motion without the need to measure the internal joint torques. Through extensive comparative simulations, the results manifested that our proposed method significantly outperformed the state-of-the-art baseline methods, especially in terms of accurate estimation of the muscle parameters (i.e., initial guess sampled from a normal distribution with the mean being the ground truth and the standard deviation being 10% of the ground truth could end up with an average of the percentage errors of the estimated values as low as 0.05%). In addition to human musculoskeletal modeling and simulation, the new parameter identification technique with the Diff-MSM has great potential to enable new applications in muscle health monitoring, rehabilitation, and sports science.