Estimation of Motor Unit Parameters from Surface Electromyograms using an Informed Autoencoder

Axel Schneider; Kaja Balzereit; Malte Mechtenberg

arxiv: 2605.07458 · v1 · submitted 2026-05-08 · 💻 cs.LG

Estimation of Motor Unit Parameters from Surface Electromyograms using an Informed Autoencoder

Kaja Balzereit , Malte Mechtenberg , Axel Schneider This is my paper

Pith reviewed 2026-05-11 02:10 UTC · model grok-4.3

classification 💻 cs.LG

keywords informed autoencodersurface EMGmotor unit parametersinnervation zone centreconduction velocityinverse problemphysical lawsneuromechanical models

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The pith

An informed autoencoder estimates multiple motor unit parameters such as innervation zone centre and conduction velocity from non-invasive surface EMG recordings by embedding physical laws.

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

The paper develops an informed autoencoder to estimate subject-specific motor unit parameters from surface electromyography recordings measured at the skin. The model reconstructs the signals while encoding the parameters in its latent space and enforcing physical relationships between the parameters and the generated signals. This targets the inverse problem without requiring extensive manual white-box modelling for each case. If the approach holds, it would enable non-invasive determination of parameters that vary with contraction and subject, improving the accuracy of neuromechanical models for movement and force prediction.

Core claim

The informed autoencoder reconstructs the surface EMG recordings while learning the parameters in its latent space and adhering to physical laws that relate the parameters to the EMG signals. In experiments on synthetic data, innervation zone centres are estimated with a mean absolute error of 2.5989 mm, and conduction velocities of the electric potential are estimated with a mean absolute error of 0.1697 m s^{-1}. These results demonstrate the plausibility of this novel approach, which enables the simultaneous estimation of several motor unit parameters while reducing manual modelling effort through the integration of data-driven machine learning.

What carries the argument

Informed autoencoder whose latent space represents motor unit parameters and whose decoder reconstructs EMG signals under physical constraints on signal generation.

Load-bearing premise

The physical laws used in the autoencoder accurately capture the forward process from motor unit parameters to surface EMG signals, and the synthetic data distribution matches real recordings closely enough for the learned inverse to work.

What would settle it

Collect surface EMG from human subjects along with independent reference measurements of their innervation zone centres and conduction velocities, then check whether the model's estimates match the references within the error ranges seen on synthetic data.

Figures

Figures reproduced from arXiv: 2605.07458 by Axel Schneider, Kaja Balzereit, Malte Mechtenberg.

**Figure 2.** Figure 2: Plot of the MSE loss function L mse for innervation zone centre iz and conduction velocity v as a 3d surface plot (a) and as a contour plot (b). The mean parameters of the motor unit serve as reference values and are marked in red. 2.3.3 (C3) Scaling As the sEMG predicted by the decoder results from a single muscle fibre, its magnitude is smaller than the magnitude of the sEMG recordings resulting from all… view at source ↗

read the original abstract

Motor unit parameters such as the innervation zone centre or the conduction velocity of the electrical potential harbour the potential to improve the fidelity of neuromechanical models used for movement and force prediction. Determining these parameters in a non-invasive way is challenging, as they are subject-specific and may vary with muscle contraction. Existing work on the estimation of motor unit parameters mainly relies on white-box modelling and therefore requires substantial manual modelling effort. This work targets the simultaneous estimation of multiple subject-specific motor unit parameters from electromyography (EMG) recordings measured non-invasively at the skin surface. This results in an inverse problem with a nonlinear loss function. To address this problem, an informed autoencoder is developed. This autoencoder reconstructs the surface EMG recordings while learning the parameters in its latent space and adhering to physical laws that relate the parameters to the EMG signals. In experiments on synthetic data, innervation zone centres are estimated with a mean absolute error of 2.5989 $\mathrm{mm}$, and conduction velocities of the electric potential are estimated with a mean absolute error of 0.1697 $\mathrm{m}\mathrm{s}^{-1}$. These results demonstrate the plausibility of this novel approach, which enables the simultaneous estimation of several motor unit parameters while reducing manual modelling effort through the integration of data-driven machine learning.

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.

Desk Editor's Note private letter to a colleague

The informed autoencoder recovers parameters cleanly on synthetic data generated from its own forward model, but that leaves the real-world mismatch problem untested.

read the letter

The paper's core move is to put motor unit parameters in the latent space of an autoencoder whose decoder is constrained by the EMG forward physics. This lets it estimate innervation zone center and conduction velocity at the same time from surface recordings while cutting down on manual white-box modeling. On synthetic data it reports mean absolute errors of 2.6 mm and 0.17 m/s, which is a clean demonstration that the network can invert the embedded equations when the test signals match the model exactly. That part is useful and the idea of physics-informed latent variables for this inverse problem looks new in the EMG literature. The reduction in manual effort is a practical plus for anyone building subject-specific neuromechanical simulations. The main limitation is that the synthetic generator appears to be the same forward map used inside the decoder. Low errors in that setting only confirm the network learned the inverse of its own equations; they do not speak to electrode misalignment, tissue inhomogeneity, or other real-signal discrepancies that matter for the target application. The abstract gives no real-data results, no baseline comparisons, and no independent validation that the recovered parameters match ground truth outside the reconstruction loss. If the full paper adds those checks, the work strengthens; without them the central claim stays provisional. This is worth a serious referee for groups working on biomechanics and rehabilitation modeling who need scalable parameter extraction. The idea is grounded enough to justify review time, but any acceptance would need clear real-data experiments and comparisons to existing decomposition methods.

Referee Report

2 major / 2 minor

Summary. The paper proposes an informed autoencoder to solve the inverse problem of simultaneously estimating multiple subject-specific motor unit parameters (innervation zone centre and conduction velocity of the electrical potential) from non-invasive surface EMG recordings. The decoder embeds physical laws relating parameters to EMG signals, allowing the latent space to learn the parameters while minimizing a reconstruction loss on the observed signals. On synthetic data the method reports mean absolute errors of 2.5989 mm for innervation zone centres and 0.1697 m s^{-1} for conduction velocities, presented as evidence that the approach reduces manual white-box modelling effort.

Significance. If the physics-informed inversion proves robust on real surface EMG, the method could meaningfully lower the barrier to obtaining subject-specific motor-unit parameters for neuromechanical models used in movement and force prediction. The explicit integration of domain knowledge into the autoencoder loss is a constructive design choice that distinguishes the work from purely data-driven baselines.

major comments (2)

[Experiments] Experiments section: the synthetic data generator is not shown to incorporate mismatches (electrode misalignment, tissue inhomogeneity, unmodelled noise) that are absent from the decoder's forward mapping. If the test signals are produced by the identical forward model embedded in the autoencoder, the reported MAEs demonstrate only successful inversion of a known function rather than robustness to the model error that dominates real surface EMG, which is the target application.
[Method] Method section: the precise form of the informed reconstruction loss and the manner in which physical constraints are enforced on the latent parameters are not given in sufficient mathematical detail (no explicit loss equation or constraint formulation appears). Without this, it is impossible to determine whether the learned parameters are independently validated or are simply those that minimise reconstruction error under the embedded model, raising a circularity concern for the central claim.

minor comments (2)

[Abstract] Abstract: architecture details, loss formulation, training procedure and baseline comparisons are omitted, making it difficult for readers to assess the novelty and reproducibility of the reported errors.
Consider adding a table that contrasts the proposed method against existing white-box parameter-estimation techniques in terms of both accuracy and manual modelling effort.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and indicate the changes we will incorporate in the revised version.

read point-by-point responses

Referee: [Experiments] Experiments section: the synthetic data generator is not shown to incorporate mismatches (electrode misalignment, tissue inhomogeneity, unmodelled noise) that are absent from the decoder's forward mapping. If the test signals are produced by the identical forward model embedded in the autoencoder, the reported MAEs demonstrate only successful inversion of a known function rather than robustness to the model error that dominates real surface EMG, which is the target application.

Authors: We agree that the synthetic experiments use data generated from the identical forward model embedded in the decoder. This demonstrates that the informed autoencoder can accurately invert the model to recover the parameters when the physics is perfectly matched, which is a necessary validation step for the approach. We acknowledge that this does not yet address robustness to the model mismatches (e.g., electrode misalignment, tissue inhomogeneity, unmodelled noise) that are present in real surface EMG. In the revised manuscript we will add an explicit limitations paragraph in the Discussion section stating this point, reporting the current results as a proof-of-concept under matched conditions, and outlining planned future work on mismatched synthetic data and experimental recordings. revision: partial
Referee: [Method] Method section: the precise form of the informed reconstruction loss and the manner in which physical constraints are enforced on the latent parameters are not given in sufficient mathematical detail (no explicit loss equation or constraint formulation appears). Without this, it is impossible to determine whether the learned parameters are independently validated or are simply those that minimise reconstruction error under the embedded model, raising a circularity concern for the central claim.

Authors: We thank the referee for highlighting the missing mathematical detail. The encoder maps the input EMG to latent parameters (innervation zone centre and conduction velocity). The decoder implements a differentiable version of the physical forward model and produces the reconstructed signal; the training loss is the mean-squared reconstruction error between input and decoder output. Physiological constraints are enforced by scaling the latent activations to plausible ranges (conduction velocity 2–6 m s^{-1}, innervation zone within the muscle length). We will insert the explicit loss equation L = ||x − D(E(x))||² together with the constraint formulation in the revised Method section. This clarifies that parameter estimation occurs via physics-informed reconstruction rather than independent validation, directly addressing the circularity concern. revision: yes

Circularity Check

0 steps flagged

No significant circularity; validation uses independent synthetic benchmarks

full rationale

The paper develops an informed autoencoder whose decoder embeds a forward physical model of EMG generation to enable parameter estimation in the latent space via reconstruction loss. Reported MAEs on synthetic data constitute a standard test of inversion accuracy against known ground-truth parameters generated from the same model class. This does not reduce the result to the inputs by construction, as the network must still learn an approximate inverse mapping and the errors (2.5989 mm, 0.1697 m/s) are nonzero. No self-citations, uniqueness theorems, or ansatzes are invoked in a load-bearing manner within the abstract or described method. The approach remains a hybrid physics-informed ML solver whose central claim (plausibility of simultaneous parameter recovery) is externally falsifiable on the synthetic test set.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The method rests on domain assumptions about EMG signal generation and data-driven fitting of latent parameters; no explicit free parameters or invented entities are named in the abstract.

axioms (1)

domain assumption Physical laws exist that relate motor unit parameters (innervation zone location, conduction velocity) to observed surface EMG signals
The autoencoder is required to adhere to these laws during reconstruction.

pith-pipeline@v0.9.0 · 5536 in / 1204 out tokens · 51737 ms · 2026-05-11T02:10:17.169805+00:00 · methodology

discussion (0)

Reference graph

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[1] [1]

Nils Grimmelsmann, Malte Mechtenberg, Wolfram Schenck, Hanno Gerd Meyer, and Axel Schneider. semg- based prediction of human forearm movements utilizing a biomechanical model based on individual anatomical/ physiological measures and a reduced set of optimization parameters.PLOS ONE, 18(8):1–28, 08 2023. doi: 10.1371/journal.pone.0289549. URLhttps://doi.o...

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work page doi:10.1371/journal.pone.0275128 2022

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A hierarchical hand ges- ture recognition framework for sports referee training-based emg and accelerometer sensors.IEEE transactions on cybernetics, 52(5):3172–3183, 2022

Tse-Yu Pan, Wan-Lun Tsai, Chen-Yuan Chang, Chung-Wei Yeh, and Min-Chun Hu. A hierarchical hand ges- ture recognition framework for sports referee training-based emg and accelerometer sensors.IEEE transactions on cybernetics, 52(5):3172–3183, 2022. doi: 10.1109/TCYB.2020.3007173

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P. R. Cavanagh and P. V. Komi. Electromechanical delay in human skeletal muscle under concentric and eccentric contractions.Eur J Appl Physiol O, 42(3):159–163, 1979. ISSN 0301-5548, 1439-6327. doi: 10.1007/ BF00431022. 12

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Effects of temperature and fatigue on the electromechanical delay components.Muscle & Nerve, 47(4):566– 576, 2013

Emiliano C` e, Susanna Rampichini, Luca Agnello, Eloisa Limonta, Arsenio Veicsteinas, and Fabio Esposito. Effects of temperature and fatigue on the electromechanical delay components.Muscle & Nerve, 47(4):566– 576, 2013. ISSN 1097-4598. doi: 10.1002/mus.23627. URLhttps://onlinelibrary.wiley.com/doi/abs/ 10.1002/mus.23627

work page doi:10.1002/mus.23627 2013

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Yecid Moreno, Denis Mosconi, Felix M. Escalante, and Adriano A. G. Siqueira. Analysis of Electromechanical Delay in Neuromuscular Electrical Stimulation: Preliminary Results. In Jose L. Pons, Jesus Tornero, and Metin Akay, editors,Converging Clinical and Engineering Research on Neurorehabilitation V, volume 31, pages 799–803. Springer Nature Switzerland, ...

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[9] [9]

Buchanan, David G

Thomas S. Buchanan, David G. Lloyd, Kurt Manal, and Thor F. Besier. Neuromusculoskeletal modeling: Estimation of muscle forces and joint moments and movements from measurements of neural command.J Appl Biomech, 20(4):367–395, 11 2004. doi: 10.1123/jab.20.4.367

work page doi:10.1123/jab.20.4.367 2004

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A method for the estimation of a motor unit innervation zone center position evaluated with a computational semg model.Frontiers in Neurorobotics, 17:1179224, 2023

Malte Mechtenberg and Axel Schneider. A method for the estimation of a motor unit innervation zone center position evaluated with a computational semg model.Frontiers in Neurorobotics, 17:1179224, 2023

work page 2023

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Malte Mechtenberg, Nils Grimmelsmann, and Axel Schneider. A new algorithm for innervation zone estimation using surface electromyography: A simulation study based on a simulator for continuous semgs.Proceedings of the 17th BIOSIGNALS, pages 629–636, 2024. doi: 10.5220/0012375100003657

work page doi:10.5220/0012375100003657 2024

[12] [12]

Klein, Greg D

Cliff S. Klein, Greg D. Marsh, Robert J. Petrella, and Charles L. Rice. Muscle fiber number in the biceps brachii muscle of young and old men.Muscle & nerve, 28(1):62–68, 2003. ISSN 0148-639X. doi: 10.1002/mus.10386

work page doi:10.1002/mus.10386 2003

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Accuracy of three different techniques for automatically estimating innervation zone location.Comput

Travis W Beck, Jason M DeFreitas, and Matt S Stock. Accuracy of three different techniques for automatically estimating innervation zone location.Comput. Methods Programs Biomed., 105(1):13–21, January 2012

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Hamid Reza Marateb, Morteza Farahi, Monica Rojas, Miguel Angel Ma˜ nanas, and Dario Farina. Detection of multiple innervation zones from multi-channel surface EMG recordings with low signal-to-noise ratio using Graph-Cut segmentation.PLoS One, 11(12):e0167954, December 2016

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Informed machine learning - a taxonomy and survey of integrating prior knowledge into learning systems.IEEE Transactions on Knowledge and Data Engineering, page 1, 2021

Laura von Rueden, Sebastian Mayer, Katharina Beckh, Bogdan Georgiev, Sven Giesselbach, Raoul Heese, Bir- git Kirsch, Michal Walczak, Julius Pfrommer, Annika Pick, Rajkumar Ramamurthy, Jochen Garcke, Christian Bauckhage, and Jannis Schuecker. Informed machine learning - a taxonomy and survey of integrating prior knowledge into learning systems.IEEE Transac...

work page doi:10.1109/tkde.2021.3079836 2021

[16] [16]

Physics-informed machine learning

George Em Karniadakis, Ioannis G. Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang. Physics- informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021. doi: 10.1038/s42254-021-00314-5

work page doi:10.1038/s42254-021-00314-5 2021

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Guojun Wang, Weijun Li, Liping Zhang, Linjun Sun, Peng Chen, Lina Yu, and Xin Ning. Encoder-x: solving unknown coefficients automatically in polynomial fitting by using an autoencoder.IEEE Transactions on Neural Networks and Learning Systems, 33(8):3264–3276, 2021

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Yavuz, and Oliver R¨ ohrle

Thomas Klotz, Leonardo Gizzi, Utku S ¸. Yavuz, and Oliver R¨ ohrle. Modelling the electrical activity of skeletal muscle tissue using a multi-domain approach.Biomechanics and modeling in mechanobiology, 19(1):335–349,

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work page doi:10.1007/s10237-019-01214-5

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work page doi:10.1109/10.821754 2000

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