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REVIEW 4 major objections 5 minor 43 references

Physics-informed Deep Learning for Muscle Force Prediction with Unlabeled sEMG Signals

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Muscle forces can be predicted from sEMG without muscle-force labels by using the Hill muscle model as a physics-based training loss.

desk verdict Drops force labels but not all labels; the evaluation measures consistency with the same Hill model family used to generate the targets, so the accuracy claims need tempering. read the letter →

arxiv 2412.04213 v1 pith:XMLELXQ5 submitted 2024-12-05 cs.LG cs.HCeess.SPphysics.bio-ph

Shuhao Ma , Jie Zhang , Chaoyang Shi , Pei Di , Ian D.Robertson , Zhi-Qiang Zhang This is my paper · ORCID
classification cs.LGcs.HCeess.SPphysics.bio-ph
keywords physics-informeddeeplearningmuscleforcepredictionunlabeledsEMGHillmodelmuscle-tendonparameteridentificationwristjointmusculoskeletalforwarddynamicsComputedControlgroundtruth
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes a physics-informed deep learning method that predicts muscle forces from sEMG signals without muscle-force labels during training. Instead of supervising the network with measured forces, it embeds the Hill muscle model's forward dynamics as additional loss terms that constrain the network's outputs. On a six-subject wrist flexion/extension dataset, the method reports RMSE and $R^2$ comparable to or better than LSTM, GRU, CNN, FNN, SVR, and ELM baselines that train on labeled muscle forces. The same optimization also identifies subject-specific Hill parameters inside physiological ranges. The authors argue this removes the expensive labeling bottleneck while keeping fast inference.

What carries the argument

The load-bearing object is the Hill-based musculoskeletal forward dynamics used as a physics regularizer inside the loss. sEMG is mapped to activation through the exponential relation $a_{t,n} = (e^{A e_{t,n}}-1)/(e^{A}-1)$; contraction dynamics then give muscle-tendon force from activation and force-length-velocity factors, with pennation angle updated as $\varphi_{t,n} = \sin^{-1}(l^m_{o,n}\sin\varphi_{o,n}/l^m_{t,n})$. The forward-dynamics residual $L_{fd}$ and the implicit force residual $L_F$ together couple the network's predicted forces and the kinematic predictions to physiological parameters $\kappa$, so the network learns force without ever seeing a force label. Identifying $\kappa$ simultaneously makes the model subject-specific.

What would settle it

Measure actual muscle forces on the same wrist task with a direct method (for example an implanted tendon transducer or instrumented joint replacement) and compare the predicted forces in absolute units; alternatively, create a synthetic dataset with known Hill parameters and known true forces, and check whether the recovered parameters match the known values. If the predictions deviate systematically from direct measurements, the reported RMSE and $R^2$ comparisons do not transfer to real physiology.

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Extended reading notes

Core claim

The paper's central claim is that a fully connected network trained with the composite loss $L_{\mathrm{total}} = L_q + L_{fd} + L_F$ can predict muscle forces from sEMG signals without any muscle-force labels, while also identifying subject-specific parameters of the Hill muscle model. The data-based term $L_q$ is the MSE between measured and predicted joint angles, $L_{fd}$ enforces the musculoskeletal forward-dynamics equation $M(q)\ddot{q} + C(q,\dot{q}) + G(q) = \tau(\kappa)$, and $L_F$ penalizes the difference between the network's force output and the force computed by the embedded Hill model. The authors report that this training scheme produces wrist flexion/extension force predictions with RMSE and $R^2$ comparable to or better than LSTM, GRU, CNN, FNN, SVR, and ELM baselines that train with labeled forces, and that the recovered parameters (maximum isometric force, optimal fiber length, activation shape factor) stay within physiological ranges. Knee examples are included to indicate generalization beyond the wrist.

Load-bearing premise

The evaluation assumes that muscle forces computed by the Computed Muscle Control tool of a scaled generic musculoskeletal model are valid ground truth, even though the same Hill-model machinery used to create those targets is embedded in the training loss.

Editorial extensions

If this is right

  • Muscle-force estimators could be trained from sEMG plus joint kinematics alone, removing the need for force/torque labels that are hard to acquire in practice.
  • A single training run yields both force predictions and personalized muscle-tendon parameters, so subject-specific modeling does not require a separate parameter-estimation stage.
  • Because inference is a one-pass network forward, the trained model is fast enough for real-time biofeedback even though training is slower than standard baselines.
  • The physics losses act as a regularizer, which the paper shows improves stability when tested on data of a different wrist speed (intrasession generalization).
  • If the approach transfers to other joints as the knee examples suggest, the same recipe could reduce labeling costs across the body.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The term 'unlabeled' is partial: the method still uses measured joint angles through $L_q$, so a fully label-free version would need a kinematic-free supervision or physics-only loss.
  • Because the ground-truth muscle forces are produced by a musculoskeletal model that contains the same Hill model family used in the physics loss, the reported accuracy partly measures self-consistency with that model rather than absolute physiological truth.
  • A natural extension is to weight the physics residuals relative to $L_q$ and test whether the identified parameters remain physiological when sEMG is noisy or training data are scarce.
  • The framework could be combined with transfer learning across subjects to shorten the long per-subject training time, a direction the paper names as future work.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes a physics-informed deep learning framework for predicting muscle forces from sEMG signals and simultaneously identifying muscle-tendon parameters. The network is trained by combining an MSE loss on joint angles with two physics-based losses derived from a Hill-type muscle model and forward-dynamics torque balance. Experiments are conducted on a wrist flexion/extension dataset from six subjects, with additional knee data, and the method is compared against LSTM, GRU, CNN, FNN, SVR, and ELM baselines that use labeled muscle forces. The authors claim that the method works with unlabeled sEMG data and achieves comparable or better RMSE/R2 than the baselines.

Significance. If the claims were fully supported, the paper would offer a practically valuable contribution: a physics-informed approach that avoids muscle-force labels, runs in real time, and yields interpretable subject-specific parameters. The paper has genuine strengths: a carefully designed composite loss, a multi-subject wrist experiment with six baselines, additional knee generalization, sensitivity analyses over architectures/hyperparameters, and convergence plots. However, the significance is conditional on resolving two central issues: the method is not label-free as claimed because joint angles are supervised through Eq. (2), and the evaluation is performed against OpenSim CMC ground truth generated from a Hill-type model of the same family as the physics loss, so the reported accuracy may measure self-consistency with a simulation model rather than physiological accuracy.

major comments (4)
  1. [Abstract and Section II-C, Eq. (2)] The paper claims training "without any label information" and "unlabeled sEMG data," but Eq. (2) computes an MSE loss between the predicted and actual joint angles, so measured joint angles are used as supervised labels during training. The claim should be narrowed to "without muscle-force labels"; as written, the label-free claim is internally inconsistent.
  2. [Section III-A and Section II-D, Eqs. (3)-(4), (8)] Ground-truth muscle forces are generated by OpenSim's Computed Muscle Control from a scaled generic Hill-type musculoskeletal model, while the physics losses embed a Hill-model forward dynamics of the same family: Eq. (8) is the same force-length-velocity relationship, and Eqs. (3)-(4) impose the same torque-balance structure. The reported RMSE/R2 values in Tables III-IV therefore quantify agreement with a model-generated target that shares the model class used for regularization, not agreement with independently measured muscle force. Independent validation (e.g., dynamometer joint torques, instrumented implant forces, or a CMC model built with deliberately different muscle parameters) is needed before "effectively predict muscle forces" and "accurately identify" parameters can be claimed.
  3. [Section IV-B, Table II] The "physiological ranges" in Table II are defined relative to the OpenSim initial guesses of Table I (±50% for F_m0 and ±0.01 m for l_m0). Thus, the finding that all identified parameters fall within these ranges is only a boundedness check around the initialization, not evidence of accurate or identifiable subject-specific parameters. Several identified values sit at or effectively on the bounds (FCR F_m0=205.2 N vs. lower bound 203.5 N; ECU F_m0=286.6 N vs. upper bound 288 N), which suggests bound-constrained optimization rather than identifiable estimates. No identifiability analysis or uncertainty quantification is provided.
  4. [Section IV-C, Tables III and IV] The conclusion that the proposed method performs "comparable and even better" than the labeled baselines is based on single point estimates without repeated-seed variability or significance testing. Several individual comparisons favor the baselines (e.g., S5 FCR RMSE 5.41 vs. LSTM 2.75; S6 ECU RMSE 3.97 vs. LSTM 1.23; S2 FCR RMSE 7.01 vs. LSTM 6.15). Aggregate claims need statistical support, such as confidence intervals over random seeds/partitions or paired tests across subject-muscle cells.
minor comments (5)
  1. [Section IV-C, Table IV] The S1 ELM row under ECRB reports R2 = 10.90, which is impossible for a coefficient of determination; this appears to be a typo and should be corrected.
  2. [Tables III and IV] All comparison results are reported as point estimates from a single 70/30 random split; reporting means and standard deviations over multiple splits or seeds would make the comparisons more convincing.
  3. [Section IV-D, Fig. 6] The intrasession (cross-speed) scenario is evaluated only with representative prediction curves; quantitative RMSE/R2 values for this scenario would substantially strengthen the robustness claim.
  4. [Section III-A] The data description does not specify how many trials per subject are used in the main results or whether the reported metrics are averaged over trials or over the two speeds beyond the statement that "the same flexion speed" is used for training and testing; this should be clarified.
  5. [Section II-C] The three loss terms Lq, Lfd, and LF have different physical units (rad^2, N^2 m^2, and N^2) and are summed without explicit weighting; the authors should justify this choice, especially given the small magnitude of Lq noted in Section IV-A.

Circularity Check

2 steps flagged · score 6.0 of 10

Reported validation is self-referential: OpenSim CMC 'ground truth' is generated by the same Hill-type forward-dynamics model embedded in the physics losses, so RMSE/R2 comparisons measure self-consistency with the target-generating model rather than physiological accuracy; parameter identification is checked only against ranges centered on the same initial guesses.

  1. self definitional [Section II-C (Eq. 5), Section II-D (Eq. 8), Section III-A]
    "Section III-A: "The muscle forces calculated by the computed muscle control (CMC) tool from OpenSim were used as ground truths in the experiments." Section II-C: "LF = 1 T Σ T t=1 Σ N n=1 ( ˆF t n − F mt t,n (κn))2" (Eq. 5). Section II-D: "F mt t,n (κn) = (F CE t,n + F P E t,n ) cosφt,n = F m o,n(at,nfv(vt,n)fa(l m t,n) + fp(l m t,n))cosφt,n" (Eq. 8)."

    The OpenSim CMC 'ground truth' is itself a Hill-type musculoskeletal simulation constructed from the same scaled generic model (initialized as in Section II-D, Table I) that supplies the muscle-tendon lengths, moment arms, and Hill force-length-velocity relations used in the physics losses (Eqs. 3, 4, 8). Eq. (5) explicitly drives the network output F̂ toward the Hill-computed force F^mt, so the network is trained to reproduce the same model family that generated the targets. The reported RMSE/R2 therefore quantify self-consistency with the embedded Hill model rather than agreement with independently measured muscle forces; the headline claim of 'comparable or even better' performance is not independent evidence of physiological accuracy.

  2. fitted input called prediction [Section IV-B, Table II]
    "Physiological ranges of the parameters are chosen according to [43]. The ranges of the maximum isometric force F m 0 are set as ±50% of the initial guess, while the ranges of the optimal muscle fiber length lm 0 are set as ±0.01 of the initial guess (Details of the initial guesses of these physiological parameters refer to Table I). The identified physiological parameters by the proposed method are all within the physiological range and possess physiological consistency."

    The 'physiological consistency' criterion is defined around the OpenSim generic-model initial guesses (Table I) that initialize the optimization. Several identified values sit at the edges of these boxes (FCR Fm0=205.2 N vs lower bound 203.5 N; ECU=286.6 N vs upper bound 288 N), indicating bound-constrained fitting. Hence 'within the physiological range' is a boundedness check around the initialization, not an independent measurement of subject-specific muscle-tendon parameters. Calling the result 'physiological consistency' or 'accurate' identification is circular: the fitted parameters are judged by a criterion constructed from their own starting point.

full rationale

The paper's central contribution—muscle-force prediction without muscle-force labels—is evaluated exclusively against OpenSim CMC outputs. CMC is a Hill-type forward-dynamics simulation built from the same scaled generic model whose muscle-tendon lengths, moment arms, and force-length-velocity relations are embedded in the physics losses (Eqs. 3–5, 8). The loss LF directly forces the network output to equal the Hill-computed force, so the network is trained to emulate the same model that produces the ground truth; the RMSE/R2 tables therefore demonstrate self-consistency with the embedded Hill model, not accuracy against measured forces. The 'unlabeled' claim is also overstated: Eq. (2) uses measured joint angles as supervised labels, so 'without any label information' in the abstract is inaccurate (the method avoids muscle-force labels, not all labels). The parameter-identification validation is similarly circular: 'physiological ranges' are centered on the OpenSim initial guesses, and final values at the bounds indicate bound-constrained optimization, so 'within range' is not evidence of subject-specific accuracy. No independent muscle-force measurements or ground-truth muscle-tendon parameters are provided. These issues make the headline claim partially circular (score 6); the engineering framework itself is self-contained and may be useful for reproducing simulator outputs, but the paper overstates physiological validation.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on fitting A and per-muscle F_m0 and l_m0 values to minimize the composite loss. These fitted values are not independently validated against direct physiological measurements, and the ground truth itself is produced by the same class of Hill-based musculoskeletal model. No new physical entities are introduced.

free parameters (3)
  • A (EMG-to-activation coefficient) = -2.29 (example wrist subject)
    Shape factor in Eq. (7), optimized via Eq. (6), reported in Table II.
  • F_m0,n (maximum isometric force per muscle) = FCR 205.2 N, FCU 644.1 N, ECRL 475.2 N, ECRB 166.7 N, ECU 286.6 N (example subject)
    Fitted per-muscle to minimize the composite loss; no independent measurement supports them.
  • l_m0,n (optimal fiber length per muscle) = FCR 0.056 m, FCU 0.061 m, ECRL 0.082 m, ECRB 0.050 m, ECU 0.052 m (example subject)
    Fitted per-muscle to minimize the composite loss; validated only against the physiological range.
assumptions (4)
  • domain assumption Hill muscle model with rigid musculotendon dynamics accurately represents wrist and knee muscle force generation.
    The physics losses L_fd and LF are built on the Hill-based forward dynamics (Eqs. 7-10), and the same model class generates the OpenSim CMC ground truth, so the entire evaluation is model-relative.
  • domain assumption The EMG-to-activation relationship in Eq. (7) with fitted coefficient A is a valid transformation of processed sEMG into muscle activation.
    Activation dynamics is assumed to follow this exponential form; the shape parameter A is fitted rather than measured.
  • domain assumption Moment arms and muscle-tendon lengths are well approximated by polynomial functions exported from OpenSim for the scaled generic model.
    The joint torque in Eq. (4) and muscle fiber length in Eq. (10) rely on moment arms and lengths from OpenSim rather than subject-specific imaging.
  • domain assumption The scaled generic OpenSim model initial parameter set is a valid starting point, and physiological ranges from reference [43] are appropriate for wrist muscles.
    Parameters are initialized by linear scaling of generic values, and the only validation of fitted parameters is checking they fall within ranges from Saul et al.

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Cite this review

Pith. "Pith review of Physics-informed Deep Learning for Muscle Force Prediction with Unlabeled sEMG Signals." pith.science (2026). https://pith.science/paper/XMLELXQ5

@misc{pith2026241204213,
  author       = {Pith},
  title        = {Pith review of: Physics-informed Deep Learning for Muscle Force Prediction with Unlabeled sEMG Signals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XMLELXQ5}},
  note         = {Machine review of arXiv:2412.04213}
}
read the original abstract

Computational biomechanical analysis plays a pivotal role in understanding and improving human movements and physical functions. Although physics-based modeling methods can interpret the dynamic interaction between the neural drive to muscle dynamics and joint kinematics, they suffer from high computational latency. In recent years, data-driven methods have emerged as a promising alternative due to their fast execution speed, but label information is still required during training, which is not easy to acquire in practice. To tackle these issues, this paper presents a novel physics-informed deep learning method to predict muscle forces without any label information during model training. In addition, the proposed method could also identify personalized muscle-tendon parameters. To achieve this, the Hill muscle model-based forward dynamics is embedded into the deep neural network as the additional loss to further regulate the behavior of the deep neural network. Experimental validations on the wrist joint from six healthy subjects are performed, and a fully connected neural network (FNN) is selected to implement the proposed method. The predicted results of muscle forces show comparable or even lower root mean square error (RMSE) and higher coefficient of determination compared with baseline methods, which have to use the labeled surface electromyography (sEMG) signals, and it can also identify muscle-tendon parameters accurately, demonstrating the effectiveness of the proposed physics-informed deep learning method.

Figures

Figures reproduced from arXiv: 2412.04213 by the authors.

Figure 1
Figure 1. Main framework of the proposed method. Inputs to the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Illustration of different loss terms over the number of iterations. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Evolution of the maximum isometric muscle force [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Representative results of the wrist case through the proposed method. The predicted outputs include FCR muscle force, FCU muscle force, ECRL [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Average RMSEs of the included muscle forces across all the subjects [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Comparison results of the proposed method and baseline methods in the intrasession scenario. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Evolution of the maximum isometric muscle force [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Representative results of the knee case of the proposed method. The [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.