Hybrid Physics-AI Framework of Body Center of Mass Dynamics from Wrist-Worn Sensors

1 Introduction

• COM acceleration is a biomechanical descriptor of dynamic stability and functional mobility, but common gold-standard or pelvis-based measurement options limit daily-life wearability or practicality.The paper identifies the wrist as a widely accepted, commonly worn sensing location.Source: §1 · pp. 2–3
• Wrist-to-COM estimation is ill-posed because different whole-body motions can produce similar wrist signals, making the mapping non-unique and sensitive to noise and distributional variability.Physics-based methods often require many body-worn IMUs, while wrist-only neural estimation had not yet been demonstrated in the described literature.Source: §1 · p. 3
• The proposed HKM-NN framework combines a simplified, reduced-order kinematic model with FCNN or LSTM networks to balance physical interpretability and data-driven adaptability.The kinematic model is designed for locomotor and transitional activities under reductive assumptions.Source: §1 · p. 3
• Serial learning makes the biomechanical model the leading representation, whereas simultaneous learning jointly optimizes the model and network using coupled losses.The two simultaneous variants differ in how strongly the physics model constrains data-driven parameter identification.Source: §1 · p. 4

2.1.1 Noise-free test data

• NN-based and most HKM-NN models had broadly comparable NRMSE and R2 across activities, with no significant difference; sim2 underperformed them and often KM, especially for acceleration magnitude.KM generally showed slightly larger NRMSE and lower R2 than NN-based and HKM-NN models.Source: §2.1.1 · pp. 5–6

2.1.2 Gaussian-noise test data

• As Gaussian SNR falls, all models degrade; sim1 maintains relatively high accuracy with gradual losses, while sim2 has lower accuracy but relatively small changes across SNR conditions.The mechanism behind sim2's lower noise sensitivity could not be determined from these results.Source: §2.1.2 · p. 7, Figure 3 · p. 8

2.1.3 Salt-and-pepper-noise test data

• Most models are less affected by salt-and-pepper than Gaussian noise; KM remains comparatively stable, while FCNN-based models degrade more than their LSTM counterparts.The results suggest temporal modeling contributes to resistance against sparse, abrupt perturbations.Source: §2.1.3 · pp. 8–9, Figure 4 · p. 9

2.2.1 Parameter influence

• The 4-segment KM model-parameter Jacobian rank is mostly 16–20 across training epochs, below full-rank 27, indicating redundancy or collinearity, a phenomenon also common in NN models.Rotation vectors between the forearm and upper arm, upper arm and shoulder, and shoulder and COM, and relative position vectors between the forearm and upper arm and upper arm and shoulder, have the highest output influence. Upper-arm-to-shoulder angular-velocity coupling has relatively low sensitivity and may be weakly identifiable or partially redundant.Source: §2.2.1 · p. 10

2.2.2 Physical interpretation of parameters

• The independently trained KM shows task-dependent rotations, averaging about 41° in natural walking versus about 70–170° in balance- and turn-intensive tasks; position vectors remain around 0.1–0.3 m.Angular-velocity coupling is largest in beam and slalom walking and minimal in sit-to-stand transitions.Source: §2.2.2 · p. 10
• Direct KM supervision in sim1 preserves active physical parameters, while sim2 permits some position and coupling parameters to approach zero, at the cost of consistently interpretable parameterization.Sim1 parameters retain task variation but can deviate from the independently trained KM.Source: §2.2.2 · p. 11

2.3.1 Simultaneous learning approach 1 (sim1-)

• Positive cosine similarity indicates that two loss objectives promote updates in similar directions, whereas negative similarity indicates gradient conflict.Values near zero indicate weak interaction between objectives.Source: §2.3.1 · p. 12
• In sim1-, ∇Lh and ∇Lc remain predominantly aligned, while ∇Lf and ∇Lc fluctuate and sometimes conflict before interactions weaken toward zero for most activities.The fluctuations between the data and coupled losses diminish as training progresses; a few activities retain moderately positive or negative alignment.Source: §2.3.1 · p. 12

2.3.2 Simultaneous learning approach 2 (sim2-)

• In sim2-, ∇Lf and ∇Lc shift from approximately 0.3–0.8 early in training to -0.1 to -0.3 for most activities after about 20–30 epochs.For TW, similarity instead recovers toward zero later in training; sim2- learns the physics branch through interaction with the neural network rather than ground-truth COM supervision.Source: §2.3.2 · p. 13

• Given wrist linear acceleration and angular velocity, the task is to recover COM acceleration through an unknown nonlinear mapping.The mapping is ill-posed because multiple whole-body configurations can produce similar wrist trajectories.Source: §3.1 · p. 14
• A reduced-order kinematic model supplies interpretable biomechanical constraints, while a neural learning operator captures residual or unmodeled nonlinear dynamics.The framework trains the combined operator using physics-consistency and data-fidelity objectives.Source: §3.1 · p. 14
• The kinematic model serves either as a structural prior in ser- or as a soft optimization constraint in sim1- and sim2-.Source: §3.1 · p. 14

3.2.1 Model structure and formulation

• The model represents the forearm, upper arm, shoulder, and COM as four segments, propagating linear acceleration, angular velocity, and angular acceleration between them.The COM is treated as a hypothetical final segment; pelvis or L5 are cited as biomechanical proxies for COM location.Source: §3.2.1 · p. 14
• Because joint angular velocities and accelerations are unmeasured, the model approximates angular-velocity propagation linearly and assumes rigid connections at the elbow and between the upper arm and shoulder.These reductive assumptions limit accuracy but are used because joint measurements are unavailable.Source: §3.2.1 · p. 15
• The four-segment formulation has 27 parameters, including intersegment rotation and position vectors and angular-velocity coupling vectors.The parameter identification procedure uses gradient descent for 125 epochs until convergence.Source: §3.2.1 · p. 16, §3.2.2 · p. 16

3.2.2 KM model identification

• The mechanistic loss combines wrist-to-COM acceleration loss with quaternion loss, which constrains each rotation quaternion to have unit norm.The KM takes wrist IMU data as input and outputs triaxial COM acceleration.Source: §3.2.2 · p. 16

3.2.3 KM model parameter analysis

• Parameter identifiability is assessed using the rank of the parameter-space Jacobian, while output sensitivity is measured using parameter-gradient norms.Source: §3.2.3 · p. 17

• The neural models use either an LSTM or FCNN, trained with Adam at a 0.00005 learning rate, 0.01 weight decay, and batches of 256-point sequences at a 128-point stride.The stateful LSTM updates its hidden and cell states every 2200 data points, corresponding to each measurement duration.Source: §3.3 · p. 17

3.4 Human kinematic model-based neural networks

• The framework combines the kinematic model (KM) with neural networks through serial learning and two simultaneous-learning variants.The approaches are designed to examine how assigning the leading role to the network or physical model changes their interplay.Source: §3.4 · p. 17

3.4.1 Serial learning

• Serial learning trains the KM first, then trains a neural network on the residual between the KM output and reference COM accelerations.The network corrects unmodeled dynamics and structural mismatches rather than replacing the KM’s physical interpretation.Source: §3.4.1 · p. 17

3.4.2 Simultaneous learning

• Sim1 jointly optimizes the network and KM using data, mechanistic, and coupled losses, with the coupled loss weighted by 0.5.The coupled term encourages agreement between KM and network predictions without allowing consistency to dominate optimization.Source: §3.4.2 · p. 19
• Sim2 omits the KM’s direct mechanistic loss and equally weights data and coupled losses, so the KM guides the network as a structural prior.Cosine similarity between data-loss and coupled-loss gradients, and between mechanistic-loss and coupled-loss gradients, is used to assess alignment; positive values indicate cooperation, negative values competition, and zero orthogonality.Source: §3.4.2 · p. 20, §3.4.3 · pp. 20–21

3.5 Dataset and experimental protocol

• Ten healthy volunteers performed six gait activities and sitting down and standing up while wearing a 17-IMU Xsens MVN Link suit.The study used the left-forearm IMU as the wrist measurement and the Xsens Link system’s COM output as reference acceleration.Source: §3.5 · p. 21
• The six gait activities were natural walking, slalom walking, walk-turn-walk, narrow beam, uneven terrain, and upstairs and downstairs walking.The uneven-terrain route included protruding surface locations; the upstairs/downstairs illustration marks a raised platform after ascending.Source: §3.5 · p. 21, Figure 10 · p. 21
• The measurement coordinate axes represent anterior–posterior (x), vertical (y), and medio-lateral (z) directions.The stairs are not explicitly shown in the activity illustration.Source: Figure 10 · p. 21

3.6.1 Evaluation metrics

• NRMSE expresses prediction error as a percentage of signal range, while R2 measures explained variance and Pearson’s r measures linear association.Lower NRMSE indicates better agreement; R2 = 1 is a perfect fit, and r ranges from −1 to +1.Source: §3.6.1 · p. 22

3.6.2 Baseline models for comparison

• The comparison baselines are the KM and pure neural networks: an FCNN with hidden size 16 and an LSTM with hidden size 8.The KM is also the mechanistic component used in the HKM-NN models.Source: §3.6.2 · pp. 22–23

3.6.3 Influence of artificial noise

• Robustness testing injects Gaussian or salt-and-pepper noise into test inputs at SNR values of 2, 4, 6, 8, and 10, while models are trained on clean data.Lower SNR means more severe corruption, making this a test of generalization under a train–test distribution shift.Source: §3.6.3 · p. 23

3.6.4 Statistical test

• Model and activity differences are evaluated with the Friedman test followed by Wilcoxon signed-rank post hoc tests with Bonferroni correction.Both tests are non-parametric and do not require normally distributed data.Source: §3.6.4 · p. 23

4 Discussion

• A single wrist IMU enabled feasible COM-acceleration estimation across multiple gait activities and sit-to-stand, though performance varied by architecture and test-noise type.The complementary limitations of mechanistic and data-driven models motivate balancing physical structure against the risk that its limitations dominate prediction.Source: §4 · pp. 23, 25
• Serial learning makes the KM an explicit physical bottleneck, but perturbations in its output can pass to the downstream NN and limit robustness.ser-FCNN behaves comparatively well under salt-and-pepper noise, while the serial dependency can be a liability under Gaussian noise.Source: §4 · p. 24
• sim1- directly supervises both branches, supporting strong prediction across clean and Gaussian-noise conditions while its jointly learned KM is less interpretable than an independently trained KM.Its physical parameters adapt to the joint objective, so supervision maintains an active physical reference rather than a fixed biomechanical rule.Source: §4 · p. 24
• sim2- can show little additional noise degradation from an already lower baseline, but that stability does not establish robust biomechanical guidance or improved accuracy.The analyses cannot determine whether this behavior reflects parameter rigidity, reduced input sensitivity, or another feature of joint optimization.Source: §4 · pp. 24–25
• Hybridization yields no universal trade-off among accuracy, robustness, and interpretability; each strategy shapes how errors and constraints propagate.sim1- is the most balanced in this study, combining relatively high predictive accuracy, resistance to Gaussian perturbations, and an active but adapted physical branch.Source: §4 · p. 25
• Architecture choice depends on the sensing environment and the physical model’s intended role; sim2- output agreement alone is insufficient to preserve interpretable KM parameters.The authors suggest parameter constraints or identifiability-aware regularization may be needed when physical interpretability is central.Source: §4 · p. 25

5 Conclusions

• A single wrist-worn IMU enabled feasible COM-acceleration estimation across multiple gait activities and the sit-to-stand transition task.The KM provides an interpretable physics-based representation, while neural networks and most HKM-NN models capture nonlinear relationships beyond its simplified formulation.Source: §5 · pp. 25–26
• sim1- achieves higher predictive accuracy and preserves a more active physical parameterization than sim2-, supporting a more effective balance than coupling-only simultaneous learning.The conclusion attributes this balance to direct supervision of the KM branch.Source: §5 · p. 26
• Robustness varies with both hybrid strategy and noise: sim1- performs comparatively well under Gaussian noise, whereas the KM remains comparatively stable under salt-and-pepper noise.The model comparisons also indicate that temporal modeling contributes to resistance against sparse impulsive perturbations.Source: §5 · p. 26
• Accuracy, robustness, and physical interpretability are not automatically improved together; broader activity coverage and better parameter identifiability remain future-work needs.The authors also call for improved biomechanical plausibility and adaptive coupling strategies.Source: §5 · p. 26