EV-PINN: A Physics-Informed Neural Network for Predicting Electric Vehicle Dynamics

Hansol Lim; Jee Won Lee; Jonathan Boyack; Jongseong Brad Choi

REVIEW 3 major objections 5 minor 12 references

EV-PINN: A Physics-Informed Neural Network for Predicting Electric Vehicle Dynamics

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read EV-PINN: a physics-informed neural network predicts EV battery power and energy from only speed and time, while learning mass, drag, and efficiency from real driving logs.

desk verdict EV-PINN does solid empirical power prediction on two real Teslas, but the regenerative-braking term in its physics loss has the wrong sign, which invalidates the advertised parameter estimates. read the letter →

arxiv 2411.14691 v1 pith:QILX4JS6 submitted 2024-11-22 cs.LG

Hansol Lim , Jee Won Lee , Jonathan Boyack , Jongseong Brad Choi This is my paper · ORCID

classification cs.LG

keywords physics-informedneuralnetworkselectricvehiclebatterypowerpredictionenergyconsumptionparameterestimationlongitudinaldynamicsregenerativebrakingRunge-Kuttanetwork

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

EV-PINN claims that a physics-informed neural network can predict an electric vehicle's instantaneous battery power and cumulative energy consumption during cruising using only vehicle speed and time, without voltage or current sensors. The network is constrained by a longitudinal-dynamics ODE for battery power, and training simultaneously fits the logged power while recovering physical parameters such as vehicle mass, aerodynamic drag coefficient, rolling resistance coefficient, motor efficiency, and regenerative braking efficiency. On 15 minutes of Tesla Model 3 Long Range data and 35 minutes of Tesla Model S data, the model reports validation losses on the order of $10^{-3}$ and predicts energy consumption that tracks the ground-truth integration. The authors argue this makes onboard energy prediction and path planning feasible with minimal sensing.

What carries the argument

The central object is the physics-informed loss $\mathcal{L}_{power} = \sum_i \left(\|P_{data}^{(i)} - P_{pred}^{(i)}\|^2 + \lambda \|P_{physics}^{(i)} - P_{pred}^{(i)}\|^2\right)$, where $P_{physics}$ is the output of the governing ODE with learnable parameters. The ODE encodes longitudinal vehicle dynamics: aerodynamic drag, rolling resistance, inertia, and an indicator-based regenerative-braking term that reduces the inertia draw during deceleration below a threshold. Automatic differentiation computes $\frac{dv}{dt}$ from the speed input, letting the network backpropagate through the physics residual. A separate Runge-Kutta neural network, with four subnetworks producing $k_1, k_2, k_3, k_4$, integrates predicted power into cumulative energy via the RK4 update. Parameter initialization from known vehicle specifications helps avoid the local minima introduced by the added physics term.

What would settle it

Run a vehicle with a known weighed mass through a cycle with sustained regenerative braking while logging voltage and current, then compare the model's predicted battery power during deceleration against the measured charging power. If the model systematically underpredicts or sign-reverses the charging during braking, the regenerative-braking term in Eq. (21) is incorrect and the learned parameters are not trustworthy; a simpler check is to compare the fitted mass against the weighed mass, since the paper already reports a 152 kg offset for the Model 3.

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Extended reading notes

Core claim

The paper's central claim is that a single physics-informed neural network, fed only with vehicle speed $v(t)$ and time $t$, can reproduce the battery power trace $P_{battery}$ of a real EV and integrate it into cumulative energy, while learning the governing physical parameters from data. The network is trained against a loss that combines a data term with a physics residual built from the ODE $P_{battery}=\frac{1}{\eta}\left(\frac{1}{2}\rho A C_d v^3 + C_{rr} m g v + m v \frac{dv}{dt}(1-\mu I_{a<\beta})\right)+P_{aux}$, where the indicator term models regenerative braking below a deceleration threshold. Automatic differentiation supplies $\frac{dv}{dt}$, and the parameters $\eta$, $\mu$, $m$, $C_{rr}$, $C_d$ are learned simultaneously with the network weights. The authors report that the fitted parameters land near realistic values (the learned Model 3 mass exceeds curb weight by 152 kg, roughly the weight of two occupants), and that the power and energy predictions closely track the logged ground truth, with validation losses around $2\times10^{-3}$ to $3\times10^{-3}$. They conclude that onboard energy prediction and path planning need only speed and time as sensor inputs.

Load-bearing premise

The load-bearing premise is that the power-dynamics equation (Eq. 21), especially its regenerative-braking term, correctly describes how battery power depends on speed, acceleration, and the physical parameters; if this ODE is wrong, the fitted parameters and the physics constraint lose physical meaning.

Editorial extensions

If this is right

Battery power and cumulative energy can be predicted from speed and time alone, eliminating the need for dedicated voltage and current sensors in energy-management and range-estimation systems.
The simultaneously learned parameters (mass, drag, rolling resistance, motor and regen efficiencies) reflect the actual test conditions, enabling per-vehicle calibration without a dynamometer.
The same architecture and physics constraint achieve low validation loss on two different Tesla models, suggesting the approach generalizes across EV platforms.
Integrating the PINN power output with a Runge-Kutta neural network yields stable cumulative energy predictions from short (15-35 minute) driving logs.
The recovered drag and rolling-resistance coefficients can feed directly into route-level energy path planning.

Reading between the lines

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

If the regenerative-braking term were replaced by one that actually charges the battery during deceleration (the current term only reduces the inertia draw), the same framework could predict net energy flow in one-pedal driving; this is an extension the paper does not make.
The framework could be extended to route planning by making road grade $\theta$ and auxiliary load time-varying inputs, since both already appear in the governing ODE.
Learned parameters could double as fleet diagnostics: a drifting inferred mass or rolling-resistance coefficient might flag added payload, tire-pressure loss, or brake drag without extra sensors.
A controlled comparison against a purely data-driven network on identical logs would isolate how much of the accuracy comes from the physics constraint rather than the network capacity; the paper does not include such a baseline.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

First, what you should know: this is a modest, honest application of PINNs to EV battery power prediction, with genuine OBD2 data from two Teslas and low held-out losses. But the physics term in Eq. (21) treats regenerative braking with the wrong sign, so the learned 'physical parameters' in Table V are not physically meaningful.

What is new and done well: They collect real voltage/current logs, define battery power consistently with Ohm's law, and formulate a PINN that takes (speed, time) and outputs instantaneous power. The RKNN integration for cumulative energy is a clever touch and works better than a plain DNN in their comparison. The held-out validation losses (0.0023 and 0.0034) and the energy traces look credible. The mass estimate of 1975 kg for a Model 3 LR is plausible given the two researchers and cargo, and they acknowledge it.

The load-bearing problem: the regenerative-braking model is wrong. Eq. (20) defines P_regen = -mu m v dv/dt, which is positive during deceleration. In Eq. (21) they replace the inertial term m v a with m v a (1 - mu I). Since a is negative in braking, (1 - mu) m v a is less negative than m v a. So higher mu gives higher battery discharge during braking. That is the opposite of what regen does. The correct form should subtract the regen credit from P_battery, not attenuate the inertial term. Because mu, eta, m, Cd, and Crr are jointly fitted against this operator, the parameters are compensating for the misspecified physics. The power prediction itself is likely still a decent curve fit because the data loss dominates, but the paper's stated contribution—learning real-world parameters—is not supported.

Minor but worth noting: there are no baselines against a physics-free NN or a simple least-squares fit of Eq. (19); no error bars or multiple runs; the generalization claim rests on two short, flat, windless drives; and the related-work discussion omits prior PINN-based EV/battery models. A few references (e.g., [2], [3]) have placeholder-looking DOIs, which suggests incomplete citation checking.

My take: the paper is competent engineering with real data, and the authors are not hiding anything—they even flag the post hoc mass explanation. But the sign error is fatal for the parameter-estimation claim. If the authors fix Eq. (21), add baselines, and validate parameters independently (e.g., weigh the car), this could become a useful contribution. As is, I would not publish it. For peer review, I'd still send it to a referee rather than desk-reject: the error is subtle and the data collection deserves expert eyes, but the expected outcome after review is rejection unless the physics is corrected.

Referee Report

3 major / 5 minor

Summary. The paper presents EV-PINN, a physics-informed neural network that predicts instantaneous battery power and cumulative energy consumption for two Tesla vehicles using only time and vehicle speed as inputs. The network is trained with a combined data and physics loss, where the physics term uses a longitudinal vehicle dynamics model with parameters for motor efficiency, regenerative braking efficiency, mass, rolling resistance, and drag coefficient. The authors report validation losses of 0.002195 and 0.002292 for the Model 3 and Model S, respectively, and provide parameter estimates in Table V. The central claims are that the model achieves high accuracy and generalization and that it can learn physically meaningful vehicle parameters.

Significance. If correct, the approach would be practically interesting: onboard battery-power prediction with minimal sensor inputs and simultaneous estimation of vehicle parameters would be useful for EV energy management and path planning. The paper uses real OBD2 data from two Tesla models, which is a strength, and the architecture and loss construction are described in sufficient detail to be reproducible. However, the central parameter-learning claim is undermined by a sign error in the regenerative-braking physics operator, and the evaluation lacks baselines and uncertainty quantification. The reported parameter values are therefore not established as physical estimates, and the claimed advantage over simpler regression models is not demonstrated.

major comments (3)

[Section III-C, Eq. (21)] The regenerative-braking term in Eq. (21) has a sign error. Eq. (20) defines P_regen = -μ (m v dv/dt) for dv/dt < β, which should be a negative contribution (i.e., energy credit) during deceleration. However, in Eq. (21) the inertial term is multiplied by (1 - μ I_{a<β}), so for a < β the term (1-μ) m v a is less negative than m v a. Equivalently, ∂P_physics/∂μ = -(1/η) m v a > 0 during braking, meaning the model predicts that higher regenerative-braking efficiency increases battery discharge. This is the opposite of the intended physics. Since this operator is used in the physics loss (Eq. 22) and the parameters are jointly optimized against it, the learned values of μ, η, m, C_rr, and C_d in Table V are not physically meaningful; the parameter-estimation claim is therefore unsupported.
[Section IV-B, Table V] The parameters listed as "Predicted Parameters" are not predictions in the usual sense; they are the optimized variables of the loss function (Eq. 22). The "Absolute Error" column compares them against the initial guesses from Eqs. (24) and (25), not against independent ground-truth measurements. The model mass for the Model 3 is rationalized post hoc as the curb weight plus the two researchers and cargo, but no independent weighing or uncertainty analysis is provided. Consequently, the statement that the network "learns real-world parameters" is circular and not validated.
[Section IV-A, Tables II-III and Fig. 9-10] The validation losses are reported without any baseline comparison, error bars, or multiple independent runs. A plain neural network with the same architecture would likely achieve comparable data-loss values because the physics-loss weight is only λ = 0.1, so the claimed superiority of the physics-informed approach is not established. In addition, the paper does not state whether the validation data come from a contiguous segment of the same drive or from separate trips; this matters for the "generalization to dynamics" claim. The evaluation needs comparison against simpler models and a clear description of the train/validation split.

minor comments (5)

[Section I and III-C] There are several typographical errors: "Reated Work" should be "Related Work," and "breaking" in the regenerative-braking discussion should be "braking."
[Section III-C and III-E] Equation numbering is not unique: the initial parameter vectors are Eqs. (24) and (25), and the RK4 update is also Eq. (25). Renumber to avoid ambiguity.
[Section III-E, Eq. (30)] The description of the RKNN loss is unclear: the loss compares E_RK4(t+Δt) with E_pred(t+Δt), but the target value used for E_pred during training is not specified. Clarify whether the target is the measured energy or the RK4 approximation of the logged power.
[Section III-C] The auxiliary power values (≈1100 W and ≈390 W) are stated without uncertainty or a formal estimation procedure; a brief explanation of the "idle state" derivation would improve reproducibility.
[Table V] The column headings "Absolute Error" and "Relative Error" are misleading because the comparison is against the initial guess, not against a ground-truth measurement; this should be stated explicitly in the caption.

Circularity Check

1 steps flagged · score 6.0 of 10

Parameter 'predictions' in Table V are the optimized variables of the loss, so the parameter-learning claim reduces to fitting; power/energy prediction is held-out and independent.

fitted input called prediction [Section IV-A (Table V); Section III-D Eqs. (22)-(23)]
"Tables V and VI show the parameters predicted by the PINN, which align with the log data and converge to realistic values. Interestingly, the predicted mass for the Tesla Model 3 differs by 152 kg from the initial curb weight. It closely matches the combined weight of the two researchers and the cargo during the test drive."

The table's 'Prediction' column is not a network output on held-out data: θ = [η, μ, m, C_rr, C_d] are the trainable scalars in Eq. (21) that the optimizer minimizes via Eq. (22). The abstract's 'learns real-world parameters' is therefore the argmin of the training loss — a fit to the same battery-power log used for the data term. No independent measurement (e.g., weighed mass, bench-tested motor/regen efficiency) validates them; the Model 3 mass discrepancy is explained post hoc by occupant/cargo weight. So the parameter-estimation claim reduces by construction to fitting θ, not to prediction.

full rationale

The paper's power and energy prediction is not circular: the PINN is trained on one portion of the battery-power log and evaluated on held-out validation segments, and the energy comparison is made against a Runge-Kutta integration of the log data, which is an external numerical benchmark. No self-citations are load-bearing; the physics model and optimizer are standard. The circularity lies in the parameter-learning contribution: the 'predicted parameters' in Table V are exactly the trainable variables appearing in Eqs. (21)-(22), so reporting them as 'predictions' reduces to reporting the fitted values of the loss. This is the pattern of a fitted input renamed as a prediction. The independent content of the paper is the power-prediction accuracy, which is why the score is 6 rather than 8. Separately, the regenerative-braking sign issue in Eq. (21) is a correctness concern, not a circularity, and is not counted in this score.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The central claim depends on several fitted parameters that are optimized to minimize the same loss used to evaluate success. The physics model itself is a domain assumption, and the regenerative braking formulation appears physically inconsistent. No new entities are introduced.

free parameters (8)

motor efficiency eta = 0.7349 (Model 3 LR), 0.7248 (Model S)
Optimized in the loss function; initialized from online sources at 0.7.
regenerative braking efficiency mu = 0.6743 (Model 3 LR), 0.7038 (Model S)
Optimized; initial guess 0.5 as it was not available online.
vehicle mass m = 1975 kg (Model 3 LR), 2313 kg (Model S)
Optimized; initialized from Tesla owner's manuals. Model 3 discrepancy explained post hoc by occupant/cargo weight.
rolling resistance coefficient Crr = 0.00915 (Model 3 LR), 0.01100 (Model S)
Optimized; initialized at 0.0096.
drag coefficient Cd = 0.2349 (Model 3 LR), 0.2457 (Model S)
Optimized; initialized at 0.23.
physics loss weight lambda = 0.1
Chosen by hand to balance data and physics losses.
regen deceleration threshold beta = -0.045 m/s^2
Chosen by hand based on the vehicle's deceleration state.
auxiliary power P_aux = 1100 W (Model 3 LR), 390 W (Model S)
Derived from idle state of each vehicle; not independently verified.

assumptions (5)

domain assumption F_motor = eta * (P_battery - P_aux) / v
Assumes constant motor efficiency and linear conversion from electrical power to motor force. Introduced in Eq. (16).
domain assumption Governing ODE in Eq. (21) including regen indicator is correct
The physics loss relies on this ODE. The regen term has a possible sign error, so this assumption is questionable.
domain assumption Road incline theta = 0
Data were collected on flat roads, so gravity terms are omitted from the dynamics.
domain assumption Standard values for air density and frontal area
rho = 1.17 kg/m^3 and A = 2.22 m^2 (Model 3), 2.40 m^2 (Model S) are taken from manuals or common sources, not measured.
domain assumption Train/validation split is representative
The paper does not describe how the split was made, yet uses validation loss as evidence of generalization.

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Cite this review

Pith. "Pith review of EV-PINN: A Physics-Informed Neural Network for Predicting Electric Vehicle Dynamics." pith.science (2026). https://pith.science/paper/QILX4JS6

@misc{pith2026241114691,
  author       = {Pith},
  title        = {Pith review of: EV-PINN: A Physics-Informed Neural Network for Predicting Electric Vehicle Dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QILX4JS6}},
  note         = {Machine review of arXiv:2411.14691}
}

read the original abstract

An onboard prediction of dynamic parameters (e.g. Aerodynamic drag, rolling resistance) enables accurate path planning for EVs. This paper presents EV-PINN, a Physics-Informed Neural Network approach in predicting instantaneous battery power and cumulative energy consumption during cruising while generalizing to the nonlinear dynamics of an EV. Our method learns real-world parameters such as motor efficiency, regenerative braking efficiency, vehicle mass, coefficient of aerodynamic drag, and coefficient of rolling resistance using automatic differentiation based on dynamics and ensures consistency with ground truth vehicle data. EV-PINN was validated using 15 and 35 minutes of in-situ battery log data from the Tesla Model 3 Long Range and Tesla Model S, respectively. With only vehicle speed and time as inputs, our model achieves high accuracy and generalization to dynamics, with validation losses of 0.002195 and 0.002292, respectively. This demonstrates EV-PINN's effectiveness in estimating parameters and predicting battery usage under actual driving conditions without the need for additional sensors.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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Optimization and solution method for electric vehicle charging and discharging load,

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Optimization strategies for real -time energy management of electric vehicles based on LSTM network learning,

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work page doi:10.1016/j.egyr.2022.10.349 2022

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Physics -informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,

M. Raissi, P. Perdikaris, and G. E. Karniadakis, "Physics -informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations," Journal of Computational Physics, vol. 378, 2019, pp. 686-707. DOI: 10.1016/j.jcp.2018.10.045

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Physics Embedded Neural Network Vehicle Model and Applications in Risk -Aware Autonomous Driving Using Latent Features,

T. Kim, H. Lee and W. Lee, "Physics Embedded Neural Network Vehicle Model and Applications in Risk -Aware Autonomous Driving Using Latent Features," 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , Kyoto, Japan, 2022, pp. 4182 -4189, doi: 10.1109/IROS47612.2022.9981303

arXiv 2022