Modelling of Underwater Vehicles using Physics-Informed Neural Networks with Control

Abdelhakim Amer; Andriy Sarabakha; David Felsager; Yury Brodskiy

REVIEW 4 major objections 7 minor 24 references

Modelling of Underwater Vehicles using Physics-Informed Neural Networks with Control

T0 review · 4 major / 7 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Adding a physics-residual loss to a one-step data loss makes a neural network model of an underwater ROV predict long-horizon motion more accurately than a data-only baseline.

desk verdict A useful PINC-for-ROV application with solid ablations and released code, but the generalization claim outruns the experiments: dev/test set initial states are all zero and the physics loss shares the same ODE that generates the data. read the letter →

arxiv 2504.20019 v1 pith:ECQPEJRM submitted 2025-04-28 cs.LG cs.AIcs.RO

Abdelhakim Amer , David Felsager , Yury Brodskiy , Andriy Sarabakha This is my paper · ORCID

classification cs.LGcs.AIcs.RO

keywords physics-informedneuralnetworksunderwatervehicledynamicsROVmodellinglong-horizonpredictionresiduallearninggradientnormalizationmodel-predictivecontrolidentification

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 claims that adding a physics-residual loss to a one-step prediction loss produces a neural-network dynamics model for an underwater remotely operated vehicle (ROV) whose long-horizon predictions stay accurate longer than those of a plain data-driven network. The proposed PINC architecture maps initial state, constant control, and time to the state increment over one sampling interval, so the network is trained both on observed next states and on the residual of the vehicle's approximate equations of motion. In simulation experiments, the best configuration keeps the predicted position within 5 centimetres of the true trajectory for over a second of autoregressive rollout, while the best data-only baseline fails sooner. This matters because cheap, accurate forward models are the bottleneck for model-predictive control of ROVs in inspection, maintenance, and exploration tasks.

What carries the argument

The load-bearing mechanism is the integral-residual parametrization of the network output. Instead of predicting the next state, the network predicts the change $x(T)-x(0)$ over one sampling interval, so its output is an ODE increment and automatic differentiation can compute a physics residual $\dot{x}-f(x,u)$ from it. Two supporting structural choices carry the argument: the yaw angle is re-parameterized as $(\cos\psi,\sin\psi)$ to remove wrap-around discontinuities, and the predicted planar increments are learned in the body frame and rotated into the world frame by the predicted yaw, which offloads the rotational geometry from the network.

What would settle it

Train the same PINC and data-only baseline on trajectories from a real instrumented ROV (or from a much higher-fidelity simulator with thruster dynamics and unmodelled hydrodynamics) and compare their 5 cm valid-prediction times. If the physics-regularized model's advantage shrinks or reverses when the nominal model no longer matches the plant, the reported gain is an artifact of training and testing on the same ODE.

Watch

Extended reading notes

Core claim

The central discovery, as the authors state it, is that the network learns the integral increment of the dynamics rather than the next state directly: $\hat{x}(T) = x(0) + \mathcal{N}([x(0), u(0), T])$, with the control held constant over the interval. Combining the one-step data loss $L_D$ with a physics loss $L_P$ that penalizes $\dot{x} - f(x,u)$ at collocation points inside each sampling interval gives the best valid prediction time under a $0.05$ m position-error threshold. The authors show that the residual/integral parametrization is essential: removing it raises the one-step data loss by more than four orders of magnitude. Their best configuration uses only data and physics losses, softplus activations, layer normalization, gradient normalization with fixed weights, a batch size of 10, and one collocation point per interval; adding a rollout loss does not consistently help once the physics loss is present.

Load-bearing premise

The evaluation assumes that the simplified four-degree-of-freedom marine-craft model in Eq. (1) is the true dynamics of the vehicle, because that same equation generates every synthetic ground-truth trajectory and also defines the physics penalty.

Editorial extensions

If this is right

A trained PINC model can be rolled out autoregressively for more than a second with position error under 5 cm, which is the accuracy regime needed for short-horizon model-predictive control.
Ablating the residual connection increases the one-step data loss by over four orders of magnitude, so any deployment of this method should keep the integral-increment architecture.
The physics loss is doing the main regularization work; the rollout loss adds no consistent benefit and sometimes hurts, so the cheapest effective loss combination is data plus physics only.
Under input noise, the physics-regularized model degrades less than the data-only baseline, suggesting the physics term acts as a regularizer against sensor noise.
Gradient normalization with fixed weights yields better long-horizon validity than the conflict-free gradient method ConFIG on this task, giving practitioners a simple default gradient-combination rule.

Reading between the lines

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

Because the dataset is generated by the same ODE that supplies the physics loss, the reported generalization is consistency with the nominal model, not evidence about real hydrodynamics; a natural next test is PINC on experimental ROV trajectories, which the paper itself lists as future work.
The sin/cos yaw re-parameterization and body-to-world rotation of increments suggest a direct path to full 6-DOF modelling: replace the planar rotation with a quaternion or rotation-matrix increment, keeping the same integral-residual architecture.
Since the model maps (state, control, time) to a differentiable state increment, it can be plugged directly into model-predictive control as the prediction model; a testable extension is measuring closed-loop tracking error with PINC-based MPC against a data-only baseline.
All development and test trajectories start from zero position and velocity, so extrapolation in state space is untested; a stronger evaluation would hold out nonzero initial conditions and compare valid prediction time.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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

Short version: this is an honest engineering application of an existing PINC framework to a simulated ROV, with clean ablations and released code. The central claim holds for the simulated, low-dimensional regime actually tested. But the paper advertises "physically consistent transitions beyond the training domain" while the evaluation only varies sampling interval and input waveform, never the initial state, and the physics loss uses the very same ODE that generated the ground truth. So the reported advantage is real, but narrower than the abstract suggests.

What is genuinely new: the application to underwater ROV dynamics, the ablation showing the residual/integral connection is essential (without it the data loss degrades by orders of magnitude), and the comparison where their gradient-normalization scheme beats ConFIG in this setting. The open-source implementation is a concrete asset; I can verify the central curves if I run the code myself, and that reproducibility is worth credit.

Soft spots, in proportion: the single-seed, no-error-bar protocol is the most serious. Every conclusion in Section V rests on one random draw, and several of the VPT differences between configurations are close enough that I would not trust them without repeated seeds. The all-zero initial states on the development and test sets (Section V-C) mean the "interpolation/extrapolation" tests only vary T and the input waveform; the model is never asked to predict from a nonzero sway velocity or yaw rate, which are identically zero in training. That is a genuine gap, not a nit. The self-referential evaluation is a known limitation of synthetic PINN studies and I would not call it fatal, but it should be stated explicitly: the experiments cannot detect physics bias because the prior is exact in the simulated world. The missing vehicle parameters (mass, added mass, drag coefficients) are annoying but minor; the code presumably has them.

Who this is for: researchers working on physics-informed models for underwater robotics, or anyone wanting a concrete example of loss-term balancing and gradient weighting. It is not a theoretical advance, but it is a solid, honest case study. It deserves a serious referee, not a desk reject, but the revision needs more seeds, varied initial states, and ideally a sensitivity check on the physics parameters.

My advice: send it to peer review. The code and ablations justify referee time, and the evaluation gaps are addressable. If those are fixed, it becomes a useful reference for the subfield.

Referee Report

4 major / 7 minor

Summary. The paper presents PINC, a physics-informed neural network with control for modeling the dynamics of an underwater vehicle in simulation. The model is a residual neural network that maps (initial state, control, time interval) to the next state and is trained with a one-step data loss, a physics residual loss based on a simplified four-DOF Fossen model, and optional initial-condition and rollout losses. The authors ablate architecture choices (network size, residual connection, activation), losses, gradient weighting, collocation points, and input noise, and report that the best configuration uses data+physics losses, gradient normalization, batch size 10, and one collocation point per interval. On a simulated BlueROV2, this configuration yields longer valid prediction times than a no-physics baseline. The implementation is released as open source.

Significance. If the result holds, the paper makes a useful empirical contribution: it shows that a computationally light physics-regularized residual network can produce accurate long-horizon state predictions for a simplified ROV model, and the open-source release is valuable for reproducibility. The strongest parts are the systematic ablation study and the explicit comparison of several gradient-combination schemes. However, the evaluation is narrower than the claimed "beyond training domain" generalization: dev/test initial conditions are all zero, all experiments use a single seed, and the synthetic ground truth is generated by the same ODE that supplies the physics prior. These limitations do not invalidate the in-simulation comparison, but they mean the central claim should be read as applying to rollouts from rest in an exact-physics world.

major comments (4)

[Section V-C (Data and Training Parameters)] The development and test sets fix all initial states except yaw to zero: Section V-C states xmax = ymax = zmax = umax = vmax = wmax = rmax = 0.0. Since the training initial states also satisfy v = r = 0 and w in [0, 0.1] (Section V-A), the interpolation and extrapolation experiments in Eq. (18) vary only the sampling interval T and the input waveform; the paper never evaluates predictions from a nonzero sway velocity, a nonzero yaw rate, or a position outside the training box. The abstract's statement that PINC enables "physically consistent transitions beyond the training domain" is therefore not supported for state-space extrapolation. I request additional development/test sets with nonzero initial states drawn from the training ranges (and ideally outside them), with VPT and rollout errors reported separately for each initial-state scenario.
[Section V-C and Figures 3-6] All experiments are run with a single seed (Section V-C: "All experiments are conducted using a single seed... fixed at 0"). Every comparison is therefore a single realization, and the reported differences -- for example, the choice of NL=4, NH=32 in Fig. 3a and the statement in Section V-G that gradient normalization "consistently outperforms" ConFIG in Fig. 6 -- come without uncertainty quantification. The main quantitative claims should be repeated over at least several seeds and reported as means with standard deviations or confidence intervals, particularly for the PINC-versus-baseline comparison and the gradient-combination comparison.
[Section V-A and Section IV-C2] The synthetic ground-truth trajectories are generated by integrating the same simplified Fossen ODE, Eq. (1), that is used as the physics residual in Eq. (12). This is not classic circularity, because no physical parameter is identified from the data, but it makes the evaluation the most favorable case possible: the physics prior is exactly correct. The reported improvement over the no-physics baseline may therefore not transfer to settings with unmodeled hydrodynamics or model mismatch. The conclusion acknowledges that real-world testing remains; the abstract and Section V-G should be correspondingly qualified, and a sensitivity experiment with perturbed model coefficients would substantially strengthen the claim.
[Section V-F (Input Noise Robustness) and Fig. 5] The "no physics information" baseline used in the noise experiment is not defined in sufficient detail: the paper does not state whether this baseline uses the same residual architecture, layer normalization, loss terms, and gradient weighting as the physics-informed model, and whether it is the same baseline that appears in the final comparisons. Since the central claim is that PINC is better than a non-physics-informed baseline, the baseline configuration must be specified precisely. Also, Section V-F states that the models are evaluated without noise, so the experiment measures robustness of training to noisy inputs, not robustness to noise at prediction time; this should be stated in the text.

minor comments (7)

[Eq. (6)] The nested expression in Eq. (6) is not fully written out: the control inputs for the intermediate autoregressive steps are not explicitly shown, and the ellipsis placement makes the recursion hard to follow. Please write the rollout as \hat{x}_{k+1}(0) = N([\hat{x}_k(0), u_k(0), T]) for k = 0, ..., N-1.
[Eqs. (12), (14), (15)] The symbol N_P is used for both the number of physics collocation points (Eq. (12)) and the number of rollout prediction steps (Eq. (14)); the denominator in Eq. (14) is then inconsistent with the earlier definition. Rename the rollout horizon (e.g., N_pred) and define N_roll before Eq. (15).
[Section V-B and Section V-G] Section V-G says the authors "evaluated the impact of adding extra collocation points, which had previously improved VPTs," but then selects a single collocation point (NP=1) for the best configuration. This is confusing; please clarify whether more collocation points improved VPTs in the final setup and report the NP ablation separately.
[Section V-A / Eq. (2)] After the yaw re-parameterization in Section IV-B3, the state vector is not the eight-dimensional x = [x,y,z,psi,u,v,w,r] of Eq. (1) but includes cos(psi) and sin(psi). The input dimension of the network is never stated explicitly; please define the actual state vector used in Eq. (2) and in the loss functions.
[Remark 5] Remark 5 lists scaling for Y, Mz, and Z but not for X; please state whether the surge force is left unscaled and why.
[Section IV-D] There is a duplicated phrase: "using the three methods following methods for combining gradients."
[Fig. 7] Figure 7 shows a single illustrative rollout with no error bands; adding multiple rollouts or a shaded region would better support the qualitative comparison.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the PINC-vs-baseline comparison is an empirical simulation study, not a derivation that reduces to its inputs.

full rationale

The paper's central claim is an empirical comparison: PINC, trained with one-step data loss and physics residual loss, yields lower long-horizon rollout error than a physics-free baseline on a simulated ROV. This claim is not obtained by fitting a parameter to the test set, nor by renaming a known result as a new contribution. The network map (Eqs. 2 and 8) and the loss definitions (Eqs. 10-15) define a genuine learning problem, and the baseline is trained on the same data without the physics term. The core PINC idea is attributed to external prior work [7], not to the authors' own previous results. Self-citations ([1], [3], [9]) are contextual and are not load-bearing for the main comparison. No uniqueness theorem is imported from the authors, and no ansatz is smuggled in solely through self-citation. The only caveat is that the synthetic ground truth is generated from the same simplified Fossen ODE (Eq. 1) that supplies the physics residual (Eqs. 11-12), making the simulation a favorable and self-consistent benchmark rather than an independent real-world test. The authors explicitly acknowledge this limitation in the conclusion: 'Training PINC models on real-world ROV trajectories would enable more realistic evaluation, potentially revealing limitations not captured in simulation.' This affects external validity and generalization claims, but it does not make the reported PINC-versus-baseline comparison circular. Therefore the appropriate finding is no significant circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The ledger is dominated by hand-selected hyperparameters and the unstated vehicle coefficients. The central result is an empirical comparison, so these are not hidden circular derivations, but they determine whether the reported advantage replicates outside the paper's exact setup.

free parameters (5)

loss weights (w_data, w_roll, w_phy, w_phy_roll, w_ic) = 1.0, 1.0, 0.5, 0.5, 0.5
Chosen by hand in Section V-C and used across experiments; no sensitivity analysis is reported, so the best-configuration result may depend on this hand choice.
gradient clip bound c = 5.0
Set in Section IV-D to avoid large gradient steps; no ablation is shown for this value.
vehicle simulation parameters (mass, inertia, added mass, drag, buoyancy) = not reported in paper
The dynamics in (1) and all synthetic data depend on these values, but they are not listed in the text; reproducibility requires the code or an external source.
network size (NL=4, NH=32) = 4 hidden layers, 32 neurons
Selected from the ablation in Section V-D1 on the development set; this is a model selection choice, not a fitted physical constant.
input scaling constants for Y, Mz, Z = Y*0.1, Mz*0.05, Z*5 (absolute)
Remark 5 in Section V-C; these are hand-designed to keep commands in a plausible range and affect the data distribution.

assumptions (4)

domain assumption Equation (1), the simplified 4-DOF Fossen model with small pitch and roll, accurately describes the BlueROV2 in the tested regime.
Used as both data generator (Section V-A) and physics residual (Section IV-C2); if it is wrong, the physics loss enforces an incorrect model and the simulation does not represent a real vehicle.
domain assumption The control input is constant over each sample interval T (zero-order hold), as stated around Equations (2) and (8).
All collocation and rollout predictions assume this; real thrusters have dynamics that are excluded from the model.
domain assumption Numerically integrated trajectories of the same ODE are treated as ground truth with no sensor noise in the main experiments.
Section V-A; this makes the evaluation a self-consistency check against the nominal model rather than against real vehicle data.
ad hoc to paper A single collocation point per interval (NP=1) is sufficient to enforce the physics loss.
Section V-G selects this based on prior ablations; no formal error bound is provided for the discretization of the residual.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Modelling of Underwater Vehicles using Physics-Informed Neural Networks with Control." pith.science (2026). https://pith.science/paper/ECQPEJRM

@misc{pith2026250420019,
  author       = {Pith},
  title        = {Pith review of: Modelling of Underwater Vehicles using Physics-Informed Neural Networks with Control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ECQPEJRM}},
  note         = {Machine review of arXiv:2504.20019}
}

read the original abstract

Physics-informed neural networks (PINNs) integrate physical laws with data-driven models to improve generalization and sample efficiency. This work introduces an open-source implementation of the Physics-Informed Neural Network with Control (PINC) framework, designed to model the dynamics of an underwater vehicle. Using initial states, control actions, and time inputs, PINC extends PINNs to enable physically consistent transitions beyond the training domain. Various PINC configurations are tested, including differing loss functions, gradient-weighting schemes, and hyperparameters. Validation on a simulated underwater vehicle demonstrates more accurate long-horizon predictions compared to a non-physics-informed baseline

Figures

Figures reproduced from arXiv: 2504.20019 by the authors.

**Figure 2.** PINC model output used to calculate the MSE data loss by comparing [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Overview of architecture experimental results: (a) Neural Network [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Effect of adding rollout loss vs. physics loss on VPT: Incorporating [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 6.** Figure 6: Comparison of PINC models trained with ConFIG and gradient [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: Many-step-ahead prediction position trajectories using the best model [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

24 extracted references · 20 canonical work pages

[1]

Unav-sim: A visually realistic underwater robotics simulator and synthetic data-generation framework,

A. Amer, O. ´Alvarez-Tu˜n´on, H. ˙I. U˘gurlu, J. L. F. Sejersen, Y . Brodskiy, and E. Kayacan, “Unav-sim: A visually realistic underwater robotics simulator and synthetic data-generation framework,” in 2023 21st Inter- national Conference on Advanced Robotics (ICAR) , 2023, pp. 570–576

work page 2023
[2]

Deep sea underwater robotic exploration in the ice-covered arctic ocean with auvs,

C. Kunz, C. Murphy, R. Camilli, H. Singh, J. Bailey, R. Eustice, M. Jakuba, K.-i. Nakamura, C. Roman, T. Sato et al. , “Deep sea underwater robotic exploration in the ice-covered arctic ocean with auvs,” in 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE, 2008, pp. 3654–3660

work page 2008
[3]

Visual tracking nonlinear model predictive control method for autonomous wind turbine inspection,

A. Amer, M. Mehndiratta, J. le Fevre Sejersen, H. X. Pham, and E. Kayacan, “Visual tracking nonlinear model predictive control method for autonomous wind turbine inspection,” in 2023 21st International Conference on Advanced Robotics (ICAR) . IEEE, 2023, pp. 431–438

work page 2023
[4]

Estimation of External Force Acting on Underwater Robots,

S. Lakshminarayanan, D. Duecker, A. Sarabakha, A. Ganguly, L. Takayama, and S. Haddadin, “Estimation of External Force Acting on Underwater Robots,” in 2024 IEEE 20th International Conference on Automation Science and Engineering (CASE) , 2024, pp. 3125–3131

work page 2024
[5]

Physics-informed machine learning,

G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang, “Physics-informed machine learning,” Nature Reviews Physics, vol. 3, no. 6, pp. 422–440, 2021

2021
[6]

Safe physics- informed machine learning for dynamics and control,

J. Drgona, T. X. Nghiem, T. Beckers, M. Fazlyab, E. Mallada, C. Jones, D. Vrabie, S. L. Brunton, and R. Findeisen, “Safe physics- informed machine learning for dynamics and control,” arXiv preprint arXiv:2504.12952, 2025

arXiv 2025
[7]

Physics-Informed Neural Nets for Control of Dynamical Systems,

E. A. Antonelo, E. Camponogara, L. O. Seman, E. R. de Souza, J. P. Jordanou, and J. F. Hubner, “Physics-Informed Neural Nets for Control of Dynamical Systems,” Neurocomputing, vol. 579, Apr. 2024, arXiv:2104.02556 [cs]

arXiv 2024
[8]

S. L. Brunton and J. N. Kutz, Data-Driven Science and Engineering . Cambridge University Press, 2021

work page 2021

Show all 24 references

[9]

Empowering autonomous underwater vehicles using learning-based model predictive control with dynamic forgetting gaussian processes,

A. Amer, M. Mehndiratta, Y . Brodskiy, and E. Kayacan, “Empowering autonomous underwater vehicles using learning-based model predictive control with dynamic forgetting gaussian processes,” IEEE Transactions on Control Systems Technology , 2025

2025
[10]

Adaptive robust control integrated with gaussian processes for quadrotors: Enhanced accuracy, fault tolerance and anti-disturbance,

W. Liang, A. Amer, M. Mehndiratta, Z. Chen, B. Yao, and E. Kay- acan, “Adaptive robust control integrated with gaussian processes for quadrotors: Enhanced accuracy, fault tolerance and anti-disturbance,” IEEE Transactions on Systems, Man, and Cybernetics: Systems , 2025

2025
[11]

A data-driven tracking control framework using physics-informed neural networks and deep reinforcement learning for dynamical systems,

R. Faria, B. Capron, A. Secchi, and M. De Souza, “A data-driven tracking control framework using physics-informed neural networks and deep reinforcement learning for dynamical systems,” Engineering Applications of Artificial Intelligence , vol. 127, Jan. 2024

2024
[12]

Ramp-net: A robust adaptive mpc for quadrotors via physics-informed neural network,

S. Sanyal and K. Roy, “Ramp-net: A robust adaptive mpc for quadrotors via physics-informed neural network,” in 2023 IEEE International Conference on Robotics and Automation (ICRA) . IEEE, 2023, pp. 1019–1025

2023
[13]

Combining physics and deep learning to learn continuous-time dynamics models,

M. Lutter and J. Peters, “Combining physics and deep learning to learn continuous-time dynamics models,” The International Journal of Robotics Research, vol. 42, no. 3, pp. 83–107, Mar. 2023

2023
[14]

Development and Implementation of Physics-Informed Neural ODE for Dynamics Model- ing of a Fixed-Wing Aircraft Under Icing/Fault,

J. Ma, Y . Li, J. Tu, Y . Zhang, J. Ai, and Y . Dong, “Development and Implementation of Physics-Informed Neural ODE for Dynamics Model- ing of a Fixed-Wing Aircraft Under Icing/Fault,” Guidance, Navigation and Control, vol. 04, no. 01, Feb. 2024

2024
[15]

Neural ordinary differential equations,

R. T. Chen, Y . Rubanova, J. Bettencourt, and D. K. Duvenaud, “Neural ordinary differential equations,” Advances in neural information pro- cessing systems, vol. 31, 2018

2018
[16]

Research on Modeling Method of Autonomous Underwater Vehicle Based on a Physics- Informed Neural Network,

Y . Zhao, Z. Hu, W. Du, L. Geng, and Y . Yang, “Research on Modeling Method of Autonomous Underwater Vehicle Based on a Physics- Informed Neural Network,” Journal of Marine Science and Engineering, vol. 12, no. 5, p. 801, May 2024

2024
[17]

Sim-to- Real of Soft Robots with Learned Residual Physics,

J. Gao, M. Y . Michelis, A. Spielberg, and R. K. Katzschmann, “Sim-to- Real of Soft Robots with Learned Residual Physics,” IEEE Robotics and Automation Letters , pp. 1–8, 2024, conference Name: IEEE Robotics and Automation Letters

2024
[18]

Domain-decoupled Physics-informed Neural Networks with Closed- form Gradients for Fast Model Learning of Dynamical Systems,

H. Krauss, T.-L. Habich, M. Bartholdt, T. Seel, and M. Schappler, “Domain-decoupled Physics-informed Neural Networks with Closed- form Gradients for Fast Model Learning of Dynamical Systems,” Aug. 2024

2024
[19]

Physics-Informed Neural Networks with Skip Connections for Model- ing and Control of Gas-Lifted Oil Wells,

J. E. Kittelsen, E. A. Antonelo, E. Camponogara, and L. S. Imsland, “Physics-Informed Neural Networks with Skip Connections for Model- ing and Control of Gas-Lifted Oil Wells,” Applied Soft Computing , vol. 158, p. 111603, Jun. 2024

2024
[20]

ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks,

Q. Liu, M. Chu, and N. Thuerey, “ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks,” Aug. 2024

2024
[21]

Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators,

J. Nicodemus, J. Kneifl, J. Fehr, and B. Unger, “Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators,” IFAC-PapersOnLine, vol. 55, no. 20, pp. 331–336, Jan. 2022

2022
[22]

Handbook of marine craft hydrodynamics and motion control,

T. I. Fossen, “Handbook of marine craft hydrodynamics and motion control,” in Handbook of marine craft hydrodynamics and motion control, 2nd ed. Hoboken, NJ: Wiley, 2021

2021
[23]

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, pp. 686–707, Feb. 2019

2019
[24]

Layer Normalization,

J. L. Ba, J. R. Kiros, and G. E. Hinton, “Layer Normalization,” Jul. 2016

2016

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [1]

Unav-sim: A visually realistic underwater robotics simulator and synthetic data-generation framework,

A. Amer, O. ´Alvarez-Tu˜n´on, H. ˙I. U˘gurlu, J. L. F. Sejersen, Y . Brodskiy, and E. Kayacan, “Unav-sim: A visually realistic underwater robotics simulator and synthetic data-generation framework,” in 2023 21st Inter- national Conference on Advanced Robotics (ICAR) , 2023, pp. 570–576

work page 2023

[2] [2]

Deep sea underwater robotic exploration in the ice-covered arctic ocean with auvs,

C. Kunz, C. Murphy, R. Camilli, H. Singh, J. Bailey, R. Eustice, M. Jakuba, K.-i. Nakamura, C. Roman, T. Sato et al. , “Deep sea underwater robotic exploration in the ice-covered arctic ocean with auvs,” in 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE, 2008, pp. 3654–3660

work page 2008

[3] [3]

Visual tracking nonlinear model predictive control method for autonomous wind turbine inspection,

A. Amer, M. Mehndiratta, J. le Fevre Sejersen, H. X. Pham, and E. Kayacan, “Visual tracking nonlinear model predictive control method for autonomous wind turbine inspection,” in 2023 21st International Conference on Advanced Robotics (ICAR) . IEEE, 2023, pp. 431–438

work page 2023

[4] [4]

Estimation of External Force Acting on Underwater Robots,

S. Lakshminarayanan, D. Duecker, A. Sarabakha, A. Ganguly, L. Takayama, and S. Haddadin, “Estimation of External Force Acting on Underwater Robots,” in 2024 IEEE 20th International Conference on Automation Science and Engineering (CASE) , 2024, pp. 3125–3131

work page 2024

[5] [5]

Physics-informed machine learning,

G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang, “Physics-informed machine learning,” Nature Reviews Physics, vol. 3, no. 6, pp. 422–440, 2021

2021

[6] [6]

Safe physics- informed machine learning for dynamics and control,

J. Drgona, T. X. Nghiem, T. Beckers, M. Fazlyab, E. Mallada, C. Jones, D. Vrabie, S. L. Brunton, and R. Findeisen, “Safe physics- informed machine learning for dynamics and control,” arXiv preprint arXiv:2504.12952, 2025

arXiv 2025

[7] [7]

Physics-Informed Neural Nets for Control of Dynamical Systems,

E. A. Antonelo, E. Camponogara, L. O. Seman, E. R. de Souza, J. P. Jordanou, and J. F. Hubner, “Physics-Informed Neural Nets for Control of Dynamical Systems,” Neurocomputing, vol. 579, Apr. 2024, arXiv:2104.02556 [cs]

arXiv 2024

[8] [8]

S. L. Brunton and J. N. Kutz, Data-Driven Science and Engineering . Cambridge University Press, 2021

work page 2021