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arxiv: 2604.18277 · v1 · submitted 2026-04-20 · 💻 cs.LG

Recognition: unknown

Dissipative Latent Residual Physics-Informed Neural Networks for Modeling and Identification of Electromechanical Systems

Youyuan Long , Gokhan Solak , Arash Ajoudani
Authors on Pith no claims yet

Pith reviewed 2026-05-10 04:43 UTC · model grok-4.3

classification 💻 cs.LG
keywords physics-informed neural networksdissipative systemselectromechanical modelingresidual learninglatent statessystem identificationhelicopter dynamicsenergy conservation
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The pith

A residual network restricted to latent states and parameterized in skew-dissipative form guarantees non-increasing energy for any choice of its parameters in physics-informed models of electromechanical systems.

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

First-principles models of electromechanical systems miss many dissipative effects such as friction, stray losses, and structural damping, which causes poor long-term simulation accuracy. Standard residual PINNs add data-driven corrections through unconstrained networks that can inadvertently create artificial energy. The proposed method places the residual correction exclusively on unmeasurable latent state components and enforces a skew-dissipative structure so that energy cannot increase no matter how the network weights are set. A recurrent rollout procedure that gradually lengthens the training sequences allows stable learning when only partial state measurements are available. Experiments on a real helicopter platform show that the resulting model captures dissipation more faithfully and produces better multi-step forecasts than a pure physical model, an unconstrained residual MLP, a soft-constraint variant, or a black-box LSTM.

Core claim

The DiLaR-PINN architecture ensures physical consistency by restricting the residual correction to latent states and parameterizing it in skew-dissipative form, which guarantees non-increasing energy for arbitrary network weights, combined with a curriculum-extended recurrent rollout for stable training under partial state measurability.

What carries the argument

skew-dissipative parameterization of the residual network that operates only on latent state components

If this is right

  • The model captures unmodeled dissipative phenomena such as joint friction and structural damping more accurately than an unconstrained residual network.
  • Long-horizon extrapolation performance improves on real electromechanical systems because artificial energy injection is structurally prevented.
  • Training remains stable and data-efficient even when only a subset of states can be measured.
  • The non-increasing energy property holds for every possible choice of network parameters without requiring additional regularization during optimization.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same latent-only skew-dissipative construction could be applied to other partially observed physical systems where energy balance must be preserved, such as robotic manipulators or vehicle dynamics.
  • Because the residual acts only on hidden states, the learned correction may reveal specific unmeasured phenomena without directly altering the evolution of observed variables.
  • The curriculum rollout strategy might generalize to other physics-constrained sequence learning tasks where initial instability from long unrolled predictions is a problem.

Load-bearing premise

Unmodeled dissipative effects can be captured accurately by a residual network that receives input solely from latent states, and the recurrent rollout with curriculum extension permits stable training from partial measurements.

What would settle it

If closed-loop simulations of the trained model ever exhibit increasing total energy for any parameter values, or if its long-horizon prediction error on held-out helicopter trajectories is no smaller than that of the unstructured residual MLP baseline, the claimed advantages of the latent skew-dissipative structure would be refuted.

Figures

Figures reproduced from arXiv: 2604.18277 by Arash Ajoudani, Gokhan Solak, Youyuan Long.

Figure 1
Figure 1. Figure 1: Overview of the DiLaR-PINN architecture and its learning strategy. The DiLaR-PINN block presents the model structure, which combines a nominal physical model with a structured dissipative residual network as described in Sec. 2.2. The Learning Strategy block illustrates how the unknown parameters of DiLaR-PINN are learned from sampled data using recurrent RK4 rollouts, as detailed in Sec. 2.3. hysteresis, … view at source ↗
Figure 2
Figure 2. Figure 2: Schematic of the fourth-order Runge-Kutta (RK4) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The recurrent RK4 rollout structure for model [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) The physical helicopter setup. (b) Schematic [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: All models predict the system’s 100 s output solely based on the given input [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

Accurate dynamical modeling is essential for simulation and control of embodied systems, yet first-principles models of electromechanical systems often fail to capture complex dissipative effects such as joint friction, stray losses, and structural damping. While residual-learning physics-informed neural networks (PINNs) can effectively augment imperfect first-principles models with data-driven components, the residual terms are typically implemented as unconstrained multilayer perceptrons (MLPs), which may inadvertently inject artificial energy into the system. To more faithfully model the dissipative dynamics, we propose DiLaR-PINN, a dissipative latent residual PINN designed to learn unmodeled dissipative effects in a physically consistent manner. Structurally, the residual network operates only on unmeasurable (latent) state components and is parameterized in a skew-dissipative form that guarantees non-increasing energy for any choice of network parameters. To enable stable and data-efficient training under partial measurability of the state, we further develop a recurrent rollout scheme with a curriculum-based sequence length extension strategy. We validate DiLaR-PINN on a real-world helicopter system and compare it against four baselines: a pure physical model (without a residual network), an unstructured residual MLP, a DiLaR variant with a soft dissipativity constraint, and a black-box LSTM. The results demonstrate that DiLaR-PINN more accurately captures dissipative effects and achieves superior long-horizon extrapolation performance.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces DiLaR-PINN, a physics-informed neural network for modeling electromechanical systems that augments imperfect first-principles models with a residual term. The residual network acts exclusively on latent (unmeasurable) states and is parameterized in a skew-dissipative form that structurally guarantees non-increasing energy for any choice of network weights. Training stability under partial observability is achieved via a recurrent rollout scheme combined with curriculum-based extension of sequence length. The approach is validated on a real helicopter system, where it outperforms a pure physical model, an unstructured residual MLP, a soft-constraint DiLaR variant, and a black-box LSTM in capturing dissipative effects and long-horizon extrapolation accuracy.

Significance. If the empirical results hold, the work offers a principled structural solution to the problem of artificial energy injection in residual PINNs, which is relevant for stable long-term simulation and control of physical systems. The fact that the dissipativity guarantee is independent of the data-fitting process (as confirmed by the low circularity score) is a clear methodological strength. Real-world validation on a helicopter system provides a concrete test case for embodied systems modeling.

major comments (2)
  1. The methods section describing the skew-dissipative parameterization: while the abstract states that the form guarantees non-increasing energy for arbitrary parameters, the explicit layer construction (e.g., how the power-port term is rendered non-positive) must be given with equations so that readers can verify the claim and reproduce the architecture.
  2. Experiments section on the helicopter system: the superiority claim over the four baselines requires tabulated quantitative metrics (e.g., RMSE or energy-error over multi-step rollouts) with error bars or statistical tests; without these, it is difficult to assess whether the dissipativity structure actually improves real-world behavior beyond the unstructured residual MLP.
minor comments (2)
  1. Abstract: the list of baselines is clear, but the main text should explicitly number them (e.g., Baseline 1: pure physical model) for easy cross-reference in the results tables.
  2. Notation: define the latent-state vector and the precise form of the dissipation inequality (power-port term) at first use to avoid ambiguity when the recurrent rollout is introduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation for minor revision. We appreciate the recognition of the methodological contributions, particularly the structural dissipativity guarantee. We address each major comment below and will incorporate the suggested improvements in the revised manuscript.

read point-by-point responses

  1. Referee: The methods section describing the skew-dissipative parameterization: while the abstract states that the form guarantees non-increasing energy for arbitrary parameters, the explicit layer construction (e.g., how the power-port term is rendered non-positive) must be given with equations so that readers can verify the claim and reproduce the architecture.

    Authors: We agree that the explicit layer construction should be provided in full detail to support verification and reproducibility. In the revised manuscript, we will expand the methods section with the complete equations for the skew-dissipative parameterization. This will include the decomposition into skew-symmetric and dissipative components, the explicit form of the power-port term, and the proof that it remains non-positive for arbitrary weights, thereby guaranteeing non-increasing energy independently of the data-fitting process. revision: yes

  2. Referee: Experiments section on the helicopter system: the superiority claim over the four baselines requires tabulated quantitative metrics (e.g., RMSE or energy-error over multi-step rollouts) with error bars or statistical tests; without these, it is difficult to assess whether the dissipativity structure actually improves real-world behavior beyond the unstructured residual MLP.

    Authors: We acknowledge that tabulated quantitative metrics with variability measures would strengthen the presentation of the empirical results. Although the current manuscript demonstrates the advantages through rollout figures and energy plots, we will add a dedicated table in the revised experiments section. This table will report RMSE and energy-error values for multi-step predictions across all baselines (including the unstructured residual MLP), with means and standard deviations computed over multiple independent runs to enable statistical assessment of the improvements due to the dissipativity structure. revision: yes

Circularity Check

0 steps flagged

No significant circularity; structural guarantee is by design

full rationale

The paper's core claim is that a deliberately chosen skew-dissipative parameterization of the latent residual network enforces non-increasing energy for arbitrary parameters. This is a mathematical property of the architecture itself, not a quantity fitted from data or reduced to prior self-citations. The recurrent rollout and curriculum strategy are training heuristics that do not alter the dissipativity guarantee. No load-bearing step equates a prediction to its own inputs by construction, nor does any uniqueness theorem or ansatz collapse into self-reference. The derivation remains self-contained against external benchmarks such as the helicopter validation and baseline comparisons.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

Limited information from abstract; the claim depends on the mathematical properties of the skew-dissipative form and assumptions about latent states and training stability.

free parameters (1)
  • Curriculum sequence length extension parameters
    The strategy for extending sequence length during training is mentioned but no specific values or fitting process detailed in abstract.
axioms (2)
  • standard math Skew-dissipative parameterization ensures non-increasing energy for any network parameters
    Relies on properties of skew-symmetric and dissipative matrix structures in dynamical systems modeling.
  • domain assumption Unmodeled effects reside only in latent unmeasurable states
    Assumes first-principles model captures all measurable dynamics and residuals apply only to hidden components.
invented entities (1)
  • DiLaR-PINN with skew-dissipative latent residual no independent evidence
    purpose: To enforce physical dissipativity in residual learning for electromechanical systems
    New architecture combining latent operation and structural constraint introduced to address energy injection issue.

pith-pipeline@v0.9.0 · 5556 in / 1544 out tokens · 67200 ms · 2026-05-10T04:43:20.764760+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

48 extracted references · 6 canonical work pages

  1. [1]

    arXiv preprint arXiv:1907.04490 , year=

    Deep lagrangian networks: Using physics as model prior for deep learning , author=. arXiv preprint arXiv:1907.04490 , year=

    work page arXiv 1907

  2. [2]

    International journal of control , volume=

    Non-linear system identification using neural networks , author=. International journal of control , volume=. 1990 , publisher=

    1990

  3. [3]

    Automatica , volume=

    Deep networks for system identification: a survey , author=. Automatica , volume=. 2025 , publisher=

    2025

  4. [4]

    IEEE transactions on control systems technology , volume=

    Application of feedforward neural networks to dynamical system identification and control , author=. IEEE transactions on control systems technology , volume=. 1993 , publisher=

    1993

  5. [5]

    nature , volume=

    Learning representations by back-propagating errors , author=. nature , volume=. 1986 , publisher=

    1986

  6. [6]

    Neural Computation MIT-Press , year=

    Long Short-term Memory , author=. Neural Computation MIT-Press , year=

  7. [7]

    Advances in Neural Information Processing Systems , year=

    Attention is all you need , author=. Advances in Neural Information Processing Systems , year=

  8. [8]

    IFAC-PapersOnLine , volume=

    Deep state space models for nonlinear system identification , author=. IFAC-PapersOnLine , volume=. 2021 , publisher=

    2021

  9. [9]

    Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data

    Deep variational bayes filters: Unsupervised learning of state space models from raw data , author=. arXiv preprint arXiv:1605.06432 , year=

    work page Pith review arXiv

  10. [10]

    IFAC-PapersOnLine , volume=

    Deep learning and system identification , author=. IFAC-PapersOnLine , volume=. 2020 , publisher=

    2020

  11. [11]

    Advances in neural information processing systems , volume=

    Embed to control: A locally linear latent dynamics model for control from raw images , author=. Advances in neural information processing systems , volume=

  12. [12]

    IEEE Transactions on Power Systems , volume=

    Applications of physics-informed neural networks in power systems-a review , author=. IEEE Transactions on Power Systems , volume=. 2022 , publisher=

    2022

  13. [13]

    Journal of Computational physics , volume=

    Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations , author=. Journal of Computational physics , volume=. 2019 , publisher=

    2019

  14. [14]

    Thin-Walled Structures , pages=

    Physics-informed Neural Networks (PINN) for computational solid mechanics: Numerical frameworks and applications , author=. Thin-Walled Structures , pages=. 2024 , publisher=

    2024

  15. [15]

    AI , volume=

    Understanding physics-informed neural networks: techniques, applications, trends, and challenges , author=. AI , volume=. 2024 , publisher=

    2024

  16. [16]

    Advances in neural information processing systems , volume=

    Hamiltonian neural networks , author=. Advances in neural information processing systems , volume=

  17. [17]

    Robotics and Autonomous Systems , volume=

    Physics-informed Neural Network for Quadrotor Dynamical Modeling , author=. Robotics and Autonomous Systems , volume=. 2024 , publisher=

    2024

  18. [18]

    2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , pages=

    PINN-Ray: A Physics-Informed Neural Network to Model Soft Robotic Fin Ray Fingers , author=. 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , pages=. 2024 , organization=

    2024

  19. [19]

    IEEE Robotics and Automation Letters , volume=

    Physics-informed recurrent neural networks for soft pneumatic actuators , author=. IEEE Robotics and Automation Letters , volume=. 2022 , publisher=

    2022

  20. [20]

    2024 IEEE International Conference on Robotics and Automation (ICRA) , pages=

    Physics-Informed Neural Networks for Continuum Robots: Towards Fast Approximation of Static Cosserat Rod Theory , author=. 2024 IEEE International Conference on Robotics and Automation (ICRA) , pages=. 2024 , organization=

    2024

  21. [21]

    2024 IEEE-RAS 23rd International Conference on Humanoid Robots (Humanoids) , pages=

    Physics-Informed Learning for the Friction Modeling of High-Ratio Harmonic Drives , author=. 2024 IEEE-RAS 23rd International Conference on Humanoid Robots (Humanoids) , pages=. 2024 , organization=

    2024

  22. [22]

    2024 IEEE International Conference on Advanced Intelligent Mechatronics (AIM) , pages=

    Research on Parameter Identification Method for Robotic Manipulators Joint Friction Model Based on PINN , author=. 2024 IEEE International Conference on Advanced Intelligent Mechatronics (AIM) , pages=. 2024 , organization=

    2024

  23. [23]

    IEEE Transactions on Industrial Electronics , year=

    A PINN-Based Friction-Inclusive Dynamics Modeling Method for Industrial Robots , author=. IEEE Transactions on Industrial Electronics , year=

  24. [24]

    Nonlinear Dynamics , volume=

    Parameter estimation and modeling of nonlinear dynamical systems based on Runge--Kutta physics-informed neural network , author=. Nonlinear Dynamics , volume=. 2023 , publisher=

    2023

  25. [25]

    Physics-informed Neural Networks for Robot Motion under Constraints , author=

  26. [26]

    , month = mar, year =

    Physics-informed Neural Motion Planning on Constraint Manifolds , author=. arXiv preprint arXiv:2403.05765 , year=

    work page arXiv

  27. [27]

    2017 IEEE-RAS 17th international conference on humanoid robotics (Humanoids) , pages=

    First-order-principles-based constructive network topologies: An application to robot inverse dynamics , author=. 2017 IEEE-RAS 17th international conference on humanoid robotics (Humanoids) , pages=. 2017 , organization=

    2017

  28. [28]

    IEEE Robotics and Automation Letters , year=

    Physics-Informed Neural Network for Model Prediction and Dynamics Parameter Identification of Collaborative Robot Joints , author=. IEEE Robotics and Automation Letters , year=

  29. [29]

    Lagrangian neural networks.arXiv:2003.04630,

    Lagrangian neural networks , author=. arXiv preprint arXiv:2003.04630 , year=

    work page arXiv 2003

  30. [30]

    Електромагнітна сумісність та безпека на залізничному транспорті , number=

    Modeling of electromechanical systems , author=. Електромагнітна сумісність та безпека на залізничному транспорті , number=

  31. [31]

    Automatica , volume=

    Closed-loop identification revisited , author=. Automatica , volume=. 1999 , publisher=

    1999

  32. [32]

    2012 , publisher=

    Subspace identification for linear systems: Theory—Implementation—Applications , author=. 2012 , publisher=

    2012

  33. [33]

    1998 , publisher=

    System Identification: Theory for the User , author=. 1998 , publisher=

    1998

  34. [34]

    2024 7th Iberian Robotics Conference (ROBOT) , pages=

    Robot Modeling With Autoregressive Transformers , author=. 2024 7th Iberian Robotics Conference (ROBOT) , pages=. 2024 , organization=

    2024

  35. [35]

    IEEE Access , volume=

    Deep learning aided dynamic parameter identification of 6-DOF robot manipulators , author=. IEEE Access , volume=. 2020 , publisher=

    2020

  36. [36]

    IEEE Sensors Journal , year=

    Errors in Radiation Temperature Measurement Methods for Aero-Engine Turbine Blades: A Review , author=. IEEE Sensors Journal , year=

  37. [37]

    arXiv preprint arXiv:1902.08705 , year=

    A general framework for structured learning of mechanical systems , author=. arXiv preprint arXiv:1902.08705 , year=

    work page arXiv 1902

  38. [38]

    Micromachines , volume=

    Thermo-mechanical fluid--structure interaction numerical modelling and experimental validation of MEMS electrothermal actuators for aqueous biomedical applications , author=. Micromachines , volume=. 2023 , publisher=

    2023

  39. [39]

    Mechanism and Machine Theory , volume=

    A new iterative identification algorithm for estimating the LuGre friction model parameters , author=. Mechanism and Machine Theory , volume=. 2024 , publisher=

    2024

  40. [40]

    2011 50th IEEE Conference on Decision and Control and European Control Conference , pages=

    Dissipativity of general Duhem hysteresis models , author=. 2011 50th IEEE Conference on Decision and Control and European Control Conference , pages=. 2011 , organization=

    2011

  41. [41]

    2009 , publisher=

    Modeling and control of complex physical systems: the port-Hamiltonian approach , author=. 2009 , publisher=

    2009

  42. [42]

    Universal differential equations for scientific machine learning.arXiv preprint arXiv:2001.04385, 2020

    Universal differential equations for scientific machine learning , author=. arXiv preprint arXiv:2001.04385 , year=

    work page arXiv 2001

  43. [43]

    International conference on machine learning , pages=

    Lyanet: A lyapunov framework for training neural odes , author=. International conference on machine learning , pages=. 2022 , organization=

    2022

  44. [44]

    IFAC-PapersOnLine , volume=

    Modeling system dynamics with physics-informed neural networks based on Lagrangian mechanics , author=. IFAC-PapersOnLine , volume=. 2020 , publisher=

    2020

  45. [45]

    Adaptive control of nonsmooth dynamic systems , pages=

    Adaptive friction compensation for servo mechanisms , author=. Adaptive control of nonsmooth dynamic systems , pages=. 2001 , publisher=

    2001

  46. [46]

    Journal of Manufacturing and Materials Processing , volume=

    Accuracy Optimization of Robotic Machining Using Grey-Box Modeling and Simulation Planning Assistance , author=. Journal of Manufacturing and Materials Processing , volume=. 2025 , publisher=

    2025

  47. [47]

    International Journal on Technical and Physical Problems of Engineering (IJTPE) , volume=

    Design and performance analysis of a three winding transformer used in solar system , author=. International Journal on Technical and Physical Problems of Engineering (IJTPE) , volume=

  48. [48]

    Ocean Engineering , volume=

    An investigation on internal damping behavior of fiber rope , author=. Ocean Engineering , volume=. 2019 , publisher=

    2019