cs.ROSep 23, 2026

Learning Dissipative Dynamics with Dissipativity-by-Construction Discrete-Time Neural Networks

Authors: Tuan Luong, Hyungpil Moon

Organizations: Department of Mechanical Engineering, Sungkyunkwan University, Suwon 16419, South Korea

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Abstract

Dissipativity is a fundamental system-theoretic property closely related to stability, passivity, and input--output stability, and is particularly important in robotics, where learned dynamics models are often embedded within feedback control loops. However, most existing approaches for learning dissipative dynamics are based on continuous-time formulations, which require ODE solvers during training or inference and can therefore be computationally expensive. Moreover, because practical implementations are inherently discrete-time, direct discretization of a continuous-time passive system does not necessarily preserve passivity, motivating the need for explicit discrete-time guarantees. This study proposes a method for learning incrementally dissipative dynamics from input--output time-series data using a deep multilayer perceptron formulated directly in discrete time. Through a constrained parameterization and a dedicated training procedure, the proposed model guarantees incremental dissipativity by construction rather than through regularization. Lyapunov-based analysis establishes the corresponding dissipativity and stability guarantees, while simulations on robotic dynamical systems demonstrate competitive prediction accuracy, computational efficiency, and consistent preservation of incremental dissipativity compared with baseline methods.

Figures & tables

Figure 1: Performance comparison for the mass–spring–damper (MSD) system. (a) Noise-free case, where data from 00 – 10 s10\,\mathrm{s} are used for training and data from 1010 – 20 s20\,\mathrm{s} for testing; an additional disturbed input is used to verify incremental dissipativity. (b) Noisy case with Gaussian training noise (σ=0.3)(\sigma=0.3) , showing that the proposed dissipative network maintains good prediction accuracy and robustness. (c) The standard MLP without dissipativity constraints fails to preserve incremental dissipativity, evaluated using Eq. ( 3 ) with known MSD parameters.
SystemNNNoiseMLPDMLP
MSD100Yes38.9±0.0238.9\pm 0.0214.3±0.0214.3\pm 0.02
No11.1±0.0311.1\pm 0.038.21±0.018.21\pm 0.01
200Yes5.02±0.015.02\pm 0.014.42±0.004.42\pm 0.00
No2.53±0.022.53\pm 0.023.06±0.013.06\pm 0.01
2-DOF100Yes32.80±0.0232.80\pm 0.0215.3±0.0115.3\pm 0.01
No23.2±0.0123.2\pm 0.0114.7±0.0214.7\pm 0.02
Table 1: Mean prediction errors ( ±\pm std) of MLP and DMLP on the MSD, 2-DOF, and 3-DOF systems for different training sizes NN and noise settings.
Figure 2: Training loss histories of the baseline model, the original dissipative network, and the improved dissipative network, demonstrating the effectiveness of the improved training algorithm. (a) MSD system. (b) 2-DOF manipulator. (c) 3-DOF manipulator.
ModelPerformanceMLPDMLPDissipative Neural ODE
MSD (10000 epochs)Mean error2.53±0.02  (×10−2)2.53\pm 0.02\;(\times 10^{-2})3.06±0.01  (×10−2)3.06\pm 0.01\;(\times 10^{-2})0.108±0.030.108\pm 0.03
Computation time403±10403\pm 10 s491.7±5491.7\pm 5 s6.33±0.26.33\pm 0.2 h
2-DOF manipulator (5000 epochs)Mean error6.96±0.02  (×10−2)6.96\pm 0.02\;(\times 10^{-2})11±0.03  (×10−2)11\pm 0.03\;(\times 10^{-2})0.15±0.020.15\pm 0.02
Computation time262±11262\pm 11 s442±8442\pm 8 s4.15±0.54.15\pm 0.5 h
3-DOF manipulator (5000 epochs)Mean error2.44±0.01  (×10−2)2.44\pm 0.01\;(\times 10^{-2})5.79±0.02  (×10−2)5.79\pm 0.02\;(\times 10^{-2})0.10±0.010.10\pm 0.01
Computation time302±15302\pm 15 s525±10525\pm 10 s7.22±0.77.22\pm 0.7 hour
Table 2: Performance comparison between MLP, DMLP, and Dissipative Neural ODE.
Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 3: Comparison of the performance between baseline MLP model and the dissipative model. (a) 2-DOF manipulator without training noise, where data from 0 s0\,\mathrm{s} to 20 s20\,\mathrm{s} were used for training and data from 20 s20\,\mathrm{s} to 40 s40\,\mathrm{s} were used for testing. (b) 3-DOF manipulator without training noise, where data from 0 s0\,\mathrm{s} to 10 s10\,\mathrm{s} were used for training and data from 10 s10\,\mathrm{s} to 20 s20\,\mathrm{s} were used for testing. In both cases, besides the input used in training, a disturbed input signal was also used to check the incremental dissipativity condition of the proposed network.
Ablation casesMSD (10000 epochs)2-DOF manipulator (5000 epochs)3-DOF manipulator (5000 epochs)
Mean error (×10−2)(\times 10^{-2})Training timeMean error (×10−2)(\times 10^{-2})Training timeMean error (×10−2)(\times 10^{-2})Training time
Dissipativity constraintsNo (MLP)2.53±0.022.53\pm 0.02403±10403\pm 10 s6.96±0.026.96\pm 0.02262±11262\pm 11 s2.44±0.012.44\pm 0.01302±15302\pm 15 s
Yes (DMLP)3.06±0.013.06\pm 0.01491.7±5491.7\pm 5 s11±0.0311\pm 0.03423±10423\pm 10 s5.79±0.025.79\pm 0.02525±10525\pm 10 s
Training algorithm (DMLP)Improved3.06±0.013.06\pm 0.01491.7±13491.7\pm 13 s11±0.0311\pm 0.03423±10423\pm 10 s5.79±0.025.79\pm 0.02525±10525\pm 10 s
Original4.98±0.024.98\pm 0.02625±12625\pm 12 s13.4±0.0213.4\pm 0.02472±12472\pm 12 s6.02±0.036.02\pm 0.03578±11578\pm 11 s
Number of layers (DMLP)15.02±0.015.02\pm 0.01500±15500\pm 15 s15.5±0.0115.5\pm 0.01412±13412\pm 13 s7.33±0.027.33\pm 0.02502±13502\pm 13 s
Appendix
Table 3: Ablation study with the number of data samples N=100N=100 .
HyperparameterMSD2-DOF3-DOF
Input size123
Hidden size323232
Output size246
Number of layers222
Activation functiontanhtanhtanh
Appendix
Table 4: Hyperparameters used in the simulation.
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