Research map / Probabilistic and scientific modeling / Dynamical systems
Learning Deep Dissipative Dynamics
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes a differentiable projection, derived from a general solution of the nonlinear KYP lemma, that forces neural-network dynamics to be dissipative (stable, input-output stable, or energy-conserving) and trains them on time-series data.
Problem
Learning neural-network dynamical systems from time-series data that strictly satisfy dissipativity (generalizing stability, input-output stability and energy conservation), so that predictions remain bounded on out-of-domain inputs.
Approach
Analytically solves the nonlinear KYP lemma matrix equation and derives a differentiable projection mapping any neural dynamics (f,g,h) onto the subspace of dissipative dynamics parameterized by a storage function V and residual map ℓ; training with this projection yields strictly dissipative models by construction.
Key results
- On the mass-spring-damper benchmark with N=100, the energy conservation model achieved RMSE 0.077 on in-domain rectangle test versus 0.250 for the naive model, and 0.046 vs 0.205 on step test inputs.
- On out-of-domain inputs for the n-link pendulum and mass-spring-damper, the naive and stable models diverge on unexpectedly long inputs, while the IO-stable and dissipative models stay bounded.
- For fluid cylinder prediction, the proposed model maintained good accuracy over extended out-of-domain clipped wave inputs, outperforming the naive model in long-term simulation.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Enforce energy conservation rather than use the naive neural model | Mass-spring-damper model trained on Rectangle (N=100) · Rectangle test | RMSE: 0.250 ± 0.184 -> 0.077 ± 0.066 | Helped |
| Enforce energy conservation rather than use the naive neural model | Mass-spring-damper model trained on Rectangle (N=100) · Step test | RMSE: 0.205 ± 0.195 -> 0.046 ± 0.021 | Helped |
| Enforce energy conservation rather than use the naive neural model | Mass-spring-damper model trained on Rectangle (N=100) · Random test | RMSE: 0.049 ± 0.044 -> 0.023 ± 0.031 | Helped |
| Enforce dissipativity rather than use the naive neural model | Mass-spring-damper model trained on Rectangle (N=100) · Rectangle test | RMSE: 0.250 ± 0.184 -> 0.212 ± 0.144 | No clear effect |
| Enforce dissipativity rather than use the naive neural model | Mass-spring-damper model trained on Rectangle (N=100) · Step test | RMSE: 0.205 ± 0.195 -> 0.197 ± 0.147 | No clear effect |
| Enforce dissipativity rather than use the naive neural model | Mass-spring-damper model trained on Rectangle (N=100) · Random test | RMSE: 0.049 ± 0.044 -> 0.040 ± 0.028 | No clear effect |
| Enforce energy conservation rather than use the naive neural model | Mass-spring-damper model trained on Rectangle (N=1000) · Rectangle test | RMSE: 0.029 ± 0.000 -> 0.029 ± 0.000 | No clear effect |
| Enforce energy conservation rather than use the naive neural model | Mass-spring-damper model trained on Rectangle (N=1000) · Step test | RMSE: 0.024 ± 0.000 -> 0.024 ± 0.001 | No clear effect |
| Enforce energy conservation rather than use the naive neural model | Mass-spring-damper model trained on Rectangle (N=1000) · Random test | RMSE: 0.005 ± 0.001 -> 0.006 ± 0.003 | Mixed |
| Enforce dissipativity rather than use the naive neural model | Mass-spring-damper model trained on Rectangle (N=1000) · Rectangle, Step, and Random tests | RMSE: 0.029 ± 0.000 -> 0.060 ± 0.061; 0.024 ± 0.000 -> 0.039 ± 0.029; 0.005 ± 0.001 -> 0.021 ± 0.030 | Hurt |
Surprising findings
- When the training data size increases to 1000, differences between methods become small on in-domain tests, suggesting the dissipative constraint mainly helps with small data.
Limitations
- Requires choosing dissipative hyperparameters (supply rate Q, S, R) based on rough properties of the target system.
- Only the Euler method is used for solving neural ODEs and the projection is restricted to the case without direct feedthrough in many results.
- Non-uniqueness of the projection and dependence on space metric make the projection not canonical.
Experimental setup
Datasets: mass-spring-damper simulated data n-link pendulum simulated data fluid flow around cylinder simulation data
Benchmarks: mass-spring-damper benchmark n-link pendulum benchmark fluid cylinder benchmark
Metrics: RMSE time-averaged RMSE(t)
Baselines: Naive neural ODE Stable projection Input-output stable projection Energy conservation projection
Builds on: nonlinear KYP lemma neural ODE Hamiltonian neural networks
Closest papers by meaning
- Stable Port-Hamiltonian Neural Networks (NeurIPS 2025 · similarity 0.88)
- Neural Contractive Dynamical Systems (ICLR 2024 · similarity 0.86)
- Input-to-State Stable Coupled Oscillator Networks for Closed-form Model-based Control in Latent Space (NeurIPS 2024 · similarity 0.85)
- Physics-Informed Regularization for Domain-Agnostic Dynamical System Modeling (NeurIPS 2024 · similarity 0.85)
- Safely Learning Controlled Stochastic Dynamics (NeurIPS 2025 · similarity 0.85)
- A Riemannian Framework for Learning Reduced-order Lagrangian Dynamics (ICLR 2025 · similarity 0.85)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.