Research map / Probabilistic and scientific modeling / Dynamical systems
Stable contractive dynamics
Learns dynamics with stability guarantees through contraction analysis and control-oriented structure.
42 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2017–2026) · an approach in Dynamical systems, keyword cluster “dynamical systems · nonlinear · linear dynamical”
State History Tried Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
9 papers in 2023–24 and 13 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 4.0% to 3.4%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2017 · Learning and Policy Search in Stochastic Dynamical Systems with Bayesian Neural Networks (ICLR 2017 · 52 citations)
- 2018 · Deep Dynamical Modeling and Control of Unsteady Fluid Flows (NeurIPS 2018 · 106 citations)
- 2019 · Learning Stable Deep Dynamics Models (NeurIPS 2019 · 54 citations)
- 2020 · Learning Compositional Koopman Operators for Model-Based Control (ICLR 2020 · 50 citations)
- 2021 · Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systems (NeurIPS 2021 · 2 citations)
- 2022 · Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopes (AAAI 2022 · 33 citations)
- 2023 · Reachability Analysis of Neural Network Control Systems (AAAI 2023 · 11 citations)
- 2024 · Meta-Learning-Based Adaptive Stability Certificates for Dynamical Systems (AAAI 2024 · 4 citations)
- 2025 · Neural Continuous-Time Supermartingale Certificates (AAAI 2025 · 5 citations)
- 2026 · Neural Vector Lyapunov–Razumikhin Certificates for Delayed Interconnected Systems (ICML 2026 · 0 citations)
Earliest papers here
- Learning and Policy Search in Stochastic Dynamical Systems with Bayesian Neural Networks (ICLR 2017 · 52 citations)
- Learning Stable Stochastic Nonlinear Dynamical Systems (ICML 2017 · 16 citations)
- Predictive State Recurrent Neural Networks (NeurIPS 2017 · 15 citations)
What has been tried
29 papers here report 238 measured changes (a component added, removed or swapped, compared with a baseline): helped 66%, no clear effect 9%, hurt 18%, mixed 7%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Add Zubov-guided sampling to two-stage training with domain expansion | Cartpole · Formal success rate | 0 -> 100% | Helped | Two‑Stage Learning of Stabilizing Neural Controllers via Zubov Sampling and Iterative Domain Expansion (NeurIPS 2025 · 1 citation) |
| Remove the negative-definiteness constraint on the Jacobian | LASA-2D · contraction stability | Hurt | Neural Contractive Dynamical Systems (ICLR 2024 · 1 citation) | |
| Make Δ non-selective while retaining selective B and C | Induction-head task · accuracy | 97.35 to 98.3 -> 97.9 to 98.62 | No clear effect | Provable Benefits of Complex Parameterizations for Structured State Space Models (NeurIPS 2024 · 1 citation) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 22 papers; from OpenAlex and the papers' affiliations).
- University of Illinois, Urbana Champaign · 2 papers
Use it
Download BibTeX of 36 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- State-space inference for stochastic systems (104 papers)
- Switching and law-discovery dynamics (81 papers)
Elsewhere in the topic
- Physics-informed dynamics learning (127 papers)
- Latent dynamics models (111 papers)
- Latent-space control and planning (78 papers)
- Synaptic plasticity learning rules (72 papers)
- Latent models of neural activity (70 papers)
- Recurrent circuit models of inference (70 papers)
- Data assimilation from sparse observations (58 papers)
- Stochastic population dynamics (53 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).