Research map / Probabilistic and scientific modeling / Dynamical systems
Switching and law-discovery dynamics
Models multiple dynamical regimes and discovers laws using recurrent switching or invariant models.
81 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Dynamical systems, keyword cluster “dynamical systems · nonlinear · linear dynamical”
State History Tried Checklist 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.
24 papers in 2023–24 and 29 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 10.7% to 7.6%.
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
- 2016 · Understanding City Traffic Dynamics Utilizing Sensor and Textual Observations (AAAI 2016 · 21 citations)
- 2018 · Graph Networks as Learnable Physics Engines for Inference and Control (ICML 2018 · 271 citations)
- 2019 · Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling (ICLR 2019 · 33 citations)
- 2020 · Symplectic Recurrent Neural Networks (ICLR 2020 · 103 citations)
- 2021 · Learning Dynamics Models with Stable Invariant Sets (AAAI 2021 · 11 citations)
- 2022 · iLQR-VAE : control-based learning of input-driven dynamics with applications to neural data (ICLR 2022 · 30 citations)
- 2023 · Geometric Clifford Algebra Networks (ICML 2023 · 10 citations)
- 2024 · Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems (NeurIPS 2024 · 4 citations)
- 2025 · Learning Deep Dissipative Dynamics (AAAI 2025 · 3 citations)
- 2026 · Meta-learning Structure-Preserving Dynamics (ICML 2026 · 1 citation)
Earliest papers here
- Understanding City Traffic Dynamics Utilizing Sensor and Textual Observations (AAAI 2016 · 21 citations)
- Automated Verification and Tightening of Failure Propagation Models (AAAI 2016 · 13 citations)
- Graph Networks as Learnable Physics Engines for Inference and Control (ICML 2018 · 271 citations)
What has been tried
59 papers here report 498 measured changes (a component added, removed or swapped, compared with a baseline): helped 64%, no clear effect 11%, hurt 18%, mixed 6%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Optimize kernel hyperparameters using the partially optimized ELBO rather than standard coordinate-ascent vEM | Synthetic data · decision-boundary estimation accuracy | Helped | Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems (NeurIPS 2024 · 4 citations) | |
| Replace the control-term rate network with two convolutional layers | Hindmarsh-Rose · MSE | 0.783 -> 0.408 | Helped | ControlSynth Neural ODEs: Modeling Dynamical Systems with Guaranteed Convergence (NeurIPS 2024 · 3 citations) |
| add nonlinear behavior decoder (C_z) to input-driven model | Simulation, sinusoidal behavior mapping · behavior decoding CC | 0.8696 vs 0.4558 for linear BRAID | Helped | BRAID: Input-driven Nonlinear Dynamical Modeling of Neural-Behavioral Data (ICLR 2025 · 2 citations) |
| omit the third-order term present in the Duffing equations from the SINDy library | Duffing system · OOD generalization | Hurt | Out-of-Domain Generalization in Dynamical Systems Reconstruction (ICML 2024 · 2 citations) | |
| Add loop closure loss | Dynamical systems · Jacobian estimation accuracy | Helped | Characterizing control between interacting subsystems with deep Jacobian estimation (NeurIPS 2025 · 1 citation) | |
| Increase identifier pool size | MD17 · reconstruction error | Hurt | LaM-SLidE: Latent Space Modeling of Spatial Dynamical Systems via Linked Entities (NeurIPS 2025 · 1 citation) | |
| Use periodic reencoding at inference instead of no reencoding | Pendulum, 100 steps · MSE | 0.0512 -> 0.0042 | Helped | Course Correcting Koopman Representations (ICLR 2024 · 1 citation) |
| Increase the number of PWL units from too few to a sufficient number | Lorenz-63 and Rössler · reconstruction performance | Helped | Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstruction (NeurIPS 2024 · 1 citation) | |
| Use the invariant function rather than the full function for invariant trajectory prediction | ME-Pendulum invariant trajectory (X^c) · NRMSE | 0.7884 -> 0.3561 | Helped | Discovering Physics Laws of Dynamical Systems via Invariant Function Learning (ICML 2025 · 0 citations) |
| increase assumed number of environments M beyond true value | LV, M sweep 1 to 36 · Test MSE and learned label count | learned labels stay in 8-11 range for M from 5 to 36 (true M=9) | No clear effect | Environment Inference for Learning Generalizable Dynamical System (NeurIPS 2025 · 0 citations) |
| remove balance regularization | 2-bit flip-flop, 2D GRU · separatrix identification | Hurt | Finding separatrices of dynamical flows with Deep Koopman Eigenfunctions (NeurIPS 2025 · 0 citations) | |
| Add the Adaptive Spectrum Layer to Seq2Seq | Our dataset test · MAE | 0.1471 -> 0.1323 | Helped | A deep inverse-mapping model for a flapping robotic wing (ICLR 2025 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 21 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Baselines
- NeuralODE · 3 of 21 papers
- LatentODE · 2 of 21 papers
- LFADS · 2 of 21 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 53 papers; from OpenAlex and the papers' affiliations).
- University of Amsterdam · 5 papers
- Massachusetts Institute of Technology · 4 papers
- Ruprecht-Karls-Universität Heidelberg · 3 papers
- Heidelberg University · 3 papers
- University of Oxford · 3 papers
- University of California, Los Angeles · 3 papers
- Stanford University · 3 papers
- University of Cambridge · 2 papers
- Google · 2 papers
- Mila · 2 papers
Use it
Download BibTeX of 40 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)
- Stable contractive dynamics (42 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).