Research map / Probabilistic and scientific modeling / Dynamical systems
State-space inference for stochastic systems
Learns filters and amortized inference for nonlinear stochastic dynamical systems.
104 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.
25 papers in 2023–24 and 42 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic held steady, from 11.1% to 10.9%.
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 · Poisson-Gamma dynamical systems (NeurIPS 2016 · 26 citations)
- 2017 · Scalable Variational Inference for Dynamical Systems (NeurIPS 2017 · 9 citations)
- 2018 · Group Sparse Bayesian Learning for Active Surveillance on Epidemic Dynamics (AAAI 2018 · 27 citations)
- 2019 · A Dynamical Systems Perspective on Nesterov Acceleration (ICML 2019 · 49 citations)
- 2020 · Collapsed Amortized Variational Inference for Switching Nonlinear Dynamical Systems (ICML 2020 · 11 citations)
- 2021 · Bayesian Dynamic Mode Decomposition with Variational Matrix Factorization (AAAI 2021 · 6 citations)
- 2022 · Constrained Physical-Statistics Models for Dynamical System Identification and Prediction (ICLR 2022 · 6 citations)
- 2023 · Score-based Data Assimilation (NeurIPS 2023 · 13 citations)
- 2024 · ODEFormer: Symbolic Regression of Dynamical Systems with Transformers (ICLR 2024 · 6 citations)
- 2025 · Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximations (ICLR 2025 · 1 citation)
- 2026 · Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systems (ICLR 2026 · 1 citation)
Earliest papers here
- Poisson-Gamma dynamical systems (NeurIPS 2016 · 26 citations)
- Sparse Coding and Dictionary Learning With Linear Dynamical Systems (CVPR 2016 · 25 citations)
- Learning to Filter with Predictive State Inference Machines (ICML 2016 · 14 citations)
What has been tried
71 papers here report 628 measured changes (a component added, removed or swapped, compared with a baseline): helped 69%, no clear effect 9%, hurt 18%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Increase system dimensionality | Synthetic data · accuracy | Hurt | ODEFormer: Symbolic Regression of Dynamical Systems with Transformers (ICLR 2024 · 6 citations) | |
| Set β=0.0 instead of β=0.01 | Power Plant · RMSE | 0.02 -> 18.2 | Hurt | Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximations (ICLR 2025 · 1 citation) |
| Use ground-truth-to-reverse-trajectory loss instead of forward/reverse alignment | Simple Spring, multi-agent · MSE (10^-2) | 1.1178 -> 1.1313 | Hurt | Physics-Informed Regularization for Domain-Agnostic Dynamical System Modeling (NeurIPS 2024 · 1 citation) |
| Vary hidden layers from 1 to 4 and neurons per layer from 250 to 350 | Pendulum · spectral approximation | Mixed | ResKoopNet: Learning Koopman Representations for Complex Dynamics with Spectral Residuals (ICML 2025 · 0 citations) | |
| add observation history (C>0) rather than use no history | Lorenz 96 (n_s=40) · NRMSE (%) | 11.7 ± 3.4 -> 9.3 ± 2.8 | Helped | Tensor-Var: Efficient Four-Dimensional Variational Data Assimilation (ICML 2025 · 0 citations) |
| add global sparsity constraint | VN SP 30 · AUROC | 92.76% to 96.90% | Helped | Guided Structural Inference: Leveraging Priors with Soft Gating Mechanisms (ICML 2025 · 0 citations) |
| Restrict the multiscale scheme to the same 3-step past horizon as autoregressive inference | Synthetic sinusoidal series · Wasserstein distance | 0.021 -> 0.08 | Hurt | Predicting partially observable dynamical systems via diffusion models with a multiscale inference scheme (NeurIPS 2025 · 0 citations) |
| Increase matched moment order from r=2 (BLUE) to r=4 | N=5 measurements · covariance | 3.26e^{-1} -> 1.87e^{-1} | Helped | Max Entropy Moment Kalman Filter for Polynomial Systems with Arbitrary Noise (NeurIPS 2025 · 0 citations) |
| Use parallel rather than sequential natural-to-mean conversion | LDS with Gaussian observations, single trials · runtime | roughly 100 \times faster for T = 4096 | Helped | SING: SDE Inference via Natural Gradients (NeurIPS 2025 · 0 citations) |
| add sequential nesting | Chignolin 300 K, low-rank (k=16), H=64, B=384 · VAMP-E | 10.27 -> 12.29 | Helped | Efficient Parametric SVD of Koopman Operator for Stochastic Dynamical Systems (NeurIPS 2025 · 0 citations) |
| Use fast selection rather than top-k selection for mask binarization | Bio-CDL and physics system sequences · prediction error | Helped | Learning system dynamics without forgetting (ICLR 2025 · 0 citations) | |
| Increase latent dimension | SWE, 225x spatial data reduction · relative RMSE | Helped | Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data (ICLR 2025 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 28 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- ERA5 · 2 of 28 papers
- Lorenz system (simulated) · 2 of 28 papers
Baselines
- EDMD · 2 of 28 papers
- EDMD-DL · 2 of 28 papers
- SDE Matching · 2 of 28 papers
- iVAE · 2 of 28 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 67 papers; from OpenAlex and the papers' affiliations).
- Stanford University · 5 papers
- University of Luxembourg · 4 papers
- Massachusetts Institute of Technology · 3 papers
- University of Illinois, Urbana Champaign · 2 papers
- Swiss Federal Institute of Technology Lausanne · 2 papers
- EPFL · 2 papers
- Istituto Italiano di Tecnologia · 2 papers
- University College London · 2 papers
- Carnegie Mellon University · 2 papers
- University of Michigan - Ann Arbor · 2 papers
Use it
Download BibTeX of 39 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Switching and law-discovery dynamics (81 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).