Research map / Probabilistic and scientific modeling / Dynamical systems
Stochastic population dynamics
Learns stochastic dynamics from samples with action matching and mean-field models.
53 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2020–2026) · an approach in Dynamical systems, keyword cluster “physical · physics · simulation”
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.
9 papers in 2023–24 and 40 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 4.0% to 10.4%.
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
- 2020 · TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics (ICML 2020 · 44 citations)
- 2021 · An Extensible Benchmark Suite for Learning to Simulate Physical Systems (NeurIPS 2021 · 3 citations)
- 2022 · Variational Mixtures of ODEs for Inferring Cellular Gene Expression Dynamics (ICML 2022 · 7 citations)
- 2023 · Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamics (NeurIPS 2023 · 20 citations)
- 2024 · From Biased to Unbiased Dynamics: An Infinitesimal Generator Approach (NeurIPS 2024 · 3 citations)
- 2025 · Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models (NeurIPS 2025 · 4 citations)
- 2026 · Constrained hybrid modelling to predict microbial dynamics and organic matter turnover in soil systems (ICML 2026 · 1 citation)
Earliest papers here
- TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics (ICML 2020 · 44 citations)
- JAX MD: A Framework for Differentiable Physics (NeurIPS 2020)
- An Extensible Benchmark Suite for Learning to Simulate Physical Systems (NeurIPS 2021 · 3 citations)
What has been tried
27 papers here report 223 measured changes (a component added, removed or swapped, compared with a baseline): helped 61%, no clear effect 10%, hurt 21%, mixed 9%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| use three conservative diffusion experts instead of one Diffusion model | Alanine dipeptide (sim) · JS divergence | 0.0695 ± 0.0517 -> 0.0264 ± 0.0085 | Helped | Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models (NeurIPS 2025 · 4 citations) |
| add energy conservation enforcement | Liquid water, NVT · overall effective-temperature deviation (ΔT_all) | 33.8\U{1.0} -> 0.2\U{0.8}; 10.7\U{1.0} -> -0.7\U{0.8}; -22.5\U{0.7} -> 0.4\U{0.9} | Helped | FlashMD: long-stride, universal prediction of molecular dynamics (NeurIPS 2025 · 2 citations) |
| add biology-informed closure to the Neural Hamiltonian | Cellular MNIST · p_volume | 0.11 -> 1.00 | Helped | Deep Neural Cellular Potts Models (ICML 2025 · 1 citation) |
| Add noise alignment (M1) | Molecular density OOD · relative-error standard deviation σ | 5.06±4E-3 -> 2.32±3E-3 | Helped | Dynamic Diffusion Schrödinger Bridge in Astrophysical Observational Inversions (NeurIPS 2025 · 1 citation) |
| vary the GCN neighbor count k | Synthetic letters unseen test populations · W1 | 0.202 ± 0.002; 0.205 ± 0.008; 0.201 ± 0.006; 0.206 ± 0.008 | No clear effect | Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifold (ICLR 2025 · 1 citation) |
| Increase the number of paths from 1 to 100 | Ablation study · RMSE | 0.193 ± 0.031 -> 0.048 ± 0.011 | Helped | Foundation Inference Models for Markov Jump Processes (NeurIPS 2024 · 1 citation) |
| add unified representation pretraining | PepMD test set · VAL-CA | 0.332 -> 0.505 | Helped | UniSim: A Unified Simulator for Time-Coarsened Dynamics of Biomolecules (ICML 2025 · 0 citations) |
| use independent coupling instead of the learned coupling | Ocean currents · Cos. Dist. | 0.230 ± 0.003 vs 0.231 ± 0.004 | No clear effect | Curly Flow Matching for Learning Non-gradient Field Dynamics (NeurIPS 2025 · 0 citations) |
| Add multiple future pinned points rather than conditioning only on the next point | Gulf of Mexico · Mean W2 distance of left-out marginals | Helped | Momentum Multi-Marginal Schrödinger Bridge Matching (NeurIPS 2025 · 0 citations) | |
| Add another iteration of the learned reference and bridge procedure | Repressilator leave-one-out · EMD | 3.38 ± 1.52 -> 2.22 ± 1.12 -> 1.59 ± 0.66 -> 1.49 ± 0.64 -> 1.40 ± 0.57 | Helped | Learning non-equilibrium diffusions with Schrödinger bridges: from exactly solvable to simulation-free (NeurIPS 2025 · 0 citations) |
| use multiplicative rather than additive noise | Bifurcating CLE · Path energy distance | 1.22 ± 0.38 -> 1.69 ± 0.14 | Hurt | Inferring stochastic dynamics with growth from cross-sectional data (NeurIPS 2025 · 0 citations) |
| Add distribution fitting loss L_OT | EB (50D), t1 · W1 | 8.915 -> 7.951 | Helped | Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modeling (NeurIPS 2025 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 24 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- embryoid body scRNA-seq · 2 of 24 papers
Baselines
- OT-CFM · 4 of 24 papers
- MMFM · 3 of 24 papers
- TIGON · 3 of 24 papers
- DeepRUOT · 3 of 24 papers
- SF2M · 3 of 24 papers
- TrajectoryNet · 2 of 24 papers
- SBIRR · 2 of 24 papers
- MIOFlow · 2 of 24 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 49 papers; from OpenAlex and the papers' affiliations).
- Microsoft · 3 papers
- Peking University · 3 papers
- The University of Tokyo · 2 papers
- Google · 2 papers
- Freie Universität Berlin · 2 papers
- Georgia Institute of Technology · 2 papers
- Université de Montréal · 2 papers
- Shanghai Jiao Tong University · 2 papers
- University of Toronto · 2 papers
Use it
Download BibTeX of 28 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Physics-informed dynamics learning (127 papers)
- Latent dynamics models (111 papers)
- Latent-space control and planning (78 papers)
- Data assimilation from sparse observations (58 papers)
Elsewhere in the topic
- State-space inference for stochastic systems (104 papers)
- Switching and law-discovery dynamics (81 papers)
- Synaptic plasticity learning rules (72 papers)
- Latent models of neural activity (70 papers)
- Recurrent circuit models of inference (70 papers)
- Low-rank and diffusion neural dynamics (53 papers)
- Functional connectivity modeling (50 papers)
- Stable contractive dynamics (42 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).