Research map / Probabilistic and scientific modeling / Dynamical systems
Physics-informed dynamics learning
Learns physical laws using Hamiltonian, Lagrangian and geometric neural dynamics models.
127 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2017–2026) · 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.
29 papers in 2023–24 and 48 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic held steady, from 12.9% to 12.5%.
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 · A Compositional Object-Based Approach to Learning Physical Dynamics (ICLR 2017 · 153 citations)
- 2018 · End-to-End Differentiable Physics for Learning and Control (NeurIPS 2018 · 256 citations)
- 2019 · Hamiltonian Neural Networks (NeurIPS 2019 · 447 citations)
- 2020 · Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control (ICLR 2020 · 128 citations)
- 2021 · Incorporating Symmetry into Deep Dynamics Models for Improved Generalization (ICLR 2021 · 78 citations)
- 2022 · Deconstructing the Inductive Biases of Hamiltonian Neural Networks (ICLR 2022 · 13 citations)
- 2023 · Spatial Attention Kinetic Networks with E(n)-Equivariance (ICLR 2023 · 11 citations)
- 2024 · Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators (NeurIPS 2024 · 23 citations)
- 2025 · Stable Port-Hamiltonian Neural Networks (NeurIPS 2025 · 4 citations)
- 2026 · MoSA: Motion-constrained Stress Adaptation for Mitigating Real-to-Sim Gap in Continuum Dynamics via Learning Residual Anisotropy (ICML 2026 · 0 citations)
Earliest papers here
- A Compositional Object-Based Approach to Learning Physical Dynamics (ICLR 2017 · 153 citations)
- End-to-End Differentiable Physics for Learning and Control (NeurIPS 2018 · 256 citations)
- Flexible neural representation for physics prediction (NeurIPS 2018 · 160 citations)
What has been tried
80 papers here report 776 measured changes (a component added, removed or swapped, compared with a baseline): helped 67%, no clear effect 10%, hurt 19%, mixed 4%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Add signed distance function feature engineering and use a 64³ grid | ShapeNet-Car test · MSE ×100 | 2.31 -> 2.24; 2.14 | Mixed | Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators (NeurIPS 2024 · 23 citations) |
| use CFA-CON instead of CON-M | D-P+F · RMSE | 0.1323 ± 0.0018 -> 0.1307 ± 0.0012 | Helped | Input-to-State Stable Coupled Oscillator Networks for Closed-form Model-based Control in Latent Space (NeurIPS 2024 · 6 citations) |
| Learn the Hamiltonian minimum instead of fixing it | Noise-free test set, 5% training noise · RMSE | 1.170 -> 2.420 | Hurt | Stable Port-Hamiltonian Neural Networks (NeurIPS 2025 · 4 citations) |
| Add velocity to temporal convolution | N-body · F-MSE | 0.0057 -> 0.0055 | Helped | Equivariant Graph Neural Operator for Modeling 3D Dynamics (ICML 2024 · 3 citations) |
| Replace time composition with a single diffusion model over 44 steps | 2-body 44 steps · design_obj | 0.1326 ± 0.0087 -> 0.2779 ± 0.0197 | Hurt | Compositional Generative Inverse Design (ICLR 2024 · 2 citations) |
| Add the divergence-free conservation-law architecture to GFNO | Navier–Stokes, T_in=10, T=20; 10, 100, and 1000 training samples · relative L2 error | 29.56% ± 3.32% -> 12.10% ± 1.08%; 7.59% ± 0.34% -> 4.76% ± 0.24%; 3.11% ± 0.93% -> 1.21% ± 0.09% | Helped | Harnessing the Power of Neural Operators with Automatically Encoded Conservation Laws (ICML 2024 · 2 citations) |
| Use latent size 4 instead of 32 | Elastic · reconstruction error | 1.1e-4 -> 7.8e-4 | Hurt | UniPhy: Learning a Unified Constitutive Model for Inverse Physics Simulation (CVPR 2025 · 1 citation) |
| Use full-unrolling rather than one-step training | Plume Rise, ϵ = 0.05, p = 6 · discrepancy loss after 3k iterations | 57.39 -> 6.37; 24.12 | Helped | Learning Reduced Fluid Dynamics (AAAI 2024 · 1 citation) |
| apply HMT before CMT instead of contact-then-propagate order | Impact Plate · Position RMSE | 20.34 -> 42.90 | Hurt | Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer (ICLR 2024 · 1 citation) |
| Add prior reweighting (rather than using γ=1) | PO-FC · control error | 0.01139 -> 0.01103 | Helped | DiffPhyCon: A Generative Approach to Control Complex Physical Systems (NeurIPS 2024 · 1 citation) |
| Add Lagrangian-guided feature evolving (LagToEu) | Bounded Navier-Stokes · Relative L2 | 0.0556 -> 0.0543 | Helped | DeepLag: Discovering Deep Lagrangian Dynamics for Intuitive Fluid Prediction (NeurIPS 2024 · 1 citation) |
| set downsampling ratio r¹=2 rather than r¹=8 | 2D Navier-Stokes, Re=10^4, 256×256; 50-step rollout · MSE | 1.606e-01 (6.496e-02) vs 3.774e-01 (1.797e-01) | Hurt | Hierarchical Implicit Neural Emulators (NeurIPS 2025 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 23 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Baselines
- UNet · 2 of 23 papers
- FNO · 2 of 23 papers
- FFNO · 2 of 23 papers
- PHNN · 2 of 23 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 77 papers; from OpenAlex and the papers' affiliations).
- Massachusetts Institute of Technology · 10 papers
- Tsinghua University · 5 papers
- Carnegie Mellon University · 4 papers
- Princeton University · 4 papers
- Inria · 3 papers
- MIT-IBM Watson AI Lab · 3 papers
- Wuhan University · 3 papers
- University of Wisconsin - Madison · 2 papers
- Kumo.AI · 2 papers
- Westlake University · 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
- Latent dynamics models (111 papers)
- Latent-space control and planning (78 papers)
- Data assimilation from sparse observations (58 papers)
- Stochastic population dynamics (53 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).