Model catalog¶
The built-in executable registry contains 55 methods and uses multi-label categories. The table below cites representative primary papers for the models named in each family. These references identify the originating scientific methods; they do not imply that every NAVIER-CFD native reference implementation is a bit-for-bit reproduction of the authors' code or checkpoints.
| Family | Representative models in NAVIER-CFD | Representative primary citations |
|---|---|---|
| Physics-informed neural fields | PINN, NSFnets, PINNsFormer, PINO, PIBERT | Raissi, Perdikaris & Karniadakis, JCP 2019, Physics-informed neural networks; Jin et al., JCP 2021, NSFnets; Zhao, Ding & Prakash, PINNsFormer; Li et al., PINO; Chakraborty, Pan & Chen, PIBERT (2026), project source. |
| Branch-trunk and spectral neural operators | DeepONet, MIONet, Fourier-DeepONet, Fourier-MIONet, FNO, F-FNO, U-FNO, U-NO, LSM | Lu et al., Nature Machine Intelligence 2021, DeepONet; Jin, Meng & Lu, MIONet; Li et al., FNO; Tran et al., F-FNO; Rahman, Ross & Azizzadenesheli, U-NO. |
| Geometry, graph and mesh operators | Geo-FNO, GINO, MeshGraphNets, Transolver, GNOT, UPT, DoMINO, ReViT | Li et al., Geo-FNO; Li et al., GINO; Pfaff et al., MeshGraphNets; Wu et al., Transolver. Cite the corresponding primary paper or official project for GNOT, UPT, DoMINO and ReViT when using those methods. |
| Transformer and foundation-style PDE models | DPOT, Poseidon, PROSE-FD, BCAT, PDEformer-1, PI-MFM, P3D, AeroTransformer, Tadpole | Liu et al., PROSE-FD; Liu, Sun & Schaeffer, BCAT; Ye et al., PDEformer-1. For DPOT, Poseidon, PI-MFM, P3D, AeroTransformer and Tadpole, cite the exact primary paper/version represented by the experiment. |
| Generative and probabilistic PDE models | FourierFlow, PDE-Refiner, FunDiff, Flow Matching for PDEs, Conformalized-DeepONet | Wang et al., FourierFlow; Lippe et al., PDE-Refiner. Cite the original FunDiff, flow-matching and conformal-operator papers for experiments using those variants. |
| Hybrid numerical acceleration | Solver-in-the-Loop, INC, PICT, NeuroSEM, neural-operator preconditioned Newton, geometry-aware neural preconditioner | Um et al., Solver-in-the-Loop; Wei et al., INC (NeurIPS 2025), official implementation; Franz et al., PICT, Journal of Computational Physics 2025. Cite the exact NeuroSEM and neural-preconditioning papers used in the experiment. |
| Particle and multiphase learning | diffSPH, NeuralDEM, Nested Fourier-DeepONet, Fourier-MIONet, U-FNO | Winchenbach & Thuerey, diffSPH, Journal of Computational Physics 2026; Wen et al., U-FNO, Advances in Water Resources 2022. Cite the official NeuralDEM and Fourier-operator source associated with the selected implementation and dataset. |
| Specialized coupled and inverse models | DeepM&Mnet, RiemannONet, Energy Transformer flow reconstruction, TANTE | Mao et al., JCP 2021, DeepM&Mnet; Wu et al., TANTE, JCP 562 (2026), 115041. Cite the primary RiemannONet and Energy Transformer papers when reporting those results. |
Citation practice¶
When publishing results produced with NAVIER-CFD, cite:
- NAVIER-CFD for the integration, dataset configuration, training, evaluation or recommendation workflow;
- the original model paper for each architecture used;
- the original dataset or benchmark paper;
- the official upstream implementation and checkpoint, when applicable.
A model card, native reference implementation, official author implementation and numerical reproduction are different levels of evidence. The reference field displayed by the model registry and recommender is intended to preserve this attribution.
navier models list
navier models list --category acceleration
navier models info pibert
The model atlas lists every registered model and provides detailed cards for the most important CFD architectures.