Leibovici, Kossaifi, Kovachki, … Ashton, Kautz · arXiv 2026 · Transformers
Tokenizes native NURBS CAD patches and predicts continuous surface and volume fields at any query point.
Why it matters: Removes meshing and sampling from the loop, and gives CAD-parameter gradients for design optimisation, verified with CFD.
Alkin et al. (Emmi AI) · TMLR 2025 · Transformers
A few anchor points carry full attention; millions of query points read only the anchors, with separate surface and volume branches.
Why it matters: Made full-car CFD fields at production resolution trainable on a single GPU.
Giral, …, Vinuesa et al. · arXiv 2026 · Latent models
Predicts the latent representation of the flow from geometry and conditions, and decodes a field only when one is needed.
Why it matters: Brings joint-embedding predictive training to aerodynamics, with a latent space that is meaningful on its own.
Luo et al. · ICML 2025 · Transformers
Sharper physics-attention slices and parallel training across GPUs.
Why it matters: Takes slice attention to million-point industrial meshes.
Holzschuh et al. · ICML 2025 · Transformers
A diffusion-transformer backbone adapted to large physics simulations on grids.
Why it matters: Pretrained once, it fine-tunes better than training from scratch: a step toward physics foundation models.
Wu et al. · ICML 2024 · Transformers
Groups mesh points into learned physical states (slices) and runs attention among the slices.
Why it matters: Linear cost in the number of points, on any mesh, with strong accuracy on car and airfoil benchmarks.
Alkin et al. · NeurIPS 2024 · Latent models
Encode any input to a fixed-size latent, evolve it there, decode at any query point.
Why it matters: Separates the cost of the model from the size of the mesh.
Li et al. · NeurIPS 2023 · Operators
Graph operator from the surface to a latent grid, Fourier operator there, graph operator back.
Why it matters: One of the first neural operators on full 3D car geometries.
Pfaff, Fortunato, Sanchez-Gonzalez, Battaglia · ICLR 2021 · Graphs
Message passing on the simulation mesh itself, node to node along edges.
Why it matters: Made mesh-native learning standard; still the baseline for structures and crash.
Li et al. · ICLR 2021 · Operators
Learns the solution operator by mixing modes in Fourier space.
Why it matters: Launched neural operators: resolution-independent, fast, global.
Lu, Jin, Pang, Zhang, Karniadakis · Nature Machine Intelligence 2021 · Operators
A branch net encodes the input function, a trunk net the query point; their product is the output.
Why it matters: The template for query-anywhere decoders used across today’s models.
Ohana et al. · NeurIPS D&B 2024 · Data
Fifteen terabytes of simulations across many physics, in one format.
Why it matters: The common ground for pretraining and comparing physics foundation models.
Ashton et al. · arXiv 2024 · Data
Hundreds of scale-resolving simulations of parametric car variants, surface and volume.
Why it matters: The reference benchmark for automotive surrogates.
Bonnet, Mazari, Cinnella, Gallinari · NeurIPS D&B 2022 · Data
Over a thousand RANS airfoil simulations with full volume fields.
Why it matters: A small, honest benchmark that checks physical consistency, not only error.
Patel et al. · arXiv 2026 · Design & trust
Conformal bounds on neural-operator outputs, used directly in the design optimisation.
Why it matters: Optimisers exploit surrogate errors; this keeps the chosen design robust to them.
Winovich et al. · arXiv 2025 · Design & trust
Cheap predictive uncertainty for operator networks, used to choose the next simulations.
Why it matters: Spends the simulation budget where the surrogate is unsure.