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Model atlas

Ten surrogate families at a glance, grouped by the data they consume.

• Gaussian process (Kriging) (Scalar & reduced-order): A probabilistic regression over the design space: every prediction comes with an uncertainty estimate. Good for: Small datasets, Bayesian optimisation, knowing when the model is unsure.
• POD reduced-order model (Scalar & reduced-order): Snapshots are compressed onto a few dominant modes (POD/PCA); a regression model predicts the mode coefficients. Good for: Parametric studies on one fixed mesh, fast and interpretable.
• U-Net (CNN) (Grid / voxel): Convolutional encoder–decoder with skip connections between matching resolutions. Good for: Fields on regular grids; robust and easy to train. Used early on for RANS airfoil flows.
• Fourier Neural Operator (Grid / voxel): Layers mix information globally by learning weights on the lowest Fourier modes of the field. Good for: Smooth, global PDE solutions; can be evaluated at resolutions it was not trained on.
• MeshGraphNets (Graph): Encode–process–decode: message passing along mesh edges, one hop per layer. Good for: Unstructured meshes, complex geometry, transient simulation by rollout.
• Graph Network Simulator (Graph): Learns particle accelerations by message passing, then integrates in time. Good for: Fluids, granular media and deformables represented as particles.
• PointNet (Point cloud): A shared MLP per point plus a symmetric global pooling, so point order does not matter. Good for: A simple baseline for geometry-to-field prediction on raw points.
• GINO (Point cloud): A graph neural operator maps points onto a latent grid, an FNO works there, and a second graph operator maps back. Good for: Large 3D geometries, such as full car aerodynamics, at fixed cost per latent grid.
• Transolver (Point cloud): Physics-attention: points are softly grouped into learned slices, attention runs between slice tokens, results broadcast back to points. Good for: Large unstructured geometries with linear cost in the number of points; strong across PDE benchmarks.
• DeepONet (Operator learning): A branch net encodes the input function, a trunk net encodes where to evaluate; their dot product is the output. Good for: Evaluating the field at arbitrary query points; theory-backed operator learning.

Related

• Model families: Neural fields, U-Nets, graph networks and transformers, and what each is good for.
• Lineages: Four families of field surrogates, from their founding idea to 2026.
• Technique library: Thirty techniques that make surrogates work in practice, from basics to the frontier.