Foundations / The idea

A short history

Seventy years from response surfaces and kriging to neural fields on any geometry.

• 1951: Response surfaces. Box & Wilson fit low-order polynomials to experiments: the first surrogate models, still used in design of experiments.
• 1960s–80s: Kriging. Gaussian-process interpolation from geostatistics: a surrogate that also says how uncertain it is.
• 1990s–2000s: Design optimisation. Kriging, radial basis functions and POD reduced-order models enter aerospace and automotive design loops.
• 2015–20: Deep learning on grids. Convolutional U-Nets predict full flow fields on images and voxel grids; physics-informed networks appear.
• 2020–23: Geometry-native models. Graph networks on simulation meshes, point-cloud networks and neural operators learn directly on engineering geometry.
• 2024–26: Transformers and foundation models. Latent-token transformers scale to 100M-cell CFD; pretrained physics models fine-tune to new problems with little data.

Related

• What a surrogate is: A fast, learned map from a design to its physics, from a few numbers to the full field.
• Lineages: Four families of field surrogates, from their founding idea to 2026.
• Recent papers: Recent field-surrogate architectures from NeurIPS, ICML and ICLR, 2023 to 2026, in order.