How does a surrogate learn?
Move through a deterministic toy run. The target is fixed; the model’s mean, uncertainty and proposed next evaluation evolve as information arrives.
Watch the surrogate learn
The target is an illustrative asymmetric log posterior. At each iteration, the Gaussian process updates its mean and uncertainty from the marked evaluations; the acquisition function then balances posterior relevance against what the model still does not know.
How to read it
In one dimension, the dashed curve is the expensive target and GPry only sees the marked evaluations. The petrol curve and band show the Gaussian process’s current estimate and uncertainty. The acquisition function is high where an evaluation is both relevant to the posterior and capable of reducing uncertainty.
In two dimensions, the first three panels separate the GP mean, predictive standard deviation, and LogExp acquisition. The final panel shows how NORA explores the surrogate posterior and ranks a diverse four-point batch using sequential Kriging-believer conditioning. Advancing an iteration adds that batch to the training set and updates all four views.