Multi-Fidelity Neural Operator Thompson Sampling

We study cost-aware optimization of expensive scientific simulations available at multiple spatial resolutions. We extend Neural Operator Thompson Sampling (NOTS) to this multi-fidelity (MF) setting by deriving a two-stage acquisition rule that uses a single neural operator surrogate across resolutions. Candidate inputs are selected from a target-resolution posterior sample, while the evaluation fidelity is chosen by balancing query cost against a single-sample proxy for the expected reduction in posterior uncertainty about the target objective. We show that this criterion becomes maximally informative as fidelity is refined under suitable assumptions. We evaluate MF-NOTS on shallow-water and two-dimensional Navier–Stokes benchmarks, comparing it against the original NOTS and GP-based Bayesian optimization baselines.