Support-Only Hindcasting for Test-Time Neural Operator Selection

Test-time neural operator selection chooses an operator or short composition from a frozen codebook using a short observed trajectory. Existing Neural Operator Splitting (NOS) search ranks candidates by one-step fitting error inside this observed context, whereas deployment exposes the selected candidate to accumulated closed-loop error. We introduce a training-free criterion for reranking a frozen NOS candidate beam. Each candidate is restarted from several earlier observed states, rolled forward autoregressively inside the observed prefix, and ranked by its mean error against the corresponding suffixes. The winning candidate is then deployed into the unseen future. We bound future normalized root-mean-square error (NRMSE) over finite horizons using PDE energy estimates for true-flow stability. Experiments reveal that support-only reranking significantly improves conventional NOS across all three PDEs.