PDE foundation models enable data-efficient adaptation but are deployed autoregressively, so short-horizon accuracy need not imply reliable simulation.
We ask whether the short-horizon advantage of a foundation-model recipe persists when its predictions are repeatedly fed back as inputs for a long horizon.
We define error amplification as G=E(H_f)/E(H_s), which measures full-horizon error relative to short-horizon error.
We evaluate seven models on seven two-dimensional time-dependent PDE datasets: scratch-trained FNO and DeepONet; fine-tuned DPOT, GPhyT, Poseidon, and Walrus; and frozen in-context VICON. We report VRMSE, relative L_2, and relative MAE.
Six datasets provide paired short- and full-horizon scores, while CE-RM contributes short-rollout sweeps only.
At least one fine-tuned foundation model outperforms both scratch baselines in 26 of 30 short-rollout dataset--budget cells under every metric.
Nevertheless, full-horizon VRMSE exceeds short-horizon VRMSE in 140 of 144 paired trained configurations, with a median error amplification of $2.04$.
The count below VRMSE one falls from 104 to