Stabilizing Autoregressive PDE Foundation Model Rollouts with Event-Triggered Context Healing

2026-09-26

AI Summary

This study addresses the error accumulation problem in long-horizon rollout predictions of autoregressive PDE foundation models by proposing an event-triggered context repair mechanism. The method leverages twelve sparse pressure probes to monitor deviations in real time, invoking a hourglass diffusion Transformer to reconstruct the velocity–pressure context only when errors exceed a predefined threshold, thereby avoiding full computational overhead. Evaluated on the RealPDEBench benchmark, this approach reduces the prediction errors of DPOT and Poseidon-T to approximately 6% and 7%, respectively. Notably, sustained long-term accuracy is achieved by correcting merely 14.56% of the temporal windows, while enabling real-time inference on A100 GPUs.

Abstract

Autoregressive PDE foundation models enable fast full-field forecasting but accumulate errors as predicted states are recursively reused. We introduce Event-Triggered Context Healing (ETCH), which compares forecasts with measurements from 12 cylinder-surface pressure taps. When their discrepancy exceeds a threshold, pressure-conditioned hourglass diffusion transformers reconstruct the velocity--pressure context for subsequent predictions. On 43 RealPDEBench Cylinder trajectories, ETCH reduces velocity and pressure errors from 48.05 and 63.71% to 6.29 and 7.25% for DPOT, and from 74.97 and 76.91% to 5.16 and 6.84% for Poseidon-T, using the same reconstructors and threshold. For DPOT, correcting 14.56% of windows maintains errors close to reconstructing every window and supports average real-time forecasting and correction on an A100 GPU. These results show that sparse physical feedback stabilizes long autoregressive rollouts across PDE foundation models while reducing reconstruction cost.

Problem

• Autoregressive PDE foundation models
• Error accumulation
• Rollout stabilization
• Full-field forecasting

Innovation

• Autoregressive PDE foundation models
• Event-Triggered Context Healing
• Diffusion Transformers
• Sparse physical feedback
• Error accumulation mitigation