Gradient-Informed Temporal Sampling Improves Rollout Accuracy in PDE Surrogate Training

TL;DR

This paper introduces Gradient-Informed Temporal Sampling (GITS), a novel data sampling method that improves neural PDE surrogate training by balancing local gradient information and temporal coverage, leading to more accurate rollouts.

Contribution

GITS is the first sampling method tailored for neural PDE simulators that jointly optimizes local gradients and temporal coverage for better accuracy.

Findings

GITS outperforms baseline sampling methods in reducing rollout error.

Ablation studies confirm the importance of combined optimization objectives.

Analysis reveals effective sampling patterns and limitations of GITS.

Abstract

Researchers train neural simulators on uniformly sampled numerical simulation data. But under the same budget, does systematically sampled data provide the most effective information? A fundamental yet unformalized problem is how to sample training data for neural simulators so as to maximize rollout accuracy. Existing data sampling methods either tend to collapse into locally high-information-density regions, or preserve diversity but remain insufficiently model-specific, often leading to performance that is no better than uniform sampling. To address this, we propose a data sampling method tailored to neural simulators, Gradient-Informed Temporal Sampling (GITS). GITS jointly optimizes pilot-model local gradients and set-level temporal coverage, thereby effectively balancing model specificity and dynamical information. Compared with multiple sampling baselines, the data selected by GITS achieves lower rollout error across multiple PDE systems, model backbones and sample ratios. Furthermore, ablation studies demonstrate the necessity and complementarity of the two optimization objectives in GITS. In addition, we analyze the successful sampling patterns of GITS as well as the typical PDE systems and model backbones on which GITS fails.