Gradient-Informed Temporal Sampling Improves Rollout Accuracy in PDE Surrogate Training
This addresses a fundamental problem for researchers training neural simulators on PDEs, offering a novel data sampling method that improves accuracy, though it is incremental as it builds on existing sampling approaches.
The paper tackled the problem of sampling training data for neural simulators to maximize rollout accuracy, proposing Gradient-Informed Temporal Sampling (GITS) which achieved lower rollout error compared to baselines across multiple PDE systems, model backbones, and sample ratios.
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.