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

arXiv: https://arxiv.org/abs/2603.18237 · HTML: https://mlsanity.com/paper/2603.18237/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 23 references that are in the map.
- First posted on arXiv 18 Mar 2026.

## Builds on (most cited first, 18 of 18)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [GLISTER: Generalization based Data Subset Selection for Efficient and Robust Learning](https://mlsanity.com/paper/2012.10630/) (2020)
- [Poseidon: Efficient Foundation Models for PDEs](https://mlsanity.com/paper/2405.19101/) (2024)
- [DeepCore: A Comprehensive Library for Coreset Selection in Deep Learning](https://mlsanity.com/paper/2204.08499/) (2022)
- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [Coverage-centric Coreset Selection for High Pruning Rates](https://mlsanity.com/paper/2210.15809/) (2022)
- [D2 Pruning: Message Passing for Balancing Diversity and Difficulty in Data Pruning](https://mlsanity.com/paper/2310.07931/) (2023)
- [PRISM: A Rich Class of Parameterized Submodular Information Measures for Guided Subset Selection](https://mlsanity.com/paper/2103.00128/) (2021)
- [Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learning](https://mlsanity.com/paper/2402.15734/) (2024)
- [Active Learning for Neural PDE Solvers](https://mlsanity.com/paper/2408.01536/) (2024)
- [CFO: Learning Continuous-Time PDE Dynamics via Flow-Matched Neural Operators](https://mlsanity.com/paper/2512.05297/) (2025)
- [Active Learning with Selective Time-Step Acquisition for PDEs](https://mlsanity.com/paper/2511.18107/) (2025)
- [PICore: Physics-Informed Unsupervised Coreset Selection for Data Efficient Neural Operator Training](https://mlsanity.com/paper/2507.17151/) (2025)
- [Data-Augmented Few-Shot Neural Emulator for Computer-Model System Identification](https://mlsanity.com/paper/2508.19441/) (2025)

## Abstract (arXiv)

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.