# PICore: Physics-Informed Unsupervised Coreset Selection for Data Efficient Neural Operator Training

arXiv: https://arxiv.org/abs/2507.17151 · HTML: https://mlsanity.com/paper/2507.17151/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 54 references that are in the map.
- First posted on arXiv 23 Jul 2025.

## Builds on (most cited first, 30 of 36)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [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)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (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)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [GLISTER: Generalization based Data Subset Selection for Efficient and Robust Learning](https://mlsanity.com/paper/2012.10630/) (2020)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [DeepCore: A Comprehensive Library for Coreset Selection in Deep Learning](https://mlsanity.com/paper/2204.08499/) (2022)
- [Active Learning on a Budget: Opposite Strategies Suit High and Low Budgets](https://mlsanity.com/paper/2202.02794/) (2022)
- [Online Coreset Selection for Rehearsal-based Continual Learning](https://mlsanity.com/paper/2106.01085/) (2021)
- [RETRIEVE: Coreset Selection for Efficient and Robust Semi-Supervised Learning](https://mlsanity.com/paper/2106.07760/) (2021)
- [Adaptive Second Order Coresets for Data-efficient Machine Learning](https://mlsanity.com/paper/2207.13887/) (2022)
- [A Survey on Deep Active Learning: Recent Advances and New Frontiers](https://mlsanity.com/paper/2405.00334/) (2024)
- [Learning Dissipative Dynamics in Chaotic Systems](https://mlsanity.com/paper/2106.06898/) (2021)
- [Small-GAN: Speeding Up GAN Training Using Core-sets](https://mlsanity.com/paper/1910.13540/) (2019)
- [Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learning](https://mlsanity.com/paper/2402.15734/) (2024)
- [In Defense of Core-set: A Density-aware Core-set Selection for Active Learning](https://mlsanity.com/paper/2206.04838/) (2022)
- [Core-set Sampling for Efficient Neural Architecture Search](https://mlsanity.com/paper/2107.06869/) (2021)
- [Multi-Resolution Active Learning of Fourier Neural Operators](https://mlsanity.com/paper/2309.16971/) (2023)
- [Active Learning for Neural PDE Solvers](https://mlsanity.com/paper/2408.01536/) (2024)
- [Inexact Non-Convex Newton-Type Methods](https://mlsanity.com/paper/1802.06925/) (2018)
- [Speculative Coreset Selection for Task-Specific Fine-tuning](https://mlsanity.com/paper/2410.01296/) (2024)

## Built on by (most cited first, 2 of 2)

- [Gradient-Informed Temporal Sampling Improves Rollout Accuracy in PDE Surrogate Training](https://mlsanity.com/paper/2603.18237/) (2026)
- [Data-Efficient Neural Operator Training via Physics-Based Active Learning](https://mlsanity.com/paper/2605.21348/) (2026)

## Abstract (arXiv)

Neural operators offer a powerful paradigm for solving partial differential equations (PDEs) that cannot be solved analytically by learning mappings between function spaces. However, there are two main bottlenecks in training neural operators: they require a significant amount of training data to learn these mappings, and this data needs to be labeled, which can only be accessed via expensive simulations with numerical solvers. To alleviate both of these issues simultaneously, we propose PICore, an unsupervised coreset selection framework that identifies the most informative training samples without requiring access to ground-truth PDE solutions. PICore leverages a physics-informed loss to select unlabeled inputs by their potential contribution to operator learning. After selecting a compact subset of inputs, only those samples are simulated using numerical solvers to generate labels, reducing annotation costs. We then train the neural operator on the reduced labeled dataset, significantly decreasing training time as well. Across four diverse PDE benchmarks and multiple coreset selection strategies, PICore achieves up to 78% average increase in training efficiency relative to supervised coreset selection methods with minimal changes in accuracy. We provide code at https://github.com/Asatheesh6561/PICore.