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

TL;DR

PICore is an unsupervised framework that efficiently selects the most informative data samples for training neural operators on PDEs, reducing data labeling costs and training time while maintaining accuracy.

Contribution

It introduces a physics-informed, unsupervised coreset selection method that minimizes the need for labeled data in neural operator training.

Findings

Achieves up to 78% increase in training efficiency.

Reduces labeling costs by only simulating selected inputs.

Maintains comparable accuracy with fewer training samples.

Abstract

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.