Data-Efficient Neural Operator Training via Physics-Based Active Learning

TL;DR

This paper introduces a physics-informed active learning method for neural operators that reduces data requirements and improves training efficiency by focusing on physics residuals, validated on fluid dynamics equations.

Contribution

It proposes a novel physics-based acquisition strategy for active learning that enhances data efficiency and incorporates physical knowledge into neural operator training.

Findings

Physics-based acquisition outperforms random sampling in experiments.

The method matches state-of-the-art data efficiency levels.

It injects physics inductive bias, improving model understanding.

Abstract

Solving partial differential equations with neural operators significantly reduces computational costs but remains bottlenecked by high training data requirements. Active learning offers a natural framework to mitigate this by selectively acquiring the most informative samples in an iterative manner. We introduce physics-based acquisition - a novel physics-informed active learning algorithm that leverages the partial differential equation residual to guide data selection. We validate the method by presenting numerical experiments for the 1D Burgers equation and the 2D compressible Navier-Stokes equations. We show that, in our experiments, physics-based acquisition consistently outperforms random acquisition and matches the state of the art in data efficiency. At the same time, it has the unique advantage of injecting a physics inductive bias into the training process, ensuring that simulation cost is spent where the model's physical understanding is weakest.