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

Alicja Polanska, Vignesh Gopakumar, Lorenzo Zanisi, Stanislas Pamela

Keywords: Active Learning, Neural Operators, Partial Differential Equations, Physics Informed Machine Learning

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 acquisition. We validate the method, showcasing numerical experiments for 1D Burgers, and 2D compressible Navier-Stokes partial differential equations. We show that in our experiments, physics-based acquisition consistently significantly outperforms random acquisition, and matches the state of the art in terms of 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.

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Submission Number: 91