Data-Efficient Neural Operator Training via Physics-Based Active Learning
For researchers training neural operators to solve PDEs, this method reduces the high data requirements by actively selecting informative samples, though the gains are incremental over existing active learning approaches.
The paper introduces a physics-informed active learning algorithm that uses PDE residuals to select training data for neural operators, achieving data efficiency comparable to state-of-the-art methods while reducing simulation costs by focusing on regions where the model's physical understanding is weakest.
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.