Neural Operator-based Curriculum Learning for Physics-Informed Neural Networks

In this paper, we tackle the critical failure modes of Physics-Informed Neural Networks (PINNs), such as spectral bias, which lead to poor convergence on complex PDEs. We identify two key shortcomings in existing curriculum learning methods for PINNs: unreliable knowledge transfer between stages and a reliance on manual, ad-hoc curriculum design. To overcome these limitations, we present Neural Operator-based Curriculum Learning (NOCL), a unified framework that leverages Neural Tangent Kernel (NTK) theory to automate curriculum generation and employs neural operators to enable robust, dynamic knowledge transfer across curriculum stages. By dynamically training neural operators and filtering data for PINN initialization, our approach ensures scalable and effective learning across progressively difficult tasks. Experiments verify that NOCL leads to marked gains in convergence and generalization relative to prior methods, resulting in substantially better performance on test suite.