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arXiv Machine Learning By Juan Molina, Paris Perdikaris, Mircea Petrache, Mat\'ias Courdurier, Francisco Sahli Costabal

Operator-informed initialization for Fourier features physics-informed neural networks

Read the original on arXiv Machine Learning →

The paper introduces an operator-informed initialization for Fourier Feature Physics-Informed Neural Networks (PINNs) to mitigate spectral bias, where certain frequencies converge slower. By analyzing training dynamics in the Neural Tangent Kernel regime, the authors derive an evolution equation linking convergence rates to the product of the differential operator’s symbol and the spectral density of initialization weights. They propose tailoring the initial weight distribution to the specific PDE, which balances convergence across frequencies and improves prediction accuracy without extra training cost, as confirmed by experiments on linear and nonlinear PDEs.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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