אתחול מודע למפעיל עבור רשתות נוירונים פיזיקליות

תקציר מקורי באנגליתarXiv:2610.03378v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) typically exhibit spectral bias, where some frequencies of the target function converge more slowly than others. In this work, we analyze the training dynamics of Fourier Feature PINNs in the Neural Tangent Kernel regime to address this limitation. We derive an explicit evolution equation to estimate the residual error in the frequency domain, demonstrating that the convergence rate of specific frequencies is primarily governed by the product of the differential operator's symbol and the spectral density of the initialization weights. Leveraging this theoretical insight, we propose an informative initialization strategy that tailors the initial weight distribution to the specific PDE being solved. With