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This study investigates the benefits of frequency decomposition for Physics-Informed Neural Networks (PINNs) by proposing a dual-branch, spectrally-gated architecture (DBSG-PINN). Ablation experiments on 1D PDE benchmarks indicate that frequency decomposition is most effective on spectrally complex problems, reducing error by up to 59.2%.
This paper identifies a Signal-to-Noise Ratio timestep (SNR-t) bias in diffusion probabilistic models during inference, where SNR-timestep alignment from training is disrupted at inference time. The authors propose a differential correction method that decomposes samples into frequency components and corrects each separately, improving generation quality across models like IDDPM, ADM, DDIM, EDM, and FLUX with minimal computational overhead.