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When Does Frequency Decomposition Benefit Physics-Informed Neural Networks? A Preliminary Ablation Study
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PDEsneural networksfrequency decompositionspectral analysis
2608.24940
Builder Relevance
3h ago70%
Abstract
This study explores the effectiveness of frequency decomposition in enhancing the performance of Physics-Informed Neural Networks (PINNs) on various partial differential equations (PDEs).
Reality Card
Core Claim
Frequency decomposition significantly improves the accuracy of PINNs on spectrally complex PDEs, reducing relative $L_2$ error by up to 59.2% on a multimodal wave problem.
Method / Result
Frequency decomposition helps most on spectrally complex benchmarks, achieving up to 59.2% reduction in $L_2$ error.
Limitations
All results are based on a single training seed across five benchmarks, raising concerns about reproducibility and generalizability.
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