待翻譯：When Does Frequency Decomposition Benefit Physics-Informed Neural Networks? A Preliminary Ablation Study
AI 服務暫時不可用，以下為來源摘要，待恢復後補全翻譯：arXiv:2608.24940v1 Announce Type: new Abstract: Partial differential equations (PDEs) often have high-frequency and multi-scale features that neural networks struggle to approximate. Physics-Informed Neural Networks (PINNs) build the governing equations directly into training, but suffer from spectral bias: they learn low-frequency components faster than high-frequency ones. Techniques such as Fourier feature embeddings and sinusoidal activations address this, but most studies assume they help across the board without checking which spectral regimes actually benefit. We introduce a dual-branch, spectrally-gated architecture (DBSG-PINN) that splits low- and high-frequency components into separate subnetworks joined by an adaptive gate, and use it to run a partially controlled ablation of frequency decomposition and spectral routing. We test this on five one-dimensional benchmark PDEs, ranging from smooth, single-scale problems to oscillatory, multi-scale ones. Frequency decomposition helps most on the spectrally complex benchmarks, cutting relative $L_2$ error by up to $59.2\%$ on a multimodal wave problem, but gives little benefit on smoother PDEs. On one benchmark (1D Wave), it performs substantially worse than a simpler fixed-combination variant. The gate's benefit scales with how spectrally rich the target solution is: the full model's advantage over the ablations is largest on multi-scale benchmarks and smallest (or negative) on single-scale ones, consistent with the gate exploiting frequency structure rather than acting as noise,though we do not directly visualize or quantify its spatial activations in this study. All results come from a single training seed across five 1D benchmarks, so we present this as an exploratory study meant to raise questions rather than answer them, and outline the additional seeds and benchmarks needed to test whether the pattern holds.
AI 服務暫時不可用，以下為來源正文，待恢復後補全翻譯。
--> [Submitted on 24 Aug 2026] Title:When Does Frequency Decomposition Benefit Physics-Informed Neural Networks? A Preliminary Ablation Study View a PDF of the paper titled When Does Frequency Decomposition Benefit Physics-Informed Neural Networks? A Preliminary Ablation Study, by Shubham Rai View PDF HTML (experimental) Abstract:Partial differential equations (PDEs) often have high-frequency and multi-scale features that neural networks struggle to approximate. Physics-Informed Neural Networks (PINNs) build the governing equations directly into training, but suffer from spectral bias: they learn low-frequency components faster than high-frequency ones. Techniques such as Fourier feature embeddings and sinusoidal activations address this, but most studies assume they help across the board without checking which spectral regimes actually benefit. We introduce a dual-branch, spectrally-gated architecture (DBSG-PINN) that splits low- and high-frequency components into separate subnetworks joined by an adaptive gate, and use it to run a partially controlled ablation of frequency decomposition and spectral routing. We test this on five one-dimensional benchmark PDEs, ranging from smooth, single-scale problems to oscillatory, multi-scale ones. Frequency decomposition helps most on the spectrally complex benchmarks, cutting relative $L_2$ error by up to $59.2\%$ on a multimodal wave problem, but gives little benefit on smoother PDEs. On one benchmark (1D Wave), it performs substantially worse than a simpler fixed-combination variant. The gate's benefit scales with how spectrally rich the target solution is: the full model's advantage over the ablations is largest on multi-scale benchmarks and smallest (or negative) on single-scale ones, consistent with the gate exploiting frequency structure rather than acting as noise,though we do not directly visualize or quantify its spatial activations in this study. All results come from a single training seed across five 1D benchmarks, so we present this as an exploratory study meant to raise questions rather than answer them, and outline the additional seeds and benchmarks needed to test whether the pattern holds. Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI) Cite as: arXiv:2608.24940 [cs.LG] (or arXiv:2608.24940v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.24940 arXiv-issued DOI via DataCite Submission history From: Shubham Rai [view email] [v1] Mon, 24 Aug 2026 09:48:16 UTC (4,616 KB) Full-text links: Access Paper: View a PDF of the paper titled When Does Frequency Decomposition Benefit Physics-Informed Neural Networks? A Preliminary Ablation Study, by Shubham Rai View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-08 Change to browse by: cs cs.AI References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)