The paper investigates when frequency decomposition aids Physics-Informed Neural Networks (PINNs) by introducing a dual‑branch, spectrally‑gated architecture (DBSG‑PINN) that separates low‑ and high‑frequency components. Experiments on five one‑dimensional PDE benchmarks show that frequency decomposition significantly reduces error—up to 59.2% on a multimodal wave problem—when the target solution is spectrally complex, but offers little improvement on smoother problems and can even worsen performance on a simple 1D wave benchmark. The adaptive gate’s effectiveness scales with the spectral richness of the solution, suggesting it exploits frequency structure rather than adding noise.
By Shubham Rai
arXiv:2609. 04549v1 Announce Type: new Abstract: The FitzHugh-Nagumo (FHN) system serves as a simplified model of neuronal voltage dynamics, capturing the activator-inhibitor structure behind both isolated action potentials and the rhythmic spiking seen across the brain.
By Andrew Franck, Justin Li
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arXiv:2606. 02623v1 Announce Type: cross Abstract: Solving time-dependent partial differential equations (PDEs) is an important problem in computational science and engineering.
By Abhishek Chandra, Taniya Kapoor
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By Heechang Kim, Qianying Cao, Hyomin Shin, Seungchul Lee, George Em Karniadakis, Minseok Choi
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By Conor Rowan
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By Xizhe Wang, Xiaobin Song, Hongbo Zhao, Qingshan Jia, Qianchuan Zhao, Hao Sun, Benben Jiang
arXiv:2606. 19853v1 Announce Type: new Abstract: We introduce SEA-PINN, a novel architecture that incorporates a Squeeze-Excitation-like attention mechanism into physics-informed neural networks to dynamically recalibrate the importance of neurons across layers.
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arXiv:2607. 23466v1 Announce Type: new Abstract: Parameterized and coupled partial differential equations (PDEs) are central to modeling phenomena in science and engineering, yet neural operator methods that address both aspects remain limited.
By Cheng Jing, Uvini Balasuriya Mudiyanselage, Abhishek Verma, Kallol Bera, Shahid Rauf, Kookjin Lee
arXiv:2601. 00473v4 Announce Type: replace-cross Abstract: We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms.
By Abhisek Ganguly, Santosh Ansumali, Sauro Succi
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By Matteo Tomasetto, Nicol\`o Botteghi, Gabriele Bruni, Andrea Manzoni
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By Takehiro Ishikawa