{"@context":"https://schema.org","@type":"CreativeWork","@id":"https://froggit.ai/public/capsules/46a9d5c9-6062-4ca1-bddc-24209b4b1083","identifier":"46a9d5c9-6062-4ca1-bddc-24209b4b1083","url":"https://froggit.ai/public/capsules/46a9d5c9-6062-4ca1-bddc-24209b4b1083","name":"An adaptive wavelet-based PINN for problems with localized high-magnitude source","text":"# An adaptive wavelet-based PINN for problems with localized high-magnitude source\n\nSource-backed public reference for arXiv:2604.28180.\n\n**Authors:** Himanshu Pandey, Ratikanta Behera\n**Primary source:** https://arxiv.org/abs/2604.28180\n**Published:** 2026-04-30T17:57:22Z\n**Updated:** 2026-04-30T17:57:22Z\n**Categories:** cs.LG\n\n## Abstract Summary\nIn recent years, physics-informed neural networks (PINNs) have gained significant attention for solving differential equations, although they suffer from two fundamental limitations, namely, spectral bias inherent in neural networks and loss imbalance arising from multiscale phenomena. This paper proposes an adaptive wavelet-based PINN (AW-PINN) to address the extreme loss imbalance characteristic of problems with localized high-magnitude source terms. Such problems frequently arise in various physical applications, such as thermal processing, electro-magnetics, impact mechanics, and fluid dynamics involving localized forcing. The proposed framework dynamically adjusts the wavelet basis function based on residual and supervised loss. This adaptive nature makes AW-PINN handle problems with high-scale features effectively without being memory-intensive. Additionally, AW-PINN does not rely on automatic differentiation to obtain derivatives involved in the loss function, which accelerates the training process. The method operates in two stages, an initial short pre-training phase with fixed bases to select physically relevant wavelet families, followed by an adaptive refinement that adapts scales and translations without populating high-resolution bases across entire domains....\n\n## Public Use Notes\n- This capsule summarizes the paper's arXiv metadata and abstract; it is not an independent replication or endorsement of the paper's claims.\n- Use it as a cited research reference for discovery, retrieval, and agent context.\n- For clinical, security, operational, or deployment-sensitive topics, treat the paper as research context","keywords":["cs.LG"],"about":[],"citation":["https://arxiv.org/abs/2604.28180"],"isPartOf":{"@type":"Dataset","name":"Forge Cascade Knowledge Graph","url":"https://froggit.ai"},"publisher":{"@type":"Organization","name":"Forge Cascade","url":"https://froggit.ai"},"dateCreated":"2026-05-01T06:00:02.959000Z","dateModified":"2026-06-19T14:20:13Z","isBasedOn":"https://arxiv.org/abs/2604.28180","additionalProperty":[{"@type":"PropertyValue","name":"trust_level","value":40},{"@type":"PropertyValue","name":"verification_status","value":"sources_verified"},{"@type":"PropertyValue","name":"provenance_status","value":"valid"},{"@type":"PropertyValue","name":"evidence_level","value":"primary_source"}]}