{"slug": "lino-lifting-based-multiresolution-neural-operator", "title": "LiNO: Lifting based multiresolution neural operator", "summary": "Researchers introduced the Lifting Neural Operator (LiNO), a multiresolution neural operator built on the second-generation wavelet lifting scheme, to learn solution operators of differential equations. LiNO adaptively decomposes data into multiscale features while preserving information through invertible lifting transforms, outperforming state-of-the-art operators on benchmarks including Darcy flow, Poisson equation, and Navier-Stokes equations.", "body_md": "arXiv:2607.02715v1 Announce Type: new\nAbstract: Recently, neural operators have shown promising outcomes for learning solution operators of differential equations directly from data. This framework learns a functional mapping from the parameter field to the solution field, enabling the prediction of an entire class of solutions rather than a specific instance. However, existing operators often struggle to capture both global dynamics and fine-scale structure simultaneously. To design an effective operator capable of representing multiscale features, a hierarchical multiscale decomposition framework is required. In this study, we develop the Lifting Neural Operator (LiNO), a multiresolution operator built on the second-generation wavelet lifting scheme. LiNO learns a multiresolution decomposition directly from data by parameterizing the lifting transform. This lifting transformation is adaptive to the underlying solution function and exactly invertible by construction, enabling information-preserving multiscale operator learning. In the lifted multiresolution space, the operator evolves coarse and directional detail coefficients separately, resulting in scale-aware modeling of the underlying physics. We evaluate LiNO on several benchmarks, including Darcy flow, the Poisson equation, the Allen-Cahn equation, the compressible Navier-Stokes equation, and the Gray-Scott reaction-diffusion system. Together, these benchmarks cover a wide range of physical behaviors, including multiscale phenomena, transport-dominated dynamics, and chaotic systems. LiNO demonstrates strong performance on these challenging benchmarks compared with state-of-the-art neural operators. These results suggest that adaptive multiresolution operators provide a promising direction for scientific machine learning.", "url": "https://wpnews.pro/news/lino-lifting-based-multiresolution-neural-operator", "canonical_source": "https://arxiv.org/abs/2607.02715", "published_at": "2026-07-07 04:00:00+00:00", "updated_at": "2026-07-07 04:11:27.337886+00:00", "lang": "en", "topics": ["machine-learning", "neural-networks", "ai-research"], "entities": ["LiNO", "Lifting Neural Operator", "Darcy flow", "Poisson equation", "Allen-Cahn equation", "Navier-Stokes equation", "Gray-Scott reaction-diffusion system"], "alternates": {"html": "https://wpnews.pro/news/lino-lifting-based-multiresolution-neural-operator", "markdown": "https://wpnews.pro/news/lino-lifting-based-multiresolution-neural-operator.md", "text": "https://wpnews.pro/news/lino-lifting-based-multiresolution-neural-operator.txt", "jsonld": "https://wpnews.pro/news/lino-lifting-based-multiresolution-neural-operator.jsonld"}}