LiNO: Lifting based multiresolution neural operator
LiNO is a multiresolution neural operator built on the second-generation wavelet lifting scheme, learning data-driven multiscale decomposition and evolving coarse and directional detail coefficients separately for scale-aware physics modeling. It outperforms state-of-the-art neural operators on benchmarks including Darcy flow, Poisson equation, Allen-Cahn equation, compressible Navier-Stokes equation, and Gray-Scott reaction-diffusion system.
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[Submitted on 2 Jul 2026]
Title:LiNO: Lifting based multiresolution neural operator
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Abstract: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.
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2607.02715 [cs.LG]
(or arXiv:2607.02715v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.02715
arXiv-issued DOI via DataCite
Submission history
From: Himanshu Pandey [view email] [v1] Thu, 2 Jul 2026 19:05:08 UTC (3,088 KB)
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