arXiv:2605.24658v1 Announce Type: new Abstract: This work introduces the Wavelet-Laplace Neural Operator (WLNO), a novel neural operator that fuses Haar wavelet multi-scale spatial decomposition with the Laplace-domain pole-residue formulation of the Laplace Neural Operator (LNO). While LNO captures transient and steady-state dynamics through learnable system poles and residues, it lacks an explicit mechanism for extracting spatially localized multi-scale features inherent in complex PDE solutions. WLNO addresses this by augmenting the LNO core with a parallel single-level Haar discrete wavele
The continuous drive for more efficient and accurate AI models for scientific computing and PDE solutions, especially amidst increasing computational demands, makes this development timely.
This development represents an advancement in neural operators, offering a more robust and multi-scale approach to solving partial differential equations, which are fundamental to many scientific and engineering domains.
The WLNO introduces a method that better captures both transient dynamics and localized multi-scale features in complex PDE solutions, improving upon previous neural operator designs.
- · AI researchers (scientific computing)
- · Engineers (simulations)
- · Computational scientists
- · Deep learning frameworks
- · Traditional numerical solvers (in specific applications)
- · Less advanced neural operators
Improved accuracy and efficiency in solving complex scientific and engineering problems using AI.
Accelerated discovery and design processes across various fields by reducing computational bottlenecks.
Potentially enables new classes of simulations and modeling previously intractable due to computational limits.
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Read at arXiv cs.LG