WLNO: Wavelet-Laplace Neural Operator for Solving Partial Differential Equations
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 wavelet transform (DWT) branch that decomposes the lifted feature map into four frequency subbands: approximation (LL), horizontal detail (LH), vertica...
| Authors | Muhammad Abid, Arth Sojitra, Omer San |
|---|---|
| Primary category | cs.LG |
| Published | 23 May 2026 |
| Last updated at source | 23 May 2026 |
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