Tootfinder

Monte Carlo-Type Neural Operator for Differential Equations
Salah Eddine Choutri, Prajwal Chauhan, Othmane Mazhar, Saif Eddin Jabari
https://arxiv.org/abs/2510.05620 https://

Monte Carlo-Type Neural Operator for Differential Equations
The Monte Carlo-type Neural Operator (MCNO) introduces a framework for learning solution operators of one-dimensional partial differential equations (PDEs) by directly learning the kernel function and approximating the associated integral operator using a Monte Carlo-type approach. Unlike Fourier Neural Operators (FNOs), which rely on spectral representations and assume translation-invariant kernels, MCNO makes no such assumptions. The kernel is represented as a learnable tensor over sampled in…