[2603.24143] Linear-Nonlinear Fusion Neural Operator for Partial Differential Equations

Computer Science > Machine Learning arXiv:2603.24143 (cs) [Submitted on 25 Mar 2026] Title:Linear-Nonlinear Fusion Neural Operator for Partial Differential Equations Authors:Heng Wu, Junjie Wang, Benzhuo Lu View a PDF of the paper titled Linear-Nonlinear Fusion Neural Operator for Partial Differential Equations, by Heng Wu and 2 other authors View PDF HTML (experimental) Abstract:Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial differential equations (PDEs) - an advantage that is difficult to achieve with traditional numerical methods. In this work, we find that explicitly decoupling linear and nonlinear effects within such operator mappings leads to markedly improved learning efficiency. This yields a novel network structure, namely the Linear-Nonlinear Fusion Neural Operator (LNF-NO), which models operator mappings via the multiplicative fusion of a linear component and a nonlinear component, thus achieving a lightweight and interpretable representation. This linear-nonlinear decoupling enables efficient capture of complex solution features at the operator level while maintaining stability and generality. LNF-NO naturally supports multiple functional inputs and is applicable to both regular grids and irregular geometries. Across a diverse suite of PDE operator-learning benchmarks, inc...