3 accepted papers
Neural operators have shown promise in accelerating PDE solvers, yet they remain unreliable for the sparse linear systems induced by discretization due to limited generalization across physical parameters and insufficient accuracy, and hybrid neural iterative schemes face stagnation as the residual …
Neural operators have emerged as a promising approach for solving high-dimensional partial differential equations (PDEs). However, existing neural operators often have difficulty in dealing with constrained PDEs, where the solution must satisfy additional equality or inequality constraints beyond th…
We present a novel framework, StochastIc Network Graph Evolving operatoR (SINGER), for learning the evolution operator of high-dimensional partial differential equations (PDEs). The framework uses a sub-network to approximate the solution at the initial time step and stochastically evolves the sub-n…