Graph Neural Operator Framework for Scalable Modeling of Complex Dynamical Systems

Abstract

Simulation of complex dynamical systems is essential in scientific and engineering applications, but the costliness and inability to scale to irregular and high-dimensional domains of standard numerical solvers make modeling computationally expensive. More recent neural operator methods, including Fourier Neural Operators (FNO) and DeepONet have shown promise, but are mostly restricted to structured grids and poorly deal with non-Euclidean data. The paper suggests Graph Neural Operator (GNO) architecture of scalable modeling of complex dynamical systems on irregular domains. The method combines operator learning with graph neural networks to allow the direct mapping of functional spaces. With the aid of graph-based representations and a message passing mechanism implemented as a kernel, the model is very effective in capturing nonlinear spatial interactions with flexibility to different discretizations. The architecture also has sparse computation and parallel processing that enhances scalability. Benchmark experimental assessments of dynamical systems reveal that the GNO model is more accurate, generalizes better, and less expensive to compute, compared to state-of-the-art approaches. The framework provides a scalable and generalizable solution to data-driven modelling in scientific computing and engineering problems.