A high-speed numerical simulation method for diverse boundary conditions for real time applications unleashing MeshGraphNet

• Structured literature on attempts for accelerating numerical simulation. • Customized MeshGraphNet, a novel GNN framework with distributed computation. • Solved accuracy-time complexity trade-off with conventional FEM. • Outperforms FEM in time efficiency and boundary condition adaptability. • 23,400x and 4,800x speedups in 1D thermal and 2D solid mechanics. The study presents an adapted MeshGraphNet for real-time field prediction in digital twins, surpassing traditional FEM in efficiency and boundary condition adaptability but falling short of real-time computational demands. Trained with true labels, MeshGraphNet accurately predicts nodal variables on coarse graphs and reduces simulation time through parallel sub-mesh processing. Applied to a 1D mesh, it solved an ordinary differential equation with similar FEM accuracy for finer meshes, retaining high precision only on trained resolutions, highlighting limited generalizability. Time complexity was evaluated by plotting solution timings against node count and analyzing trend line slopes. MeshGraphNet predicts the solutions, achieving 97–100 % accuracy through subdivision, with a slope of 4 × 10 −5 whereas for FEM it is 0.117, which is lagging due to its calculative nature. With 8-core processing, the time ratio of prediction of proposed method is 5 × 10 −6 . In a thermal case, accuracy reached 98–100 %, while maintaining a time consumption slope of 2 × 10 −6 and 2 × 10 −5 with and without sub-mesh division respectively. In solid mechanics case, subdivision reduced RMSE from 0.14 to 0.02 with a slope of 0.1803,.003, and 3 × 10 −5 for FEM, without and with subdivision respectively. This efficient processor utilization paves the way for real-time execution of complex simulations using the proposed method.