Fuse-PINN: Combining Finite Element Methods and Physics-Informed Neural Networks to enable massively parallel simulations of non-linear PDEs

Research in the domain of Physics-Informed Neural Networks applied to PDE modelling has advanced significantly in recent years, providing a wide ecosystem of novel methods. However, one frequent limitation is the inability of PINNs to scale out on High-Performance Computing architectures to address more ambitious challenges, particularly non-linear physics models with turbulent dynamics in large spatial domains. Typical studies restrain demonstrations to toy models with simple physics equations, few variables, and rarely any complex non-linear dynamics evolved over long timescales. Part of the AI community has even adopted the idea that “PINNs don't scale”. This work proves otherwise. We present a mathematically robust formulation of Finite-Element-Method for Neural Networks (FEM-NN) implemented into a comprehensive, modular framework: Fuse-PINN. This formulation provides the basis for a sclable parallelisation of Physics-Informed Neural Networks on GPU-based HPC systems. Furthermore, an Energy Natural Gradient Descent optimiser is implemented to allow high-precision convergence. Fuse-PINN is demonstrated on physics models relevant to Magnetic Confinement Fusion, including non-linear convective models with fine-scale dynamics. Near-perfect scaling is achieved on multi-GPU runs with increasing problem size. The code is made fully open-source (upon publication).