Neural-Parareal: Dynamically Training Neural Operators as Coarse Solvers for Time-Parallelisation of Fusion MHD Simulations

The fusion research facility ITER is currently being assembled to demonstrate that fusion can be used for industrial energy production, while several other programmes across the world are also moving forward, such as EU-DEMO, CFETR, SPARC and STEP. The high engineering complexity of a tokamak makes it an extremely challenging device to optimise, and test-based optimisation would be too slow and too costly. Instead, digital design and optimisation must be favored, which requires strongly-coupled suites of High-Performance Computing calculations. In this context, having surrogate models to provide quick estimates with uncertainty quantification is essential to explore and optimise new design options. Furthermore, these surrogates can in turn be used to accelerate simulations in the first place. This is the case of Parareal, a time-parallelisation method that can speed-up large HPC simulations, where the coarse-solver can be replaced by a surrogate. A novel framework, Neural-Parareal, is developed to integrate the training of neural operators dynamically as more data becomes available. For a given input-parameter domain, as more simulations are being run with Parareal, the large amount of data generated by the algorithm is used to train new surrogate models to be used as coarse-solvers for future Parareal simulations, leading to progressively more accurate coarse-solvers, and thus higher speed-up. It is found that such neural network surrogates can be much more effective than traditional coarse-solver in providing a speed-up with Parareal. This study is a demonstration of the convergence of HPC and AI which simply has to become common practice in the world of digital engineering design.