Enhancing the accuracy of physics-informed neural network surrogates in flash calculations using sparse grid guidance*

Flash calculations pose a significant performance bottleneck in compositional-flow simulations. While sparse grids have helped mitigate this bottleneck by shifting it to the offline stage, the accuracy of the surrogate model based on physics-informed neural networks (PINN) is still inferior to that of the sparse grid surrogate in many cases. To address this issue, we propose the sparse-grid guided PINN training algorithm. This approach involves rearranging the collocation points using sparse grids at each epoch to capture changes in the residual space. By doing so, the PINN surrogate achieves the required accuracy using the fewest collocation points possible, thereby avoiding potential performance bottlenecks. Moreover, the training time complexity of the sparse-grid guided PINN training is significantly lower compared to the normal training while maintaining the same level of accuracy. Consequently, the sparse-grid guided PINN training method enhances the accuracy of the PINN surrogate with minimal computational overhead. During the experiments, a flash calculation of methane-propane mixture is conducted using a PINN surrogate, guided by the principles of sparse grids. The collective experimental observations underscore the clear advantages of employing sparse-grid guided PINN training, showcasing superior outcomes in terms of convergence, stability, and accuracy.