Neural network enhanced computations on coarse grids

Unresolved gradients produce numerical oscillations and inaccurate results. The most straightforward solution to such a problem is to increase the resolution of the computational grid. However, this is often prohibitively expensive and may lead to ecessive execution times. By training a neural network to predict the shape of the solution, we show that it is possible to reduce numerical oscillations and increase both accuracy and efficiency. Data from the neural network prediction is imposed using multiple penalty terms inside the domain.