Facts and Issues of Neural Networks for Numerical Simulation

Deep learning and AI has revolutionized the field of computer science and have now become the dominant approach to solving a wide problem range, from partial differential equations to molecular discovery. Indeed, numerical simulation techniques have traditionally relied on solving physically derived equations using finite differences and adding heuristic models when they become too complex to solve (Turbulence models in fluid mechanics, for example). This class of techniques remains (computationally) (very) expensive; we are talking about hours to days of simulation on petaflop or exaflop machines. The situation is even worse because the simulation must restart when an engineer wants to change the shape. Today, to achieve an accurate prediction of the simulation at low time and cost, the process is simulated based on an artificial neural network. Different artificial neural networks have been recently developed for progressive prediction of the phenomenon under consideration. The chapter overviews the most recent artificial neural networks proposed by the research communities, explains the pros and cons, and shows the limits and yet unsolved problems. The chapter also illustrates the considered challenges, most of the time, through different partial differential equations.