Data-Enabled Advancement of Computation in Engineering: A Robust Machine Learning Approach to Accelerating Variational Methods in Electromagnetics and Other Disciplines

In this letter, we propose and demonstrate a data-driven machine learning-based approach to accelerate the finite element method (FEM), method of moments (MoM), finite difference (FD) method, and related variational methods, while maintaining the attractive properties that have allowed such methods to dominate computational science and engineering fields like computational electromagnetics. We use a neural network to predict a set of macro basis functions for a given problem, using only the solution to an extremely coarse description of the problem as input. We then solve the problem using the predicted macro basis. Unlike some existing methods, ours does not rely on the direct prediction of the solution. We show that our macro basis function approach corrects errors in the raw prediction of the network, achieving a far more accurate solution. Results are presented for a class of finite element scattering problems, with error statistics presented from 1000 validation examples and compared to standard and naive approaches. These results suggest the described macro basis function approach is superior to machine learning approaches that directly predict the solution. Meanwhile, our method achieves comparable accuracy to the full solution while requiring only a fraction of the degrees of freedom.