TRANSFER LEARNING ON MULTIFIDELITY DATA

Neural networks (NNs) are often used as surrogates or emulators of partial differential equations (PDEs) that describe the dynamics complex systems. A virtually negligible computational cost such makes them an attractive tool for ensemble-based computation, which requires a large number repeated PDE solutions. Since latter also needed to generate sufficient data NN training, usefulness NN-based hinges on balance between training and gain stemming from their deployment. We rely multifidelity simulations reduce generation subsequent deep convolutional (CNN) using transfer learning. High- low-fidelity images generated by solving PDEs fine coarse meshes, respectively. use theoretical results multilevel Monte Carlo method guide our choice numbers each kind. demonstrate performance this strategy problem estimation distribution quantity interest, whose is governed system nonlinear (parabolic multiphase flow in heterogeneous porous media) with uncertain/random parameters. Our numerical experiments mixture comparatively smaller high-fidelity provides optimal speed-up prediction accuracy. The former reported relative both CNN only solution PDEs. expressed terms Wasserstein distance Kullback-Leibler divergence.