A machine learning approach for efficient uncertainty quantification using multiscale methods
This work addresses efficiency in uncertainty quantification for multiscale simulations, though it appears incremental as it applies an existing machine learning technique to a specific computational bottleneck.
The authors tackled the computational cost of generating coarse scale basis functions in multiscale methods for uncertainty quantification by introducing a data-driven neural network predictor that learns from solution samples, achieving lower computational cost for evaluating large numbers of realizations, with promising results on elliptic problems.
Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over dual-grid cells. We introduce a data-driven approach for the estimation of these coarse scale basis functions. Specifically, we employ a neural network predictor fitted using a set of solution samples from which it learns to generate subsequent basis functions at a lower computational cost than solving the local problems. The computational advantage of this approach is realized for uncertainty quantification tasks where a large number of realizations has to be evaluated. We attribute the ability to learn these basis functions to the modularity of the local problems and the redundancy of the permeability patches between samples. The proposed method is evaluated on elliptic problems yielding very promising results.