A Multi-level procedure for enhancing accuracy of machine learning algorithms
This work addresses accuracy and efficiency issues for researchers in scientific computing using machine learning, though it appears incremental as it builds on existing single-level methods.
The authors tackled the problem of improving accuracy in machine learning for approximating observables in scientific computing, particularly in differential equation systems, by proposing a multi-level method that combines cheap coarse-resolution data with expensive fine-resolution samples, achieving significant gains over single-level algorithms and considerable speed-up in forward uncertainty quantification.
We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies on judiciously combining a large number of computationally cheap training data on coarse resolutions with a few expensive training samples on fine grid resolutions. Theoretical arguments for lowering the generalization error, based on reducing the variance of the underlying maps, are provided and numerical evidence, indicating significant gains over underlying single-level machine learning algorithms, are presented. Moreover, we also apply the multi-level algorithm in the context of forward uncertainty quantification and observe a considerable speed-up over competing algorithms.