Neural Galerkin Scheme with Active Learning for High-Dimensional Evolution Equations. (arXiv:2203.01360v1 [math.NA])

Machine learning methods have been shown to give accurate predictions in high
dimensions provided that sufficient training data are available. Yet, many
interesting questions in science and engineering involve situations where
initially no data are available and the principal aim is to gather insights
from a known model. Here we consider this problem in the context of systems
whose evolution can be described by partial differential equations (PDEs). We
use deep learning to solve these equations by generating data on-the-fly …

active learning arxiv evolution learning math