GMLS-Nets: A Machine Learning Framework for Unstructured Data by Nathaniel Trask

Nathaniel Trask (SNL), GMLS-Nets: A Machine Learning Framework for Unstructured Data Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gain benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a non-parametric meshfree technique for estimating linear bounded functionals from scattered data, and has recently emerged as an effective technique for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for linear and non-linear operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators, develop predictive dynamical models, and to obtain feature extractors to predict quantities of interest. The results show the promise of these architectures as foundations for data-driven model development in scientific machine learning applications. Implementations in TensorFlow and PyTorch are available at https://github.com/rgp62/gmls-nets https://github.com/atzberg/gmls-nets AAAI 2020 Spring Symposium on Combining Artificial Intelligence and Machine Learning with Physics Sciences, March 23-25, 2020 (https://sites.google.com/view/aaai-mlps) Symposium papers: https://sites.google.com/view/aaai-mlps/proceedings Slides: https://sites.google.com/view/aaai-mlps/program