Reduced Order Machine Learning Finite Element Methods:Concept,Implementation,and Future Applications Dedicated to Professor Karl Stark Pister for his 95th birthday

This paper presents the concept of reduced order machine learning finite element(FE)method.In particular,we propose an example of such method,the proper generalized decomposition(PGD)reduced hierarchical deeplearning neural networks(HiDeNN),called HiDeNN-PGD.We described first the HiDeNN interface seamlessly with the current commercial and open source FE codes.The proposed reduced order method can reduce significantly the degrees of freedom for machine learning and physics based modeling and is able to deal with high dimensional problems.This method is found more accurate than conventional finite element methods with a small portion of degrees of freedom.Different potential applications of the method,including topology optimization,multi-scale and multi-physics material modeling,and additive manufacturing,will be discussed in the paper.