Abstract
New research on Machine Learning is the subject of a report. According to news originating from Urbana, Illinois, by NewsRx correspondents, research stated, "We propose a physics - informed machine -learning method based on space -time -dependent Karhunen-Loeve expansions (KLEs) of the state variables and the residual least -square formulation of the solution of partial differential equations. This method, which we name dPICKLE, results in a reduced -order model for solving forward and inverse time -dependent partial differential equations." Funders for this research include U.S. Department of Energy (DOE) Advanced Scientific Computing (ASCR) program, United States Department of Energy (DOE). Our news journalists obtained a quote from the research from the University of Illinois, "By conditioning KLEs on data, dPICKLE seamlessly assimilates data in forward and inverse solutions. KLEs are linear in unknown parameters. Because of this, and unlike physicsinformed deep -learning methods based on the residual least -square formulation, for well -posed partial differential equation (PDE) problems, dPICKLE leads to linear least -square problems (directly for linear PDEs and after linearization for nonlinear PDEs), which guarantees a unique solution."
NETL
NSTL
Elsevier